Enthalpies of dilution of sodium carbonate and sodium hydrogen carbonate solutions, and the standard enthalpies of ionization of aqueous carbonic acid, at 298.15 K

A-059 J. Chem. 7XernrodyMmis 1978,10, 1049-1075

Enthalpies of dilution of sodium carbonate and sodium hydrogen carbonate solutions, and the standard enthalpies of ionization of aqueous carbonic acid, at 298.15 K a ROBERT

L. BERG

and CECIL

E. VANDERZEEb

Departmentof Chemistry, University of Nebraska, Lincoln, Nebraska68588,U.S.A. (Received6 September1977; in revisedform 22 February 1978) EWhalpiesof dilution of NaaCOsand NaJ3COasolutions,togetherwith enthalpiesof protonationof CO:- and HCO ; ions,weremeasured at 298.15K by solutioncalorimetry. Compositionsof the solutionswere calculatedfrom equilibriumcoustautsand related activity-coetlkientfunctions,and through detailed consideration of correction terms, the relativeapparent molar enthalpies L& for the ion combinations (Na + + HCO 3 ) and (2Na + +COi-) were evaluated relative to the conventional reference states, and values of Lz, the equilibrium relative apparent molar enthalpies of the actual solutions, were referred to the same reference state. By similar strategies, the standard enthalpies of ionization for carbonic acidwereevahtated:mH,“., = (2188f15)calthmol-‘,and~~“,l = (3513&25)caltbmol-1. Values of both & and L.$ are needed for obtaining the standard enthalpies for the sodium salts of carbonic acid, as am the enthalpies of ionization. Strategies for making the corrections to standard states are illustrated in detail.

1. Intmduction For the standard enthalpies of reaction of aqueous solute species of weak electrolytes, such as H,CO,(aq), HCO;(aq), and CO:-(aq), the reduction of experimental results to conventional reference states is complicated by the interaction of enthalpies

of ionization and dilution, and by the need to evaluate actual solution compositions from equilibrium constants and activity coefficient functions at molalities high enough to partially suppress hydrolysis or ionization. In this paper, we present strategies and experimental results which lead to the standard enthalpies of ionization of H,CO,(aq) and HCO;(aq), and to the conventional relative apparent molar enthalpies L+ of NaHCOs and Na,C03 as “fixed” electrolytes, whose anions are not hydrolysed or ionized. The above enthalpies L+ are referred to the conventional reference state at infinite dilution, and throughout this paper the term “conventional reference state” refers to the conventions used in tabulating standard thermodynamic properties. (17’) Also presented are values of L>, the relative apparent molar enthalpies of the equilibrium states of the solutions referred to the same conventional reference state as L,. These values of L%are related to the conventional standard enthalpies of

a From the Ph.D. Thesis of R. L. Berg, University of Nebraska, August 1975. b To whom inquiries should be addressed. 0021-9614/78/111049+27

801.00/O

0 1978 Academic Press Inc. (London) Ltd.

1050

R. L. BERG AND

C. E. VANDERZEX

enthalpies of solution AH&,, by AH;,, = AH&-L\, for salts such as NaHCOJ(s) and Na&Os(s). The relation between L> and L.+ will be shown in subsequent paragraphs. The results obtained in this paper will be utilized in the following paper to extract standard enthalpies of reaction from measurements of the enthalpy of solution of C02(g), NaHCOJs), and Na&O,(s) in sodium hydroxide solutions.

solution

AH&oln and to experimental

2. Strategies and plan of measurements In this section we outline the calorimetric processes, the correction terms, and other auxiliary data needed to extract values of Lo and of the standard enthalpies of ionization AH’; from sets of information. Extrapolation procedures involved in obtaining L+ and L> are included. Considerations of each desired quantity in terms of a total set of information provides some guidance in choosing optimum solution compositions and calorimetric procedures. The most efficient procedure for assembly of the correction terms for a particular process is by charting or mapping the steps in transformation of the reactants in their standard states to the products in their standard states. The general pattern for such route mapping will be discussed elsewhere.(3b) SODIUM CARBONATE DILLJTIONS In these measurements it is necessary to recognize that trace amounts of dissolved CO2 in the distilled water used as diluent will perturb the results, especially at low molalities of sodium carbonate. Complete avoidance of such perturbations calls for very difficult procedures in preparing and handling the diluent. The relative amount of CO2 picked up by the Na,CO, solutions can be kept negligibly small, and handling procedures for the solution are somewhat easier than for the diluent. The first chart displays the overall standard-state process with traces of CO, present in the diluent. The standard enthalpies of ionization AHi,I and AH& refer to the processes : H2C03(aq) = H ‘(as) + HCO;(aq), (1) HCO; (as) = H+(aq) f CO: -(aq), (2) respectively. In reaction (I), H2COj(aq) refers as usual to the aggregate of all species, hydrated and anhydrous, and not to molecular carbonic acid. The composition of the product solution is to be calculated from the hydrolysis equilibrium: CO:-(aq)+H,O(l) = HCO;(aq)+OH-(aq), (3) where a is the fraction hydrolyzed, and AH: is the standard enthalpy of hydrolysis, related by : AH;: = -AH;--AH& (4) to -AH& the standard enthalpy of ionization of water. The quantity AH, is the enthalpy for the isothermal calorimetric process for unit amount of Na&O,, and n is the stoichiometric number of CO2 in the diluent.

ENTHALPIES

OF AQUEOUS

CARBONATE

CHART

Na,CO,

* coH,O (conventional reference state) @G(i) Na2CO:*.PH,0 (equilibrium state)

SOLUTIONS

1051

1

SO, * aoH, (conventional reference state) lnL;tCO,, i) nCOz. BH20 (equilibrium state)

~l-~-r~)Na,CO,~(~-t-2n)NaHCO,~aNaOH~(A+5-r-~~)H,O 1 - {( 1 - x - njL+(Na,CO,) + (g + &t)L,(NaHCO,) f xL,+(NaOH)) (l-~-n)Na,C0,~(~+2n)NaHCO,~rNaOH~coH,0 ln(AH;* i-AH;, i) (l- x)Na,CO,~rNaHCO,~crNaOH~nCO,~ccHH,O 1 -ctAH,” Na,CO, * coH,O + nCOz * coH,O (conventional reference state) The first steps serve to define Lz for the reactants at the initial molalities. The term for CO, is small: L:(CO,, i) = 250 Cal,,, mol -‘, for an equilibrium mixture in 3 x 10m5 mol kg- ’ of COz, but for dilutions of Na&O, down to 6 x 10m3 mol kg- ‘, II = 5 x 10T3, and nL:(C02, i) = 1.25 Cal,, mol-‘, at the lowest dilutions for this work.? The term L:(i) for Na,CO, is a constant for a given stock solution of Na,CO,* AH20, and is one of the objectives of the measurements. The correction term for COz can be calculated with sufficient accuracy, since nL>(CO,, i) will be small (negligible except at the lowest molalities of Na,CO, in the product mixture). The strategy for transforming the product solution to the reference state involves first a hypothetical dilution at fixed solute composition (constant a and n) to infinite dilution, for which process L+ for each component is taken at the ionic strength of the product solution, and the weighted L+ terms are assumed to be additive. The assumption is supported by the Debye-Htickel theory for relative apparent molar enthalpies of electrolyte mixtures, and corresponds to zero enthalpy of mixing of the components at constant ionic strength. (3b) It is a necessary assumption, and is a reasonably sound approximation for such mixtures at ionic strengths of 0.5 mol kg-’ or less, judging by results of mixing studies for a number of systems.(3bP k-7) In the second part of the strategy, the products, now at infinite dilution, are brought by standard-state processes to the final conventional reference state. One such step is the conversion : 2nNaHC0,.

coH,O = nNa,CO,*

coH,O +nCO,*

coH,O,

(5)

for which nAH” = n(AHi, i -AH”,, i). The other step is reversal of the hydrolysis of CO:-(aq), t Throughout

this paper ealtn = 4.184 J; atm = 101.325 kPa.

(6)

as shown in chart 1, to

1052

R. L. BERG AND

C. E. VANDERZEE

complete the transformations and return the substances to their conventional standardstates. The overall enthalpy change for the set of steps in chart 1 is zero: L\(i)+nL$(COZ,

i)+AH,+n(AH~,i-AH~,i)-aAH~-{(1-o!-n)L4(Na,C0,) + (a + 2n)L+(NaHCO,) + aL+(NaOH)) = 0. (7) Let us denote the sum of known terms by Y: Yl= AH, - aAH: + n(AHz, i - AH:, J + nL\(CO,, i) -(a + 2n)L4(NaHC0,) - aL+(NaOH).

(8)

Then Yl = -L:(i) + (1 - t( - n)L,(Na,CO,). (9) The dilution measurements on a given stock solution of Na&O,.AH,O yield a set of values of YI at related molalities M for the product solutions. Guidance is needed in an extrapolation of equation (9), or some modification of it, to obtain L\(i) as an intercept (limiting value) at m + 0. Two alternatives are: first, to representL+(NaCOs) by some suitable Debye-Hiickel function; second, to represent LJNa,C!03) by relation to some model electrolyte whose values of L+ are known.(*) We adopt the second alternative, in the form: L+(Na,CO,) = L+(model)+ /?m, (10) where bnz is a deviation term, not necessarily linear, but usually well behaved.@) Then we have two possible extrapolation functions: YI - (1 -a - n)L+(model) = -L;(i) + (1 -a - n)@n, (10 and Y, + (a + n)L+(model) = -L\(i) +L+(Na&O,) - (a + n)j?m. (12) Equation (11) should have a small and well behaved slope, and should lead to L\(i) more conveniently than equation (12), which has only a small deviation term (a+ n)@n and otherwise has the charactersitics and steep slope of a l-2 electrolyte pattern. With equation (12), one needs a Debye-Hiickel limiting slope, or a stronger guidance function, to obtain L>(i) by extrapolation or curve-fitting. Once L\(i) is determined, then values of L+(NazCO,) for the product solutions follow from equation (9). Except for the several correction terms, the procedures are no different in principle from those for strong electrolytes for which a and n would be zero. From chart 1 and the preceding equations it follows for any particular solution of Na,C03 that L; - (1 -a - n)L+(Na$ZO,) = (a + 2n)L+(NaHCO,) + aL+(NaOH) - n(AHi, i -AH!, *)+aAHi, (13) where all of the enthalpies L correspond to the electrolyte at the ionic strength of the mixture. This additivity concept is reasonably valid at low ionic strengths (below 0.2 mol kg-‘), but of necessity must serve as a defining relation at the higher ionic strengths. We note that once values of L, or LF+are established and scaled relative to the conventional reference state, then the other quantity can be calculated for the

ENTHAL.PIES OF AQUEOUS CARBONATE

SOLUTIONS

1053

solution by equation (13). Such a procedure is useful with smoothed results for either L!+ or 4, as an alternative to equation (9). Sample calculations for reasonable values of n and B reveal that the perturbation from dissolved CO, has less influence from equation (6) than it does indirectly through a by suppression of some hydrolysis by increasing the relative amounts of NaHCO, present. The uncertainties in the correction terms were barely tolerable at low molalities, but some runs were made according to the pattern of chart 1, after analyses of batches of distilled water established the ratio n/B. An alternative strategy for the Na,CO, dilutions is shown in chart 2, where a CHART 1

Na,CO,

. ccH,O (conventional

lL;(i) Na2C03*AH,0

(equilibrium

reference state) state)

I-NaOH * coH,O (reference state) JrL+(NaOH, i) rNaOH* BH20

(l-cc)Na,CO,~ctNaHCO,~(r+a)NaOH*(A+B-a)H,O 1 - {(l - z)L+(Na,CO,) + aL+(NaHCO,) t (I’+ x)L,(NaOH, (I-a)Na,CO,~aNaHCO,~(v+cc)NaOH~crc,H,O L- aAH;; Na2C0, * ccH,O + rNaOH* coH,O (conventional reference state)

f)]

dilute soiution of NaOH is used as diluent. In this pattern, the effect of CO2 perturbation is eliminated, and some hydrolysis of Na,CO, is suppressed, but at the loss of results at low ionic strengths. With smaller corrections to deal with, and with a suitable model electrolyte as a guidance function, this pattern is as reliable as that in chart 1 for measurement of L+(Na,CO,). The equations are : Y2 = AH, - aA& + r(L+(NaOH,

i) - L@JaOH,

f)) + a(Lb(NaOH,

f)

+ L+WaHCW), Y, = -L\(i) + (1 - a)L&Na,CO,), Y, -(l -a)L&model) = -E+(i)+(l -a)@n, Yz+ aL,&model) = - E+(i) + L+.(Na,CO,) - a/Im, and all of the remarks relative to equations (8) to (12) apply to equations (14) to SODIUM

HYDROGEN

CARBONATE

(14) (15) (16)

(17) (17).

DILUTIONS

Dilutions of these solutions are perturbed by almost equal opposing influences: hydrolysis and ionization of HCO; ion, as shown in chart 3. Neither is a strong influence because of the internal buffering in these solutions. Chart 3 is set up for the general case where the diluent water contains traces of dissolved COz. The influence

R. L. BERG AND C. E. VANDERZEE

1054

~~ CHART

NaHCO,.aH,O

(conventional

1L;(i) NaHCO,.dH,O

reference state)

3

nCO,* coH,O (conventional

reference state)

w;(cw nC0,*BH20 1 AH,,,>/An, = AH,

.uNa,CO,*(I -~-~~)N~HCO,.(~~+IZ)H~CO~.(~~-.~)N~OH.(A+B-~-~+X)H,O J- IxL+(Na,CO,j + (1 -s-.rjL&NaHCO,j + (y-t-njL,(H,CO,j xNa,C0~~(1-s-~~)NaHCO,~(?:+tr)H,CO,~(~~-xfNaOH~acrH,O JyAH;, i - sAH;. i + (y-x)AHh NaHCO, *nCOz * coHzO (conventional reference state)

+ (.Y-x)L&NaOH)}

of this CO2 on the composition of the product mixture is to cause slight reductions in x, y, and (y-x). For 0.004 mol kg- ’ of NaHCO, and n = 0.0025 (corresponding to 1 x lo-’ mol kg-’ of COz in the diluent water), the CO, has a net influence of +2 Cal,, mol - 1 on the corrections to the reference state, and above 0.01 mol kg-’ of NaHCO, the perturbation of the corrections is negligible. With reasonable precautions, the COz content can be kept at or below this level, thereby simplifying the calculations of product-mixture composition, calculations which are more complicated than for sodium carbonate solutions. As for the sodium carbonate dilution, chart 1, the overall enthalpy change for the transformations in chart 3 is zero. The equations analogous to equations (7), (8), and (9) are: 0 = L+(i) + nE+(C02, i) + AH, - xL+(Na&Os) - (1 - x - y),%+(NaHCOs) -(y + n)L+(H2CO,) - (y - x)L,@aOH) + yAHt,i -XAHi,i -t 0, - x)AH& (18) 2 = nL;(C02,

i) + AH,+ yAH;, i - xAH~, i + (Y - x)AH~ - xLo(NazCO,) -(Y + W&WW - (y - x)L+(NaOW, 2 = (1 - x - y)L+(NaHCO,) - L:(i).

Again, L+(NaHCO,) equation (IO), and

can be represented by relation

(19) (20)

to some model electrolyte,

2 - (1 - x - y)L+(model) = - L\(i) + (I- x - y)/Im.

(21)

For NaHCOs solutions, the quantity (1 -x-y) changes little over the molality range of importance to the application of equations (18) to (21). A first consequence is that uncertainties due to use of provisional values of L.+.(Na2C0,), AH:, r, and AH;, r are almost constant, and become part of the provisional value of L\(i). A second consequence is that extrapolation of equation (21) is no more ambiguous than for normal strong electrolytes, and values of L.+(NaHCOs) are then given by Lb(NaHC03) = {Z-k L>(i))/(l -x - y).

(22)

ENTHALPIES

OF AQUEOUS CARBONATE

1055

SOLUTIONS

Finally, for any given solution, the equations yield J!T+- (1 - x - y)L&NaHCOs) = xL&%COd + (Y + nW+W2CW +(y - x)L&NaOH) - yAH”,, i + xA%, l(y - x)A&. (23) Then, once L+ or L< is scaled relative to the conventional reference state, the other quantity can be calculated for that solution by equation (23). STANDARD

ENTHALPY

OF IONIZATION

OF HCO,

Chart 4 presents in detail the steps in an overall standard-state process : niH+(aq)+ n”,CO:-(as) = n”,HCO,(aq). (24) In this case, because of the complexity of the correction terms, it is advantageous to set up the chart in terms of actual amounts of substance used “per experiment”. The stoichiometric amounts of starting substances are designated by n;, and initial and final amounts for the isothermal calorimetric process by nj and ni, respectively, where subscript j identifies the substance. The overall enthalpy change ZAH corresponding to equation (24) is CAH = - n;AHz, r = (ni, - ni)AH,“, i - n$iHf, i - naAHf;+ nfL\(Na,CO,) + n$$(NaHCO,) + n:I!(HsCOs) + n\I$NaOH) + n”,Lf+(HCl) n:L$Na,COs) - n$&NaHC03) - n:I$(H,COs) +AGP(25) - niL’+(NaOH) - niL$(NaCI)+(n:n’,)AH;, i + n$H~, 1-I- n:AH& CHART 4 n;Na,CO,*n~NaHCO,.mH,O

(conventional

reference state)

n;HCI.

1 1 nlNa,C0,.n~NaHC0,.nSH2C0,.n~NaOH.ooH,0 2a 1 n~Na,CO,.n~NaHCO~*n~H,CO,.n~NaOH.(A

wH,O 2b

I n;HCI.BH20

-nb)H,O

;\--------n~Na~CO,~n~NaHCOJ~n~H,CO,~n~NaOH~n~NaCI~(A+B-n~)H~O 4 1 n:Na,CO,.n:NaHCO,.nSH,CO,.n~NaOK,n:NaCi.~H,O 5 1 (n; -~;)N~,CO,~~H,O~(~I~+~~;)N~HCO,~~~H~O+~,N~CI~ (at conventional A.H,

= (n6-nl)(-AH;.i)

- Noah’;, i-Il~A.tf~.

AH,,, = n~L~(Na,CO,)

+ niL$NaHCO,}

AH,, = c;L;(HCI), AH, == -n~.!$Na,CO,)

AH, = AH,cp, - niL:(NaHCO,)

AH,

= (II:-

n\)AH;,

xiH,O

reference states).

i + r&AH;‘. , + &AH,.

+ niL$H,CO,) - n:Li(H,CO,)

+ rrfL$NaOH).

- n:L$NaOH)

- nI,Li(NnCI),

1056

R. L. BERG AND C. E. VANDERZEE

The conservation equation is nlO= n:+n: Rearrangement of terms gives

-n;

= n;+n’.-n’1

,+--n:.

(26)

-ni)AHi, r +ZnfLi(j)-ZnjLi(j). (27) (4 -ni)AH,“, i = AHrcP+(n:-n~)AH~+(n: There are several strategic advantages in starting with ni = ni. First, hydrolysis of CO:-(aq) is strongly suppressed; second, calculations of nf are easier and much more reliable; third, ni and nd are small, and ni is almost negligible; fourth, the influence of traces of COz in the solvent becomes negligible. With ng between 80 and 90 per cent of ny, the influence of n: can be kept small enough so that existing literature values for AH;, i are an almost adequate approximation, leading to uncertainty of + 2 calti, mol- * in AH&. The term @i-n:) is the one most sensitive to uncertainties traceable to estimates of activity coefficients for calculating solution composition. With n: z ni at prudently chosen initial ionic strengths, residual uncertainties from this term might be expected within +5 Cal,, mol-‘. A choice of n$zi % 3 might lead to a somewhat smaller uncertainty from this term, but would increase the uncertainties in L+ terms because of an increase in ionic strength. One of the major sources of error in this measurement is traceable to the uncertainty in measurement of L+(Na,CO,) relative to the conventional reference state. To the extent that use of Lb for a model electrolyte provides adequate guidance in constructing the curve of L&Na&O,), this error than traces to the choice of a “best” model. In any case, the error in AH;, i due to that in L,+(Na,CO,) is a systematic one, and hence it is very desirable to use self-consistent sets of values of these quantities in subsequent calculations, to the end that some of the systematic error can be eliminated in Hess’s Law calculations. STANDARD

ENTHALPY

OF IONIZATION

OF H&O3

To HCO;

Chart 5 presents in detail the steps in the standard-state process for protonation of HCO;(aq) : niH+(aq) + n”,HCO; = n;H,CO,(aq), (28) in which H2C0, denotes the equilibrium mixture of hydrated and unhydrated neutral species. As in chart 4, nJ refers to amount of substance “per experiment”. The overall enthalpy change ZAH corresponding to equation (28) is EAH = -@AH:, i = (n$ - ni)AHz, i - n\AHi, i -r&HI;+ n&(HCl) + n~I.‘g(Na,COs)+ n\&(NaHCO,)+ n&(H&OJ + n:&,(NaOH) + AH,, - n’,L@JazCOJ) - n:L\(NaHCOJ) - nf3L!(H,C03) - @+(NaCl) - &!!!(HCl) -(n~-n~)AH~,i-n’,AHq,i.

(29)

The conservation equations lead to n\ = ni+nb,

ni = n:+ni-ni,

and these relations combine with equation (29) to give i = AHICP+(n~ -n:)AH;, i -nfrAH~+Zn$\(j)-ZniLi(j). (4 -&AH:,

(30) (31)

ENTHALPIES

OF AQUEOUS

CARBONATE

CHART

5

n”,NaHCO,

* coH,O (conventional reference state) 1 1 ~I~N~,CO,.~~N~HCO,.~:H,CO~.~~N~OH.~~H,O 2a

1057

SOLUTIONS

n;HCl.

coH,O 2b

1

I n”,HCl.BH20

~IIN~,CO,.~~N~HCO,.~~H,CO,.~~N~OH.(A-~~)H~O 3v n~Na,CO,~n~NaHCO,~rt~H,CO,~n~NaCl~nf,HCl~(~+B)H,O 1 4 ,I:Na,CO,.n’2NaHCO,.n:H,CO,.n~ NaCl*n,‘HCI+

coH,O 1 5 + n’,NaCl. zH,O

(11~-n;)NaHC0,~13~0 + n~H,CO,*~H,O (at conventional reference states). Aii, Aliz,, AHZb Atf, AH,

= (11;- ,r;)AH,, i - n;AH;, i - &AH;, = n\&(Na,CO,) + n\J&,(NaHCO,) + n$+(H2C0,) - n’&$HCI). AH, = AH,,,, = n:L’,(Na,CO,) - nSL\(NaHCO,) - rt,‘L:(H,CO,) .= (II; - t&)AH’;, i - I$~AH”,, i.

+ niL$NaOH.), - n$\NaCl)

- n$i(HCl),

When ni/ni x 0.8 to 0.85, then n: becomes negligible and nsfbecomes almost negligible ( sz 0.02 per cent of n;). The qunatities ni, ni, and n: are most susceptible to errors from uncertainties in the activity coefficients needed to calculate the initial composition, but part of the uncertainty is reduced by compensating terms in equation (29). Relatively little uncertainty will result from L+(j) terms other than from L,+(NaHC03). The primary difficulty in this measurement arises from escape of CO2 from the solution into the vapor spaces of the calorimeter. For COz pressures below ambient, the fraction which escapes is almost independent of &. The correction term for escape of CO, will be discussed elsewhere. (3b) A preliminary analysis of all potential errors indicated that the molality m’ for H&O, in the product solution should be between 0.015 and 0.020 mol kg-l for optimum results, if the vapor volume in the calorimeter was kept around 1 per cent of the solution volume. The solubility of CO2 in water at 298.15 K is about 0.034 mol kg- ’ atm- ‘, so the initial NaHCO, should be kept below 0.025 mol kg- ’ to prevent possible bubble formation at the time of mixing with the HCl solution. Visual examination of such mixing conditions verified that no bubbles were formed. Because the same identifying subscripts have been used for substances in charts 4 and 5, equations (25) and (29) have strong similarities, as do equations (27) and (31). The differences stem from the product solution being slightly basic in chart 4 and slightly acidic in chart 5. The sources of error in the two patterns are quite different,

R. L. BERG AND C. E. VANDERZEE

1058

however, and errors attributable to L, terms in equations (29) and (31) are much smaller than those in equations (25) and (27). PRELIMINARY

ESTIMATES

OF THE PROPERTIES

Examination of the charted interrelationships suggests that the best strategy is to evaluate the properties in the order: L,,(NaHCO,), L+(Na,CO,), AH;, *, AH;, i. In this order, the quantities are increasingly dependent on the preceding ones and on the accuracy of preliminary estimates. The calculations can then be “recycled” to obtain the final internally consistent set of quantities. For evaluation of L+(Na,CO,) and LJNaHCO,), preliminary values of AH;, , and AH;, i were needed. The available literature values are summarized below: Source Pitzer(‘) (calorimetric) Shedlovsky and MacInnes(“’ (conductance) Harned and Scholes(l” (e.m.f. equilibrium) Harned and Davis(“) (e.m.f. equilibrium)

AH:, &al,, mol-’ 1843 2075

AH;, &al,, mol- ’ 3500 3600

2248

For a preliminary value of AH;, i we used 3518 Cal,, mol-‘, corresponding to 9820 Cal,, mol -’ for AH;, the enthalpy of hydrolysis of COf-(as), equation (4). This selection was fortuitous, and no further recycling of calculations was required. The calorimetric value for AH;, i is considerably smaller than those based on equilibrium measurements. Fortunately, use of either 2075 or 2248 Cal,, moI-’ for AHi, i will influence AH;, i by only 1 Cal,, mol-’ in equation (27), so a simple recycling of calculations is required for refinement of AH;, i after AH;, i is measured and calculated from equation (31). Values of L+(Na,SOJ from Thompson, Smith, and Wood (13) were used for the model electrolyte in equations (lo), (1 I), (12), (16), and (17). In evaluation of L+(NasCO,), the major correction term is that for hydrolysis. The primary source of error in the hydrolysis correction is in the calculation of the fraction hydrolysed and is traceable to uncertaintites in the activity coefficients used in those calculations. As a model electrolyte for NaHCO, we first tried NaBr and NaI. It was quickly apparent that L+ values for NaHCO, lay between those for NaI and NaSCN. The correction terms in this system are small (equations 18 and 19), and lead to only small uncertainties in L+ for NaHCO,. EVALUATION

OF EQUILIBRIUM

COMPOSITIONS

For these calculations we used the equilibrium constants K,“, i = 4.45 x IO-’ for reaction (l),(l’) and Kz, i = 4.69 x IO-” for reaction (2),(“) together with KG = 1.01 x IO-r4 for the ionization of water. (13) Most of the calculations involve hydrolysis equilibria and the relations: m(OH-)m(HCO;)/m”m(CO:-)

= K&Jr,

= KG/K;. ir2,

m(OH-)m(H,CO,)/m”m(HCO~)

= Ki,,/L’r

= KS/K;, iL’t,

(32)

and (33)

ENTHALPIES

OF AQUEOUS

CARBONATE

SOLUTIONS

1059

where the activity coefficients are represented by Tz = y(OH-)y(HCO;)/y(CO$-) and r1 = y(OH-)/y(HCO;), with ye = 1 for neutral species: H&O3 and H20. For water, Tw = y(H+)y(OH-). Harned and Owen(r4’ report values of TV for several salt mixtures, with ye included for HzO. Values of y. for aqueous COz (H&O,) are obtainable from the results reported by Harned and Davis,(12) but in the equations to be presented in the following paragraphs, y0 is embedded in the functions T2 and r1 extracted from the results of e.m.f. measurements.(’ iv ’ 2, In such mixtures as encountered here, the terms r,, rl, and T2 are essentially unmeasurable, and must be evaluated by recourse to models, analogs, or other strategy. Thus for r2, one might use a Debye-Hiickel equation as an approximation, with an appropriate ion-size parameter; a second choice would be a term based on properties of the pure electrolytes at the ionic strength of the solution: r2 = y~(NaOH)&(NaHCOJ~~(Na&O~). As a third choice, one can retrieve the quantity: r; = y(Cl-)y(HCO;)l~(C03-), from the results of cell measurements by Harned and Scholes(“’ based, and can obtain T2 from r; by the conversion :

(34) (35) on which Ki, i is

r2 = r;y$(NaOH)/y:(NaCl),

(361 based on the ratio of activity coefficients for pure NaOH and pure NaCl solutions at the ionic strength of the solution. At low ionic strengths this ratio is close to unity. By the third method, equations (35) and (36) we extracted from the results by Harned and Scholes :(I ‘) log,,r, = - 1.01S(1/m”)‘~2/[1 + {2(I/m”)}“2] +0.16(1/m"), (37) in which we retained their ion-size parameter. Other values of this parameter with corresponding coefficients for the linear term seemed equally valid. We also attempted to use the activity coefficients for NaHC03 and Na,CO, reported by Han and Bernardin,(“’ Lortie and Demers,(‘@ Saegusa,(“) and Taylor(‘*) to evaluate r2 by equation (34). The resultant quantities were close to those given by equation (37), especially at ionic strengths below 0.1 mol kg- ‘, so we accepted equation (37) for the calculations used in our work. In general, a function chosen from equations (35) and (36) is more apt to imitate the behavior of T2 for the mixed electrolyte than would the analog equation (34), especially for cases where existing data for the pure substances(‘5-‘8’ are somewhat discordant as in this case. Recent work by Khvorostin, Filipova, and Reshetova(tg) on the activity coefficients of Na,CO, solutions by an isopiestic method yields values differing from those based on e.m.f. measurements by Taylor(“) and Saegusa,(“) partly because for strongly hydrolysed electrolytes the two methods do not deal with the same property. For equation (33) ,we took rl x 1, since it is a ratio for two (l-l) electrolytes with a common cation, and this approximation was considered adequate for the situations in this work. The term T,,, has little influence in the calculations. Harned and Owen(14’ list values of rw for several mixtures which are suitable analogs, and to a good approximation, rw = i/r,. 62

1060

R. L. BERG AND

C. E. VANDFiRZEJZ

By any of the methods for estimating r, the error or uncertainty increases with increasing ionic strength, so one is forced to compromise between using substantial amounts of substances to reduce calorimetric errors and low molalitics to reduce errors from estimates of r. The values of Ki, r and Ki, i appear to be reliable to f 2 per cent, and at the molalities used in this work, uncertainties in r, and ri were estimated to be &- 3 per cent or less, except for molalities above 0.1 mol kg-’ in the dilution measurements on Na,C03 and above 0.25 mol kg-’ in dilution measurements on NaHCO,. An error of +2 per cent in K, or Kr causes an error of f 1 per cent in the fraction hydrolysed. Consequently, the degree of hydrolysis must be reduced whenever feasible to minimize uncertainties in the correction terms for charts 1 to 5. The most difficult term to control is ctAHi in the dilution studies on Na,CO,, since AH: is large (almost loo00 cal,, mol-I). The strategy in chart 2, of using dilute NaOH as diluent, does reduce ctAHi considerably, but at the expense of increase in ionic strength; with reliable guidance functions for extrapolation, there is some net gain in accuracy by suppressing much of the hydrolysis. Finally, for limited extents of hydrolysis, the uncertainty in the fraction unhydrolysed is much less than that in the hydrolysed fraction, so errors in the dilution terms for the constituents can be reasonably well controlled. In our calculations, we have chosen to omit explicit consideration of possible ion-pairing (20P21) between Na+ and the ions CO:- and HCO;. Nakayama”‘) has treated the carbonate ionization equilibria with explicit consideration of an additional ion-pairing equilibrium, and obtains essentially the same values for Ki, i and Ki, i by his treatment. The primary difficulty is in making anarbitrary choice of someparticular model or equation to represent activity-coefficient factors r, and accounting for residual non-ideality in terms of an ion-pair equilibrium. When ion-pairing is a relatively small factor, the linear term in equations such as equation (37) can adequately include such a contribution. Moreover, in our procedure of utilizing values of r2 strongly related to actual measurements on an analogous mixture from the work of Harned and Scholes,(“) such behavior should be adequately included in r2. Omission of explicit consideration of ion-pairing simplifies the calculations of composition and the corrections to the standard states. The resultant values of L, will then refer to the same solution model, and will implicitly include ion-pair interactions as part of the total interaction leading to L+. A complete treatment of the equilibrium composition of carbonate solutions leads to a fourth-degree equation in m(H’) or m(OH-). There are general computer programs for treating such situations,(22-24) but for the solutions involved in this work, such measures are unnecessary. Thus for the solutions related to the dilution studies on Na,CO,, m(H+) and m(H2C0,) are negligible, and the equation simplifies to a quadratic in m(OH-). For the product solution in chart 5 for measurements of AH:, i, m(OH)-, and m(COi-) are negligible, and the equation reduces to a quadratic in m(H+), with m(H+) much smaller than the molalities of the other species. The other solutions in this work have m(H+) as the only negligible molality, so the equations reduce to a cubic in m(OH-), which can easily be solved by successive-approximation methods. The logarithmic diagrams relating pK and log m, described by Sillen et a1.(25*26) and

ENTJ3ALPiES

OF AQUEOUS

CARBONATE

SOLUTIONS

1061

by Frieser and Fernando(2’) are very useful graphical displays of solution compositions in such systems, and were used for preliminary planning of experiments and for estimating approximate compositions so that the magnitudes of correction terms could be estimated prior to the actual experiments.

3. Experimental MATERIALS

AND

ANALYSES

Distilled water from a Barnstead still was distilled a second time from an all-glass still and was collected and stored under nitrogen. Some absorption of carbon dioxide occurred during transfer and handling of the water and solutions. During measurements of the enthalpy of dilution of Na,CO, solutions, portions of water handled in the same manner as the diluent samples were analyzed by titration with dilute NaOH and were found to contain 1 x 10e5 to 3 x 10T5 mol dm-’ of C02. In most of the work, the CO2 content was close to the lower assay. All solutions were prepared and handled on a mass basis, and analyses were performed by mass buret techniques. Densities from reference sources were used for reduction of results from weighings to masses. Standard solutions of perchloric and hydrochloric acids were prepared from reagent grade materials and were standardized against TRLS, tris(hydroxymethyl)aminomethane, Fisher Primary Standard, finely ground, and dried at 353 to 363 K for 2 h as recommended.@* 29) The titrations were followed electrometrically and the equivalence points were determined by Gran’s method.‘30’ Precision was 0.02 per cent for the HC104 solution and 0.005 per cent for the HCl solution. Normal accuracy of the procedures is 0.02 per cent or better. Sodium hydroxide solutions were prepared by decanting clear supernatant 50 mass per cent sodium hydroxide solution and diluting it to the desired composition with CO,-free distilled water. The solutions were standardized against a standard acid solution (HCIO,). Merck-Reagent sodium hydrogen carbonate (Lot 72400) assayed 99.99 mass per cent of NaHCOJ by analysis against standard acid in two sets of analyses. Baker and Adamson-Reagent sodium carbonate (Lot Y123) was dried for 2 to 3 days at 400 K, and assayed greater than 99.9 mass per cent of Na2COJ by titration. This material was used in the dilution studies on Na2COs and for determination of AfJ;, i- For the other measurements, Mallinckrodt Analytical-Reagent sodium carbonate (Lot AXM) was used. This material was dried for 4 h at 543 K, and assayed greater than 99.93 mass per cent by titration with standard acid. CALORIMETRIC

EQUIPMENT

AND

PROCEDURES

The solution calorimeter has been described previously,(31-3” and these measurements followed directly after the reported work on zinc oxide,(34) with many of the same procedures. In the enthalpy-of-dilution studies by the pulse-titration method,(33+34’ corrected temperature changes were evaluated by Dickinson’s method.f35P36) In batch-type operations using ampoules, the corrected temperature changes were

1062

R. L. BERG AND

C. E. VANDERZEE

evaluated by standard procedures (integration of the time-temperature curves)(36) and programs adapted for quartz thermometry. Temperatures were measured to _+1 X lo-’ K with a Hewlett-Packard M40-2801A quartz thermometer operated in the 100 s range with minimum time between readings. All of the results refer to the isothermal reactions or processes at 298.15 K, and were referred to this reference temperature (0,) by the equation: AH,,, = ai(Qb- Qh)+ef(Qh - Q,)+ (&)A@,,

(38)

where si and sf are electrical energy equivalents determined for the initial and final states of the process, Ob and 0, are the calorimeter temperatures at the beginning and end of the main period of the experiment, and AOc is the temperature-change correction for stirring and heat exchange. The mean energy equivalent
= Ei(Q1 - Q$)+e’(Q,

- Q,),

(39)

where Or and 0, are the initial and final temperatures obtained by the extrapolation to the midtime c,. For pulse titration operations, the jacket temperature QJ was set equal to the reference temperature Oh to eliminate need for heat capacities of the sample added. Most of the results in the dilution studies were obtained by the pulse-titration procedures previously described,(33* 34) except that batch operations using glass ampoules (10 cmT3) were used for solutions above 0.2 mol kg-l of Na,C03 and 0.3 mol kg-’ of NaHCO,, The efficiency of the batch operations was improved by provision for mounting up to four ampoules in the calorimeter at one time, so that four dilution steps could be handled with one assembly of the instrument. Measurements of electrical energy equivalepts were made at the beginning and end of the series and usually at least two measurements were interspersed among the dilution steps. In a few cases, 39 cm3 ampoules were used. The other measurements employed standard single ampoule procedures.(33p 34) For the measurements of AH:, r, it was necessary to determine accurately the free vapor volume in the calorimeter in order to apply corrections for escape of COZ from the solution into a controlled vapor space. A standard internal configuration (ampoule, stirrer, etc.) was used, and then the volume of the calorimeter vessel was measured in terms of the mass (and volume) of water required to fill the vessel completely to the chimneys, all of which were sealed. The stirrer shaft was sealed at the top of the stirrer chimney by a sleeve bearing, and small vents existed at the thermometer port and the ampoule-breaker rod to equalize pressures. The volume could be defined to within _+2 cm3, and the vessel was normally tiled in these operations to leave a vapor space of 8 to 10 cm3. In this configuration, the vapor space came to equilibrium in 10 to 25 min, as evidenced by the temperature-time patterns after reaction. From the configuration of the curved section following reaction, the half-time for equilibrium was found to be about 100 s for a 10 cm3 vapor space. The correction for evaporation of CO, into the vapor space will be discussed in a later section.

ENTHALPIES

OF AQUEOUS

CARBONATE

1063

SOLUTIONS

4. Results and discussion CARBON MOLAR

DIOXIDE (CARBONIC ENTHALPIES

ACID)--RELATIVE

APPARENT

For the corrections leading to the standard enthalpy change AH;, i (chart 5), we needed in (NaCl + NaHCOJ solutions. The measurements by Harned and Davis(‘2) on the solubility of CO2 in NaCl solutions yield Henry’+law constants from which can be obtained AH, = AH,” + L2, (W where AH, is the differential enthalpy of solution and L2 the relative partial molar enthalpy of CO2 in the NaCl solutions. Their data(12) yield dAH,/dm = dL,/dm = 200 Cal,,, kg mole2, (41) where m denotes molality. For cases such as this, where L2 = am, the relations between L2, L,, and L+ lead to Ld = 0.5 am, or L+./caZ, mol- 1 = lOOm/mol kg-‘. (42) This result is valid up to ionic strengths of 1 mol kg- ‘, and should be valid for (NaCI+NaHCO,) mixtures, especially those where NaCl is the major component. In our measurements leading to AH;, 1, the correction for L,(CO,) was only 2 Cal,, mol-‘. The correction also enters into calculations of L+(NaHCO,), but again is of minor importance except at the highest ionic strengths.

L, for COz (or H&O,)

SODIUM

HYDROGEN

CARBONATE:

ENTHALPY-OF-DILUTION

STUDIES

Tables 1 and 2 present values of L; and L+ for NaHCOJ solutions at selected molalities and ionic strengths respectively. These values were taken from smooth curves based on results of three pulse-titration runs yielding 24 points below 0.2 mol kg-’ and 15 TABLE 1. Values of G for NaHCOI solutions at 298.15 K. The quantity L$ represents the enthalpy change for the isothermal process: (Na++HCO;)*coHIO (conventional reference state) = NaHC03*nH10 (equilibrium state) (calw, = 4.184 1)

nU%O) - mol

m GZi$

1OooOO o.ooo555 5oooo 0.00111 20000 0.00278 1OooO 0.00555 7000 0.00743 5000 0.01110 4000 0.01388 3000 0.01850 2iXN 0.02775

G

4-W)

calamol-l

-- mol

(47)b 44 46 50 54 58 60 65 72

1500 1100 1000 900 800 700 600 555.1 500 400 300

m - kg-l mol 0.03700 0.0500 0.05551 0.0617 0.0694 0.0793 0.0925 0.1000 0.1110 0.1388 0.1850

LJi

calth mol-’ 76 81 83 85 iii 89 89 89

nWa0) -~ mol

277.5 200 150 111 100 75 55.51 50 40

m

G

mol kg-l caltn mol-1 0.2000 0.2775 0.2700 0.500 0.555 0.7401 1.000 1.110 1.3877

77 60 38 3 -12 -62 -133 -159 (-221p6

ii

0 Calculated. b Interpolakd. c Extrapolated. d All other tabulated values are based on the experimental results, and are independent of assumptions or corrections related to hydrolysis etc.

1064

R. L. BERG AND C. E. VANDERZJSE

TABLE 2. Values of 4, the conventional relative apparent molar entbalpy for NaHCOa solutions at 298.15K. These enthalpies refer to the ion combination (Na++HCO,) at the ionic strengths Z given in the table @a&h= 4.184J) Z mol kg-l

4 Z cd, mol-1 mol kg-l

0

0.000111 0.000555 0.00111 0.00278 0.00555 0.00793 0.01110

0 5 11 :;’ 29 ii

4 calm mole1

0.01388 0.01850 0.02775 0.03700 0.0500 0.05551 0.0617 0.0694

42 47 54 57 61 63 65 66

I

4

___ I

~-- 4

molkg-’ cal, mol-1 molkg-l calthmol-’ 0.0793 0.0925 0.1000 0.1110 0.1388 0.1850 0.2000 0.2775

67 68 68 68 ti 55 38

0.3700 0.500 0.555 0.7401 1.000 1.110 1.3877

16 -20 -35 -88 -160 -186 (-250)

batch-type measurements yielding points above 0.2 mol kg-‘. At molalities above 0.5 mol kg-‘, and especially above 1.0 mol kg-‘, solutions of NaHC03 have rather large equilibrium vapor pressures of C02(g), so it was necessary to adopt handling procedures designed to avoid s&Scant errors from loss of COz from the solutions. Replicate runs at a particular molality yielded L> values which usually agreed within + 5 caJh mol- I. Equations (19) to (22) were used to relate provisional values of L+ and Li to the conventional reference state. Equation (23) permits calculation of the relation between L, and L$ for any solution, and was used to obtain values of L+ from smoothed values of L\ at low molalities and also at high molalities to complete the curves and tables. The correction terms are consistent with values of AH:, i and AH;, i obtained later in this work, and no recycling of calculations was necessary. For application of equation (21), several electrolytes were tested. The best analogs were NaI and NaSCN (data from Parker’s tables).t3’) For NaHCO,, the sum of correction terms in equation (19) ranges only from 19 to 35 cal,,, mol-l over the experimental range of molalities. The results for L,+ are judged to be accurate to 4 3 per cent up to 0.1 mol kg-‘, up to f7 cal,h mol-’ at 0.5 mol kg-‘, and up to f 12 Cal* mol-’ at 1.2 mol kg-‘, where the corrections in equation (19) become less certain. Values of L\ are judged to be reliable to within +7 Cal,, mol-’ over the range of experimental molalities, with much of the uncertainty attributable to systematic errors in the corrections linking L> to the conventional reference state. The internal consistency of the Lf+results is about 5 Cal,, mol -l for long-chord dilutions. The values of Li given in parentheses at the lowest molalities are calculated, to delineate the region of severe influence from

hydrolysis of HCO;. L.”

The limiting

value L$” at infinite dilution

= aAH;, i -B(AHi+AHy,

is given by

J = 2054 Cal, mol-‘,

(43)

where -&A is the standard enthalpy of ionization for HzO, a is the fraction of HCO; ionized to CO<-, and /3 is the fraction of HCO, hydrolysed to H,C03. At

ENTHALPIES

infinite dilution,

m(H”)

OF AQUEOUS

= m(OH-)

CARBONATE

= (Ki),)“‘,

1065

SOLUTIONS

so that

CL= K~, *K~, i/D = 3.8 X 10-4,

WV

j? = K;/D = 0.18416,

(45)

where

D=K~,i(K~):)"2+K~+K~,iK",,i.

w

The values of LT+ are tabulated as a function of molality and refer to the equilibrium properties of the pure salt relative to the conventional reference state. These values are useful directly in obtaining standard enthalpies of solution by equation (1). Values of L, are tabulated as a function of ionic strength and represent the contribution of the ion combination (Na+ +HCO;) to the relative apparent enthalpy of the solution at that ionic strength. These values are used in the corrections to standard states for reaction patterns such as in charts 1, 2,4, and 5. SODIUM CARBONATE: ENTHALPY-OF-DILUTION STUDIES Table 3 presents values of L: for Na,CO, solutions at selected molalities, taken from smooth curves based on results of five pulse-titration runs in patterns corresponding to chart 1, and two pulse-titration runs in a pattern corresponding to chart 2, with dilutions into 0.02226 mol kg-’ of NaOH partially to suppress hydrolysis of CO:-. These measurements yielded 54 points in the molality range 0.0055 to 0.112 mol kg-‘, or ionic strength Z from 0.015 to 0.35 mol kg- I. Results at higher ionic strengths are based on 20 batch-type measurements with dilute Na,CO, solutions as diluent.

TABLE 3. Values of L,$ for Na&Cl, solutions at 298.15 K. The quantity G representes the enthalpy change for the isothermal process: (2Na+ +CQ~-) * 03Ha0 (conventional reference state) = Na,CG . nH,O (equilibrium state) calm = 4.184 I) ~03~0)

mol

5& lOOOO0 moo 20000 10000 7000 moo 4ooo 3000 2mo 1500

-___ m

mol kg-l 0

0.000111 0.000555 0.00111 0.00278 0.00555 0.00793 0.0111 0.01388 0.01850 0.02775 0.03700

G

cal, mol-1 (11875)“ (3450) (2310) ‘;:;:I 1240 1138 1022 892 810

nWd3 -___

m

G

mol

mol kg-l

ca&a mol - 1

1110 1000 900 800 700 600 555 500 400 300 277.5 200

-0.0500 0.05551 0.0617 0.0694 0.0793 0.0925 0.1000 0.1110 0.1388 0.1850 0.2000 0.2775

737 714 690 665 636 604 589 568 524 462 442 328

n(H1O) mol 150 111.0 100 75 55.51 50 40 37 30 27.75 25

- m mol kg-’ 0.3700 0.500 0.5551 0.7401 1.00 1.1101 1.3877 1.5000 1.8502 2.0000 2.2202

G

c-al, mol-1 204 52 -,: -425 -520 -729 -804 -990 -1050 -1140

a Calculated values are given in parentheses. All other tabulated values are based on the experi mental results, and are independent of assumptions related to hydrolysis efc.

1066

R. L. BERG AND

C. E. VANDERZBE

Table 4 presents values of L+ for Na&Os solutions calculated from the preceding measurements by the procedures of charts 1 and 2. Equations (8) to (12) were used to organize the results and to relate values of L> and L, to the conventional reference TABLE 4. Values of &,, the conventional relative apparent molar enthalpy for Na&Os solutions at 298.15 K. T’hese enthalpies refer to the ion combination (2Na+ +COi-) at the ionic strengths I given in the table (calah = 4.184 J) - 113 mol kg-l

-- 4 Cal,, mol-1

113 mol kg-l

4 ca&,, mol-1

II3 mol kg-’

&I calth mol-1

113 mol kg-l

LQ Cal, mol-1

2: 47 65 100 136 157 188

0.01388 0.01850 0.02775 0.03700 0.0500 0.0555 0.0617 0.0694

194 214 242 260 272 276 278 279

0.0793 0.0925 0.1000 0.1110 0.1388 0.1850 0.2ooo 0.2775

279 277 274 269 256 225 212 133

0.3700 0.500 0.5551 0.7401 1.oooo 1.1101 1.3877

30 -102 -156 -333 -567 -660 -880

0

0.000111 0.000555 0.00111 0.00278 0.00555 0.00793 0.0111

state by procedures described for those equations. The correction terms are consistent with values of AH;, i and AH;, i obtained later in this work and with the values of L4 for NaHCOJ. Values of L.+ for NaOH were taken from Parker’s tables.(37) The calculations were made for a mean value of 3 x lo-’ mol kg-’ for the molality of CO, in the water used as diluent in patterns of chart 1, based on typical analyses of water samples concurrent with the work. This value may represent a small over-correction in one or two runs, but the corrected results were better behaved than those based on no corrections, or even a correction based on m(C0,) = 1 x 10m5 mol kg-‘. The influence of the corrections is small at ionic strengths of 0.03 mol kg-’ and above, and the guidance functions used for extrapolations, equations (10) to (12), were fully effective at ionic strengths 0.03 to 0.35 mol kg -I. The results from the strategy in chart 2 were fully compatible with the corrected results from the pattern of chart 1. The only suitable electrolyte available as a model or analog for Na,C03 was Na,SO,, for which there are accurate values of Lb, summarized and extended by Thompson, Smith, and Wood,f’3r and appropriately related to Debye-Htickel guidance functions. We expected Na2S04 to be a good analog, even though the CO:ion is smaller than the SO:- ion and has different symmetry, primarily because both ions are weakly hydrated. Equations (11) and (16) have almost linear residue-terms with small slopes, so L\(i), the intercept, could be determined with fair accuracy. Each pulse-titration run was processed separately, and the particular value of L\(i) for the run was then used to generate values of L+ by equations (9) and (15). The separate sets of results were then combined and smoothed on a large scale plot. Once the curves of L+ and Lf, were well established relative to a common zero, the results from batch operations were used to extend the curves to higher molalities. The curve for L> was constructed l&t, and the results were smoothed. Then equation (13) was used to calculate L+ values at the higher molalities and also for the low-molality region, to complete the curves and tables.

ENTJrIALPIES

OF

AQUEOUS

CARBONATE

SOLUTIONS

1067

Because of the large correction terms required to obtain L+ from the experimental results, the errors are judged to be + 3 per cent up to I = 0.03 mol kg-‘, increasing to 3~25 cal, mol- ’ at I= 0.1 to 0.4 molkg-’ and to +35 cal,,mol-’ at I= 1 mol kg-’ and above. Values of L’, are judged to be accurate to +30 Cal,, mol-’ in the experimental range, with much of the uncertainty arising from systematic errors in the correction terms linking Li values to the conventional reference states. Values of L?+(i) from pulse-titration runs varied by +20 calth mol- ‘, and replication of L\ from batch operations was better than f 10 Cal,, mol- ‘. The values of L> in parentheses at the lower molalities are calculated, to display the behavior of L”, in that range. The limiting value at infinite dilution : L3” = 11875cal,, coTresponds to a composition (O.O0038Na,CO, aO.81546NaHC0, * mol-‘, O.l8416H,CO,* l.l8378NaOH), and is calculated from q*

= -(AH~+AH~,

i)K4, ,(K”,)“‘/~-(2AH~+AH,q

i sAH,“, i)Kz/D,

(47)

where D is defined by equation (43). The hydrolysis effects in Na,CO, solutions are so severe that there is no minimum in the L> curve as there is for NaHCO,. It is worth noting that the limiting composition at infinite dilution is the same in either case. The values of L> are appropriately tabulated as a function of molality and refer to the equilibrium properties of the pure salt relative to the conventional reference state. These values are to be used with equation (1) in calculating standard enthalpies of solution. Values of L, are appropriately tabulated as a function of the ionic strength, and represent the contributions of the ion combination (2Naf +CO:‘) to the relative apparent enthalpy of the solution at that ionic strength. These values are to be used in corrections to standard states for reaction patterns such as charts 4 and 5. Values of L, are comparable with those for strong electrolytes such as Na,SO, and others of related valence patterns. The L+ curve for Na2C03 reaches a maximum value about 25 cal, mol-’ above that for Na,SO,, but follows the same general pattern with large negative values of L+ at high molalities. Recent measurements in this laboratory on Na,SO, solutions show a similar general pattern.(3*) The curve of Lb for Na2C03 is steeper than that for Na2S04 in the dilute region, implying a smaller ion-size parameter for Na2C03 than for Na2S0,. This relationship is also implied by activity coefficients for the two salts, ENTHALPY OF IONIZATION OF HCOi(aq) In these measurements, an initial stock solution was prepared containing Na2C03 at a molality of 0.21501 mol kg-’ and NaHCO, at a molality of 0.21526 mol kg-‘. Measured portions were diluted approximately ten-fold on a mass basis to provide the initial calorimetric solutions. Ampoules were filled with approximately 10 cm3 of HCl solution, molality : (2.0666f0.0002) mol kg- ‘. The starting amounts involved from 12 to 30 per cent excess Na,CO, compared with the amount of HCl. The amounts chosen represented a compromise between ionic strengths low enough to reduce errors in calculating activity-coefficient terms and compositions, but providing sufficient calorimetric response to maintain experimental accuracy in the measured enthalpy change. As discussed in connection with chart 4, the buffering conditions

1068

R. L. BERG AND C. E. VANDERZEE

provide for reasonably accurate calculation of solution composition when hydrolysis of CO:- is reduced as in these conditions. Values of L+ for NaHCO, and Na,CO, were taken from tables 2 and 4, and those for the other electrolytes were taken from Parker’s tables.(37) The results of measurements leading to the standard enthalpy of ionization AH;, i are given in table 5. Table 6 includes the amounts of substances for the initial and final states of the calorimetric process and a detailed calculation of correction terms for one run to illustrate the magnitude of the correction terms, following the course of chart 4 and equations (25) to (27). The results give for the standard state process

TABLE 5. Experimental results for the standard enthalpy of ionization tii., corresponding to HCO;(aq) = H+(aq)+COi-(aq), at 298.15 K. Initial and final masses of H,O are m’(I$O) and mr(I-IaO), and other symbols relate to chart 4 and equations (24) and (25). The quantity BAH ,,,,rr represents all terms following AHrcP in equation (27), and AHIcP = -eA@,, (cal,b = 4.184 J) ny(NasCOa)/mol &(NaHCO,)/mol n,“(I-ICl)/mol N%OYg mv-bO)/g P/m01 kg - 1 P/m01 kg - 1 (n: -n:)/mol +a&,, K-l A&x/K mo*/c&l =&&& AH$/calth mol- 1

0.025612 0.025642 0.019403 1067.00 1076.39 0.09591 0.07799 -0.019234 1173.9 0.07126 -83.652 16.273 3503

0.022142 0.022167 0.019546 1047.23 1056.69 0.08446 0.06543 -0.019312 1158.3 0.07287 - 84.405 16.597 3511

0.022725 0.022751 0.019042 1037.00 1046.22 0.08755 0.06877 -0.018844 1147.6 0.07185 -82.455 16.099 3521

0.021981 0.022007 0.019114 1054.85 1064.10 0.08325 0.06467 -0.018892 1166.4 0.07092 - 82.724 16.249 3518

0.022354 0.022379 0.019491 1114.14 1123.57 0.08015 0.06233 -0.019263 1195.1 0.07047 -84.217 16.560 3512

TABLE 6. Compositionandcorrectiontermsfor the first run on the enthalpyof ionizationA&& of HCO$(aq).Quantitiesaredeflnedandrelatedby chart 4 and equations(24),(25),and(27) (cabs= 4.184I) n:(Na,COs)/mol= n!JNaHCOa)/mol= n#I&O,)/mol = &‘NaOH)/mol = (PI:-&AH; = (P&-n3AH,91= n:4(NaSC0,) = n$g-NaHC03) = n$qHaCO,) z &$NaOH) = n,OL&HCl)=

2.5475x lOma, 2.5775x 10W2, 4.4x lo- 6, 1.421x lo- * ; 1.619c&j,, 0.107cal,h, 6 394caltilt 1:753c&h, 0, 0.014calthr 12.437calth;

n:(Na&ZO,)/mol= n$WICO~)/mol = n$&COa)/mol = n:(NaOH)/mol = n:(NaCl)/mol= = n,&~aHCOa) :‘,$,(NaSCOs)= = nppxo6) n,&(NaOH) = &$(NaCl) =

ZAHH,,,= 16.273cal,,.

6.241x 1O-3, 4.4959x 10Ya, 5.31x 10m6, 2.07x 10m6, 1.9403x lOma. 1.485calth, 3so1 2 G&h, 0, 0.002cabs, 1.552cabs.

EN’THALPIEB

OF AQUEOUS

CARBONATE

SOLUTIONS

1069

at 298.15 K: AH;, i = (3513 + 25) c& mol-‘.t (48) HCO;(aq) = H+(aq)+CO:-(aq); In the assigned uncertainty interval of +25 cal, mol-’ for AH:, *, the major component is the uncertainty in L+.(Na,COJ), which was estimated to be + 15 Cal,, mol-’ , primarily a systematic error resulting from the configuration and extrapolation of L,+ for Na,COs solutions. (Comparison of the L+ curves for Na,SO,, Na,CO,, and Na,SO, leads us to feel that the uncertainty in L+.(Na,CO,) may be overestimated). In many of the situations involving reactions in sodium carbonate solutions, the combination of terms {AH;, i+L+(Na,CO,)} will occur as a unit, with a residual uncertainty of + 25 Cal,, mol- ’ when the results from tables 4 and 5 are combined. In other situations, the systematic error in L,&Na&O,) may vanish when reactions are combined in a Hess’s law pattern. Attention to these possibilities is required for proper evaluation of uncertainty intervals. OF IONIZATION OF HK03(aq) Chart 5 displays the (ionization+dilution) corrections involved in measuring AH;, i for carbonic acid, and the related discussion describes the plan for measurements. Two sets of measurements were made, with different operating conditions. In the initial series, set A, the initial molalities of NaHC03 were between 0.018 and 0.021 mol kg-‘. The HCI solution, molality (2.0666 + 0.0002) mol kg- ‘, was placed in 10 cm3 ampoules. These amounts of substances provided values between 1.11 and 1.35 for the ratio $(NaHCO,)/ng(HCl). With this much excess NaHCO,, the amount n{ of Na,CO, in the final state is negligible, and the amount n’, of HCl remaining, corresponding to ionization of H,CO, is about 0.02 per cent of n,“(NaHCO,), so the composition of the final state can be obtained easily and accurately. In the second series, set B, the initial molalities of NaHCO, ranged from 0.027 to 0.030 mol kg-‘, and slightly larger amounts of HCI solution (2.6672 mol kg-‘) were used. In set A, the free vapor space V* in the calorimeter was between 8 and 10.5 cm3, with a maximum uncertainty of )2 cm3. In set B, the free vapor space I/* was made larger, 40 to 46 cm3, again with an uncertainty of +2 cm3. Set A is the set described in the thesis. Set B was studied in May 1977, to confirm the earlier work and to test the interpretation of the calorimetric time-temperature response under more adverse conditions. The determination of AHIcP from the calorimetric results requires specific correction for the effects of gaseous CO2 escaping into the free vapor space V* of the calorimeter. Several alternative procedures were used and compared, as described in following paragraphs. In procedure I, the free vapor space V* is measured as accurately as possible, and then the enthalpy correction is calculated for the gases (CO, +H,O) which have escaped from the solution. This procedure is relatively secure for closed calorimeters; ENTHALPY

t The results given in table 0X-2) of the thesis (3526 calth mol-I) have been recalculated and corrected for an interpolation error in L&(HcI). The effectof this change in AI!& is to change the values of AHi for HCO,(aS, and H&Os(aq), and also AH” 11o111 for NaHCOs(s) and CO,(g), by + 13 calth mol-a from the values given in the thesis. The change had no “feedback effect” on the other properties reported in this paper or in the thesis.

1070

R. L. BERG

AND

C. E. VANDERZBE

to apply it to open calorimeters requires stipulation of a “model” for the equilibrating process, since some COz (and H,O vapor) will be expelled from the free vapor space V* as the system equilibrates. The amount of air expelled (O,+N,) is equal to the amount of CO2 in V* at equilibrium, and some COz and H,O are expelled with it. From an analysis (3b) of this approach for open calorimeters with small rapidly equilibrated free vapor space V* the correction for restoring the evaporated COz and its accompanying HzO(g) to the solution phase at 298.15 K is given by AH(cond)/cal,,

= - 6.9ni V*/cm3.

This correction is to be added to the calorimeter-response from AHm = -&A&,,

term, from equation (38) or

AHrcp = AH=,, i- AH(cond),

(51)

(50) where A@,, is the corrected temperature rise for a main period in which equilibrium is reached in the free vapor space, to give for the isothermal calorimetric process:

which appears in equation (29), (31), and chart 5. Calibration of V* was described in the experimental section. For the conditions of set A, about 1 per cent of the COz escaped from the solution phase; this loss has no sign&ant effect on the dilution correction terms in equations (29), (31), and chart 5. From 10 to 25 min was required to attain equilibrium in set A, as judged from the behavior of the temperature-time curves. The conditions for set B required 30 to 45 min for equilibration, so procedure I was considerably less accurate in this case. Procedure IIa involves treating the escape of CO2 as a parasitic process in the main period, and embeds the effects into the temperature-change correction rather than as a separate quantity such as equation (49). The analysis of such processes leads to a procedure analgous to a Dickinson extrapolation, and would be formally equivalent if the time t, of beginning of the parasitic process coincided with the Dickinson “midtime” t,,,. We determined t,,, from the temperature-time curves, and t, should not be more than 10 s after the time of ampoule breaking for the mixing processes in our calorimeter. Procedure IIb involves treating the parasitic process as a part of the stirring-heat-exchange behavior and calculating the temperature-change correction by the usual equation, using a main period of minimum time (100 s) and drift rates from the beginning and end of the main period. The rate of escape of CO, followed (approximately) a tit&order rate law (simple exponential), so the shape of the temperaturetime curve was fairly easy to represent. The results from procedures IIa and IIb depend upon the interpretation of the temperature-time curves with no separate calculation of the vaporization correction, whereas procedure I requires an accurate value of the free vapor volume V* and complete equilibration in the vapor space to permit an accurate separate calculation of the vaporization correction to be added to the equilibrium-state results for the enthalpy change in the calorimeter. For long main periods, procedures IIa and IIb should be more reliable, since complete equilibration of the vapor space is not required for application of those procedures. A detailed treatment of procedures IIa and IIb will be given in a separate paper.(3g)

ENTHALPIES

OF AQUEOUS

CARBONATE

SOLUTIONS

1071

The results of the measurements leading to AH;, r are given in tables 7 to 9. The results from set A were treated by procedures I, IIa, and IIb, and those from set B were treated by procedures I and IIa only. In the summary of results, table 8, the precision and the uncertainty interval are shown separately. The uncertainty interval for procedure I includes a contribution of 12 cal,,, mol -i from the uncertainty in V*, and for set A, procedures IIa and IIb, a contribution of f 5 Cal,,, mol-’ was assigned as systematic error in interpretation of the temperature-time curves, corresponding to * 7 x 10m5 K in the temperature change. The uncertainty interval for set B, procedure IIa, contains an estimated contribution of f 10 Cal,,, mol-’ from systematic error in interpretation of the temperature-time curves, which had much larger slopes and longer equilibration times than those for set A. The uncertainty interval for set B, procedure I, reflects some uncertainty as to complete equilibration, as well as the error in V*. The final uncertainty interval also includes contributions from analytical and calibration uncertainties, composition calculations involving activity-coefficient terms, the dilution corrections (L+), and ionization effects. These contributions are independent of those related to the calorimetric operations and interpretation of the corrected temperature change and vaporization effects. From the results in table 8, we adopt for the standard state reaction at 298.15 K: H&Os(aq)

= H+(aq)+HCO;(aq);

LUI”,, r = (2188 f 15) Cal, mol-‘.

(52)

This result differs from the value (2195k 30) cal,, mol-’ given in the thesis partly because of a 13 caJb mol’ 1 correction on L+(HCl) and inclusion of LJCOJ in the correction terms (2 c& mol- 1 at these ionic strengths), and partly because of the new interpretations of calorimetric response and inclusion of additional and independent measurements. The reduced uncertainty interval reflects greater confidence in the validity of the treatment and the correction terms. 5. Discussion Previously reported values of AH’;, i and AH”,, r for aqueous carbonic acid have been summarized in section 2, in the discussion of preliminary estimates of the properties. Our value of AHi, i is close to that obtained by Pi&r.(“) We recalculated Pitzer’s results for AHi, r, using the values of L+ for NaHC03 and Na,COs from this paper, and obtained essentially his reported value. Our value for AH”,, r is close to the mean of the two values(‘0112) based on e.m.f. measurements, and in view of the concordance of results from different series of measurements and evaluation procedures summarized in table 8, our value of AHi, i should be fairly free from systematic errors. In a later paper we present measurements leading to AH;,,,, (COz, g), in which our AH;, i and AH;, r are vital links. The concordance of this AH&, with recently calculated values(40) from other data is excellent. There are few data for comparison with the values of L+ and L$ for NaHCO, and Na,CO,. Rupert, Hopkins, and W~lff(~~’ reported enthalpies of solution for NasCOs(s) to form final solutions with molalities ranging from 0.007 to 0.075 mol kg-‘, from which some points can be obtained for the Li curve. Other such measurements by Swallow and Alty(42) and by Water-held et ~1.c~~) are more useful for the

AH~.l/calth

A&dK AHdcahh

mol -I

0.04036 -49.958 2187

0.04036 -49.958 2187

0.04028 -49.782 2185

0.03938 -48.744 -1.030 2176

0.03911 -48.333 -1.261 2174

0.04027 -49.770 2184

0.02068 0.017581 1130.13 1138.63 0.01851 0.01816 0.017338 12.046 1237.8

A2

0.02355 0.017517 1128.73 1137.20 0.02110 0.02071 0.017240 12.114 1235.9

Al

0.04078 - 50.547 2194

0.04077 -50.534 2193

0.03992 -48.493 -0.978 2189

0.02035 0.017741 1130.65 1139.24 0.01821 0.01787 0.017508 12.132 1239.5

A3

0.04094 -50.745 2198

0.04164 -51.463 2192

IIb

0.04163 -51.447 2192

Procedure

0.04092 - 50.720 2197

IIa

0.04069 -50.286 -1.081 2187

Procedure

0.04007 -49.667 -1.008 2194

I

0.02017 0.018076 1130.00 1138.74 0.01805 0.01771 0.017845 12.339 1235.9

A5

0.03995 -49.386 2193

0.03994 -49.374 2192

0.03941 -48.719 -0.565 2187

0.020515 0.017345 1124.97 1133.36 0.01844 0.01810 0.017110 11.870 1236.2

A6

0.04724 -58.667 2180

0.04253 -52.818 -6.17 2196

0.02996 0.019775 1154.96 1162.38 0.02624 0.02577 0.019425 16.324 1241.9

Bl

0.05616 -70.083 2183

0.05024 -62.694 -6.94 2163

0.027615 0.023651 1159.98 1168.85 0.02409 0.02363 0.023320 19.183 1247.9

B2

0.04822 -59.899 2176

0.04308 -53.514 - 6.27 2171

0.02735 0.020235 1155.13 1162.72 0.02394 0.02352 0.019917 16.550 1242.2

B3

B4

The on the

--

0.04827 -59.997 2190

0.04320 -53.693 -6.20 2185

0.02739 0.020204 1155.62 1163.23 0.02397 0.02349 0.019864 16.490 1242.9

AZZ:,, at 298.15 K, corresponding to HaCOs(aq) = H+(aq)+HCO;(aq). not molecular HaC03. BAZ!Z ,,,,- is the sum of all terms except AH,,, defined in chart 5 and equations (28), (29), and (49) to (51). = 4.184 J)

Procedure

0.02027 0.017787 1130.43 1139.04 0.01813 0.01779 0.017555 12.160 1239.5

A4

7. Experimental results for the standard enthalpy of ionization H&Os(aq) denotes the equilibrium mixture (COl+HaCOs) and right-hand side of equation (31). Other symbols are (calt,,

&NaHCO~)/mol n~(HCl)jmol few)h m’(HaOl/e P/mol kg-’ Z*/mol kg- 1 GtG4Gnol WOO,JCalth e’/cal,, K-l

Run

TABLE symbol

ENTHALPIES TABLE

OF AQUEOUS

CARBONATE

8. Summary of results from table 7, for MC,, for carbonic acid; Us denotes standard deviation of the mean and 6 uncertainty interval (CaIta = 4.184 J) /calth mol-1 Set Set Set Set Set

A, A, A, B, B,

procedure procedure procedure procedure procedure

I IIa IIb I IIa

2a,/calth mol-1

2184 2191 2192 2179 2182

Selected value

TABLE

1073

SOLUTIONS

S/Cal,, mol - 1

118

:i

*13 *13

k?:: +7

*25 117

2188

&I5

9. Composition and correction terms for the first run (Al) on the enthalpy ot ionization H&O,(aq). Quantities are defined and related by chart 5 and by equations (28) to (31) (caltb = 4.184 J) n:(NapC03)/mol [email protected])/mol

= 2.699 x 10V4, = 2.3005 x 10s2,

n$(H&O,)/mol = 2.716x lo-*, n:(NaOH)/mol

= 2.17 x 10e8;

(n: -n:)AH;, n:AH;; &&Na&O,) 1 I n&,(NiHCO,) n:L;(H&03) n&(NaOH) &;(HCI)

= = = = = = =

0.948 calth, -0.029 G&h, 0.040 caltb, 1.127 calt,,, 0.0006 calth, 0, 11.23 caltb ; ZAH,,,

n:(Na&OJmol n:(NaHCOs)/mol

of

= 1 X lOma, = 6.029 x 10b3,

nH(H&Oo)/mol = 1.7512x 1O-2, n’,(NaCl)/mol &(HCl)/mol nX&(NaKO,) n!&,(NaHCO,) n$$,(HzCO,) niI$(NaCl) nBLgI-Icl)

= 1.7512x 1O-2, = 5.4 x 10eB; = = = = =

0, 0.295 calth, 0.037 calth, 0.928 calth. 0,

= 12.114 Cal,.

reverse calculation to obtain AH&,(Na,CO,, s), which will be discussed in a following paper. Recently Leung and Millero(44) measured enthalpies of dilution of Na,CO, solutions at 303.15 K over the molality range 1.0 to 0.2 mol kg-‘. Their results yield a set of points which are almost parallel to the Li curve. Their extrapolation did not make use of hydrolysis corrections as in charts 1 and 2; in the region of their measurements, the curves for L, and L\ are roughtly parallel. However, unless due account is taken of the corrections for hydrolysis, it is not possible to link properties of the equilibrium-state solutions to the conventional reference state. From recently published tables(45) we can extract values of L’, for Na,CO, solutions which when scaled to fit our curve at 1 mol kg-’ run up to 50 Cal,, mol-’ high at low molalities and 20 to 30 Cal,, mol - ’ low at the higher molalities. These results appear to be based in part on the results from Rupert, Hopkins, and Wolff, since their cnthalpies of solution AH: yield a similar pattern-when combined by AH,” = AH: - L>. The values of L; reported in this paper for NaHCO, and Na,CO, solutions have been linked by a reliable and consistent path to the conventional reference states, and these values are primarily of importance in evaluating standard enthalpies of solution for NaHCO,(s) and Na,CO,(s), and also for evaluating enthalpies of dilution of the

1074

R. L. BERG AND C. E. VANDERZEE

solutions from one molality to another. The values of 4, which represent the contributions for the ion combinations (Na’ + HCO;) and (2Na+ + CO: -) to the enthalpy of a solution or mixture relative to the conventional reference state, are to be used when dealing with composition changes (ionization, neutralization, etc.) in the solutions. The values of L+ are also of interest to electrolyte theories, since they can be compared with values for normal salts, such as NaI or Na,SO,, as the case may occur. Both sets of values should be evaluated and reported for weak electrolytes, in order to deal with the various special problems such substances present. The results reported in this paper for L+ and AH,” are an internally consistent set. In dilute solutions, where additivity of L+ values at constant ionic strength is an acceptable assumption, the results should be useful in describing the thermal behavior of buffer mixtures such as (NaHCO, + Na,CO,). We have not evaluated L1 and L,, the relative partial molar enthalpies, but these can be obtained from L+ by standard methods, and would be valuable for interpreting the effects of temperature on the activity coefficients for the ion combinations. If, in the future, more reliable values of the activity-coefficient functions r, and r, are obtained for calculation of the equilibrium compositions, such recalculations will not change the shape of the measured L\ curve but will shift its reference point and the absolute values of L>. However, such recalculations could change the shape of the L, curve to some small extent. Such changes will have little influence on the results for NaHC03, but could have larger effects on the results for Na,CO,. In the dilute region, however, the shape of the L, curves is constrained by Debye-Hiickel and analog curves. The uncertainty intervals assigned in this paper include our estimate of possible influence from such effects, and the consistency of results obtained in the following paper for AH,“,,,(Na2C0,, s) under conditions of suppressed and unsuppressed hydrolysis suggests the absence of significant errors due to the choice of rz and r1 used in this paper. In the following paper we present the results of measurements of the enthalpies on solution of CO,(g), NaHCO,(s), and Na,CO,(s), in which the results from this paper are used in the corrections to standard states, and in which the results of measurements leading to the standard Gibbs energy of solution of COz(g) are reviewed and used to obtain a consistent set of standard enthalpies of formation, standard Gibbs energies of formation, and standard entropies for the aqueous species and the solids. The support of the University of Nebraska Research Council by way of equipment is gratefully acknowledged, as is the help of Mr Norman Haas in extending the dilution studies to high molalities. REFERENCES 1. Wagman,D. D. ; Evans,W. H. ; Parker,V. B.; Halow,I. ; Bailey,S.M. ; Schumm,R. H. U.S.iVOr. Bur. Stand. Tech. Note 270-3. Selected Values of Chemical Thermodynamic Roperties.

Government Printing Office: Washington, D.C. 1968.

U.S.

2. CODATA BulletinNo. 5, ICSU CODATA CentralOffice,Frankfurt/Main, Germany,Fed.Rep., Dec. 1971. 3aBerg,R. L.; Vanderzee, C. E. J. Chem. Thermodynamics in the press. 3bVanderzee,C. E., to bepublished.

ENTHALPIES

OF AQUEOUS

CARBONATE

SOLUTIONS

1075

4. Young, T. F. ; Wu, Y. C.; Krawetz, A. A. Disc. Faruaay Sot. 1%7,24,37. 5. WU, Y. C.; Smith, M. B.; Young, T. F. J. Phys. Chem. 196!3,59, 1869, 1873. 6. (a) Wood, R. H.; Anderson, H. L. J. Phys. Chem. 1%7,71, 1877. (b) Wood, R. H.; Ghamkhar, M. J. Phys. Chem. 1964,73, 3959. I. Reilly, P. J.; Wood, R. H. J. Phys. Chem. 1972,76, 3474, and other work by Wood et al. 8. Lewis, G. N.; Randall, M.; Revised by Pitzer, K. S.; Brewer, L. Thermodynamics, 2nd Ed. McGraw-Hill: New York, 1961. 9. Pitzer, K. S. J. Am. Chem. Sot. 1937,59,2365. 10. Shedlovsky, T.; MacInnes, D. A. J. Am. Chem. Sot. 1935, 57,1705. 11. Hamed, H. S. ; Scholes, S. R. J. Am. Chem. Sot. 1941,63, 1706. 12. Hamed, H. S.; Davis, R., Jr. J. Am. Chem. Sot. 1943,65, 2030. 13. Thompson, P. T.; Smith, D. E.; Wood, R. H. J. Chem. Eng. Data 1974, 19, 386. 14. Hamed, H. S.; Owen, B. B. Physical Chemistry of EZectroZytic Solutions, 3rd Ed. Reinhold Publishing Corp.: New York. 1958. 15. Han, S. T.; Bemardin, L. J. TAPPZ 19S8,41, 540. 16. Lortie, L.; Demers, P. Can. J. Research 1940, 18B, 373. 17. Saegusa, F. Sci. Reports Tohoku Univ. Ser. I. 1950, 34, 147. 18. Taylor, C. E. J. Phys. Chem. 1955, 59, 653. 19. Khvorostin, Yh. S.; Filipov, V. K.; Reshetova, L. 1. Russ. J. Phys. Chem. 1975,49, 753, Zh. Fzz. Khim 1975,49, 1271. 20. Butler, J. N. J. Phys. Chem. 1970,74,2976. 21. (a) Nakayama, F. S. J. Phys. Chem. 1970,74,2126. (b) Nakayama, F. S. J. Znorg. Nucl. Chem. 1971, 33, 1287. 22. Ingri, N.; Kakolowicz, W.; Sillen, L. G.; Warnquist, B. Tulanta 1967, 14, 1261; 1968, 15, XI. 23. Ekelund, R.; Sill&, L. G.; Wahlbert, 0. Actu Chem. Scund. 1970,24, 3073. 24. Bard, A. J.; King, D. M. J. Chem. E&c. 196S,42, 127. 25. Sillen, L. G.; Lange, P. W.; Gabrielson, C. 0. Problems in Physicul Chemistry. Prentice Hall: New York, 1952. 26. Sillen, L. G. in Treutise on Analytical Chemistry, Part I, Vol. 1, Chap. 8. Kolthoff, I. M.; Elving, P. J.: editors. Interscience: New York. 1959. 27. Frieser, H.; Fernando, Q. J. Chem. E&c. l%S, 42, 35. 28. Fossum, J. H.; Markunas, P. C.; Riddick, J. A. Anal. Chem. 1%1,23,491. 29. Irving, R. J.; Wadso, I. Acta Chem. Stand. 1964,18, 195. 30. Gran, G. Actu Chem. Scund. 19SO,4, 559. 31. Vanderzee, C. E.; Swanson, J. A. J. Phys. Chem. 1963,67,285. 32. Vanderzee, C. E.; Gier, L. J. J. Chem. Thermodynamics 1974,6,441. 33. Vanderzee, C. E.; Rodenburg, M. L. N.; Berg, R. L. J. Chem. Thermodynamics 1974,6, 17. 34. Berg, R. L.; Vanderzee, C. E. J. Chem. Thermodynamics 1975,7, 219. 35. Gunn, S. R. J. Chem. Thermodynamics 1971, 3, 19. 36. Coops, J.; Jessup, R. S.; van NW., K. Experimental Thermochemistry, Vol. 1, Chap. 3. Rossini, F. D.: editor. Interscience: New York. 19%. 37. Parker, V. B. Thermal Properties of Aqueous U&Univalent Electrolytes. NutionaZ Stunaard Reference Data Series-NBS2. U.S. Government Printing Ofice: Washington, D.C. 1965. 38. Vanderzee, C. E., to be published. 39. Vanderzee, C. E., to be published. 40. Hu, A. T. ; Sinke, G. C. ; Mansson, M.; Ringnb, B. J. Chem. Thermodynamics 1972,4, 283. 41. Rupert. J. P.: Hopkins, H. P., Jr.; Wulff, C. A. J. Phys. Chem. 1965, 69, 3059. 42. Swallow, J. C.; Alty, S. J. Chem. Sot. 1931, 3062. 43. Waterfield, C. G.; Linford, R. G.; Goalby, B. B.; Bates, T. R.; Elyard, C. A.; Staveley, L. A. K. Trans. Furuduy. Sot. 1968,64, 868. 44. Leung, W. H.; Millero, F. J. J. Chem. Thermodynamics 1975,7, 1065. ___ 45. Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H. Chemical Thermodynamic Properties of Compounds of Sodium, Potassium and Rubidium: An Interim Tabulation of Selected Values, NBSIR 76-1034, National Technical Information Service, Springfield, VA 22151.

63