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Volumes and heat capacities of mixtures of dimethylformamide with several dialkylacetamides
Fluid Phase Equilibria, 18 (1984) 299-311 Elsevier Science Publishers IXV., Amsterdam
299 -
Printed
in The Netherlands
VOLUMES AND HEAT CAPACITIES OF MIXTURES OF DIMETHYLFORMAMIDE WITH SEVERAL DIALKYLACETAMIDES H.C. ZEGERS Department Netherlands) (Received
and G. SOMSEN of Chemistry,
February
Free
* University>
1, 1984; accepted
June
De Boelelaan
lOH3,
1081
H V Amsterdum
(The
25, 1984)
ABSTRACT Zegers, H.C. and Somsen, G., 1984. Volumes and heat capacities of mixtures of dimethylformamide with several dialkylacetamides. Fluid Phase Equilihriu, 18: 299-311.
and
Densities a series
and heat capacities per of di-n-alkylacetamides
unit volume of binary mixtures of dimethylformamide have been measured and converted into excess molar
volumes and heat capacities of the mixtures. In addition, the apparent and partial molar volumes and heat capacities of the various components have been evaluated. They vary smoothly with the mole fraction. The apparent molar heat capacities in the mixtures depend linearly on volume fraction, so that the partial molar heat capacities can be described using only one parameter for each mixture.
INTRODUCTION
As (higher) derivatives of the Gibbs energy, the heat capacities, volumes, expansivities and compressibilities of liquid solutions and mixtures show sensitivity to structural influences. This is illustrated by the importance of the heat capacity in recognizing a hydrophobic solute in water (Benson, 1978; Mirejovsky and Arnett, 1983). Also, Patterson and his group (Lam et al., 1974; Croucher and Patterson, 1974, 1975; Bhattacharyya and Patterson, 1979, 1980) have pointed out that even apparently simple mixtures, such as those of the alkanes, show local ordering of molecular orientations resulting in negative contributions to the excess heat capacity. If heat capacities are to be used as an indication of possible structural influences of solutes on solvents, it would be desirable to know the heat-capacity behaviour of solutes in a variety of solvents where structural influences will differ. Since we are interested in mixtures of polar compounds, we present in this paper the volumes and heat capacities of a number of aprotic solvent * Author
to whom
0378-3812/X4/$03.00
correspondence
should
0 1984 Elsevier
be addressed.
Science
Publishers
B.V.
300
mixtures in which structural influences are expected to be small. We have previously studied mixtures of N, N-dimethylformamide (DMF) with water (de Visser et al,, 1977), with dimethylsulphoxide, acetonitrile and N-methylformamide (de Visser and Somsen, 1979), and with a series of n-alkanols (Zegers and Somsen, 1984). Here we present results for mixtures of DMF with a series of aprotic dialkylacetamides, i.e., N, N-dimethylacetamide (DMA), N, N-diethylacetamide (DEA), N, N-di-n-propylacetamide (DPrA), N, N-di-n-butylacetamide (DBuA) and N, N-di-n-pentylacetamide (DPeA). EXPERIMENTAL
Materials
DMF (Baker, analyzed reagent), DMA (Aldrich, spectrophotometric grade) and DEA (Aldrich) were stored over molecular sieves (4 A) for at least one week and used without further purification. DPrA, DBuA and DPeA were synthesized (Chute et al., 1948; Robson and Reinhart, 1955) according to the reaction CH,COOH
+ RR’NH + CH,CONRR’
+ H,O
where R(R’) denotes an alkyl group. This reaction was made quantitative by adding acetic anhydride to the reaction mixture. Acetic acid and acetic anhydride were removed by azeotropic distillation with methylcyclohexane (Fein and Fisher, 1944). The dialkylacetamides were purified by azeotropic distillation with benzene (to remove the last traces of water and acetic acid) followed by fractional distillation under reduced pressure. The middle fraction was taken and stored over molecular sieves (4 A). The water contents of all compounds were determined by the modified Karl Fischer procedure of Verhoef and Barendrecht (1977). In all cases the volume fraction of water was less than 0.0001. Gas-liquid chromatography showed a mole-fraction purity of 0.995 or higher for each compound. Procedure
Liquid mixtures of DMF and the various dialkylacetamides were prepared by mass. Details of the procedure have been described previously (Zegers and Somsen, 1984). The usual precautions were taken to exclude water during all manipulations. The densities of the mixtures relative to the density of pure DMF were measured using a digital flow densimeter (Sodev, Model 03D, Sherbrooke, Quebec). Molar heat capacities were obtained from heat capacities per unit volume ( C,/ V) measured using a Picker flow microcalorimeter (Setaram, Model “chaleur specifique”, Lyon, France). The pro-
301
cedure was as reported previously (Zegers and Somsen, 1984) but modified in one respect. The microcalorimeter was fed from vials placed in closed boxes filled with nitrogen under pressure. For all mixtures a constant flow rate through the calorimeter cell was achieved by adjustment of the nitrogen pressure. The pressure needed to maintain a flow of - 0.010 cm3 SC’ never exceeded 0.6 bar. This modification makes the microcalorimeter more suitable for measuring rather viscous liquids such as DBuA and DPeA, and it avoids the use of pumps, which can be problematic with organic solvents. Measurements on mixtures with and without this modification gave the same results. RESULTS
Volumes
Densities d of the binary mixtures at 298.15 K relative to that of pure DMF (d,) are presented in Table 1 as function of the mole fraction x1 of DMF. The density of pure DMF as measured with respect to pure water (Kell, 1967) is 0.943289 g cme3 at 298.15 K, corresponding to a molar volume VI* = 77.489 cm3 mol-‘. The molar volumes of the pure dialkylacetamides DMA, DEA and DPrA, respectively V1*= 93.117, 127.972 and 162.012 cm3 mol-‘, compare reasonably with literature data. In our laboratory we found previously for DMA V,* = 93.07 cm3 mol-’ (de Visser et al., 1978), whereas Giaquinto et al. (1977) reported for DMA, DEA and DPrA, respectively, V, * = 92 .996, 127.831 and 161.83 cm mol-‘. The molar volumes of DBuA and DPeA are 195.948 and 229.555 cm3 mol-’ and have not been reported earlier. From the experimental densities the molar excess volumes of the mixtures can be calculated from v~=n,M,(d-‘-d,l)+x,M,rd-‘-di’) where M,, component ered here component
(1)
d, and
x, are the molar mass, density and mole fraction of i, with i = 1, 2. Smoothed values of V,” for the mixtures considare represented in Fig. 1. The apparent molar volumes y,, of i are obtained from
q/i,+ = K* + Q/Xi
(2)
For the present mixtures both V,,, and Vz.+ are smooth functions of X, and were used to calculate the partial molar volumes V, of the components according to vi = Y,+ + XIX2(W,,/ax,
I,.,-
(3)
TABLE
1
Experimental at 298.15 K X1
relative densities d - d, and changes in heat capacity per unit volume A(C,/V)
103(&d,) (g cm-‘)
Dimethylformamide
103A(CP/V) (J K-’ cmP3) (1) -I- dimethylacetamide
X,
103A( C,,‘V) (J K-’ cm-3)
0.54997
- 3.652
- 13.010
~ -
3.199 2.824 2.447 1.943 1.537 1.153 0.973
- 11.049
-0.819 - 0.368 - 0.310 0.000
- 2.386 - 1.109 - 0.802 0.000
- 6.760
0.00000
- 7.666
0.03514 0.04613 0.04941
- 7.425 - 7.341 -7.317
- 32.428 - 31.773 - 31.721
0.60887 0.65569 0.70389
0.11794 0.15054 0.19746 0.25214 0.30341 0.37263
-
-
0.76695 0.81647 0.86361 0.88454 0.90351 0.95678
28.907 27.544 25.503 23.274 21.742 18.968
- 17.406 0.39961 - 4.778 - 16.039 0.45657 - 4.353 - 14.059 0.51288 - 3.945 Dimethylformumide (I) + diethylucetamide
d,)
(2)
- 33.676
6.835 6.604 6.278 5.882 5.498 4.983
lO”(d(gem-‘)
0.96350 1 .ooooo
-
9.420 7.798 6.161 4.867 3.314 2.742
(2)
0.00000
- 43.272
- 34.494
0.53143
0.03361
-42.313
- 32.703
0.58694
- 24.903 - 22.499
0.05030 0.08421
-41.829 - 40.830
- 31.957 - 29.774
0.67928 0.69712
-18.211 - 17.341
0.10911 0.15233 0.19661
- 40.079 - 38.742 - 37.331
- 28.823 - 26.543 - 24.210
0.76747 0.79321 0.83373
.- 13.765
0.25816 0.29865
- 35.284 - 33.895
- 20.527 - 18.315
0.89494 0.92132
0.33867 0.40390 0.45067
- 32.452 - 30.044 - 28.214
- 15.977 - 13.150 - 10.465
0.94651 0.96700 1 .ooooo
- 8.470 0.49250 - 26.548 Dimethylformamide (1) + di -n-propyfacetamide - 63.720 0.00000 - 59.213 - 62.169 0.02940 - 58.385
(2) 0.55058 0.59849
- 12.390 -- 10.166 -6.618 - 5.031 - 3.470 - 2.160 0.000
- 37.466 - 34.712
- 4.608 - 1.244 - 0.722 0.846 1.333 1.493 1.595 1.315 7.137 0.858 0.000
- 29.711
- 32.072 - 28.085
- 25.849 - 22.615 - 18.403
0.80309 0.84916
- 24.301 - 20.085 - 16.037
- 14.358 - 10.438 - 7.306
- 48.723 - 46.351
0.90171 0.92657
- 10.973 - 8.400
- 47.229 - 44.835
- 42.895 - 39.567
0.95602 0.97207
- 5.180 - 3.347
- 4.235 - 2.679 - 1.522
0.45342
- 42.539
- 36.408
1.00000
0.000
0.51425
- 39.463
- 31.740
0.06081 0.06326 0.09288
- 57.471 - 57.400 - 56.502
- 60.546 - 60.320 - 58.826
0.64058 0.69942 0.75094
0.15254 0.20992
- 54.616 - 52.645
- 55.372 -51.917
0.25632 0.29606
- 50.961 - 49.432
0.35009 0.40537
- 0.839 0.000
303
Xl
103(d-
d,)
Dimethylformamide
0.00000 0.02951 0.04911 0.07488 0.07783 0.09880 0.12222 0.12989
xl
cm-‘)
10Z'(d-
d,)
103A(Cp/V)
(g cm-‘)
(J Km’ cmP3)
- 54.485 - 53.657
- 51.455 - 50.406 - 45.773 -41.911
(I) + di -n- butylacetamide (2)
- 69.153 - 68.397 - 67.876 -67.166 - 67.085 - 66.483
0.13737 0.14989
-
0.17232 0.20560
- 64.247 - 63.146
0.24477 0.25483 0.28863
- 61.772 -61.417 - 60.137 - 59.681 - 58.011
0.30050 0.34140
103Uc,,/V)
(J IV’
(gcme3)
65.794 65.562 65.339 64.951
- 76.219 - 74.794 - 73.820 - 72.468
0.41983 0.43648 0.49958 0.54832
-
72.305 71.216 69.897 69.542 69.192 68.457
0.60346 0.65069 0.70013 0.74380 0.80773 0.83836
-
- 67.197
0.85305 0.87052 0.90146
- 2.1.516 - 19.374 - 15.361
0.90270 0.92642 0.93058 0.95533
- 15.193 -11.861 - Il.257 - 7.490
- 11.312 - 8.129 - 8.087 - 5.623 - 5.426 - 3.171
0.96823 56.787 0.97601 53.441 52.905 1 .ooooo pent_placetamide (2)
- 5.427 - 4.141
- 2.118 - 1.583
0.000
0.000
- 57.260 - 54.416 - so.939
- 61.582 - 57.015
-
- 47.233 - 40.756
-
0.34480 - 57.865 0.39044 - 55.866 0.40147 - 55.334 Dimethylformamide (I) t di -n-
65.415 63.148 62.474 60.550 59.613 56.952
0.00000 0.02693
- 74.917 - 74.306
- 92.681 - 91.461
0.49938 0.54818
0.04711 0.06887 0.08105
- 73.824 - 73.287 - 72.977
- 90.546 - 89.474 - 88.882
0.60166 0.64841 0.70454
0.10277 0.13559 0.17145 0.21332
-
72.408 71.501 70.475 69.199
-
87.770 86.039 84.145 81.817
0.75383 0.79774 0.84076 0.87531
0.25175 0.29912 0.35405 0.39571 0.44609
-
67.948 66.280 64.152 62.364 60.032
-
79.489 76.703 73.016 70.057 66.043
0.90658 0.92893 0.96062 0.97818 1 .ooooo
50.350 47.529 43.994 40.640 36.743 32.947 26.640 23.233
47.513 42.856 38.144 :33.339 28.001 23.162
- 37.207 - 33.012 - 28.185 - 24.122 - 17.729 - 14.875 - 13.111
-- 51.959
---
34.375 28.380 22.615 17.626
- 18.277
- 12.652
- 14.443 -~ 8.464 -- 4.842 0.000
- 9.188 - 4.829 - 2.569 0.000
Values of 1/,+ and ( SV,.+P/SX,)~.~ were obtained by the local fitting procedure reported previously (Zegers and Somsen, 1984). This procedure allows calculation of the partial molar quantities without being dependent on the suitability of a particular analytical expression, such as the Redlich-Kister equation, for representing the excess quantities. The resulting partial molar volumes are shown in Figs. 2 and 3.
304
Heat
capacities
Changes in the heat capacities per unit volume with respect DMF, A( C,/V) = C,/V - C,T,/VI*, are also reported in Table 1. refer to a mean temperature of 298.15 ~frO.-l K. Adopting C,T,/V,* K-’ cm- 3 for DMF (Zegers and Somsen, 1984), we found for the
Fig. 1. Smoothed dialkylacetarnides.
excess molar volumes for mixtures
of dimethylformamide
to that of The results = 1.9146 J molar heat
with a series of
+0.6 L
-0.2
\( I
0.0
0.2
0.6
0.4
DEA I
0.8
1.0
Xl Fig. 2. Excess mamide.
partial
molar
volumes
of dialkylacetamides
in mixtures
with dimethylfor-
305
capacities of the pure compounds DMA, DEA, DPrA, DBuA and DPeA, c * = 175.15, 240.60, 299.87, 360.23 and 418.23 J K-’ mol-‘, respectively. O?ihese values, only the molar heat capacity of DMA can be compared with the value of 178.2 J K-’ mol-’ obtained earlier in our laboratory (de Visser et al., 1977). However, this value resulted from a different and less precise experimental procedure (static calorimetry) and its calculation was hampered by the fact that no precise densities of DMA at temperatures other than
Fig. 3. Partial molar volumes of dimethylformamide
0.0
0.2
Fig. 4. Smoothed excess series of dialkylacetamides.
0.4
0.6
0.8
Xl molar heat capacities
in mixtures with some dialkylacetamides.
1.0 for mixtures
of dimethylformamide
with a
305
298.15 K were available. Since the CP:l values for n-alkanols obtained by flow calorimetry in our previous paper (Zegers and Somsen, 1984) agreed excellently with literature data, we feel that the present value of CP,Tzfor DMA should be preferred. Excess molar heat capacities for the mixtures considered were calculated according to
and are represented
in Fig. 4. Apparent
and partial
molar heat capacities
of
IO 7
0 E -iY
-5 wd
6
0
0.0
0.2
0.4
0.6
0.8
Fig. 5. Excess partial molar heat capacities mamide.
I
0.0
I
0.2
I
1
I
0.4
I
0.6
I
1.0
of dialkylacetamides
I
0.8
in mixtures
with dimethylfor-
I
1.0
9 Fig.
6. Partial
kylacetamides.
molar
heat
capacities
of dimethylformamide
in mixtures
with
some
dial-
307
the components in the mixtures can be calculated following the same procedure as applied for the volumes. The partial molar heat capacities are shown in Figs. 5 and 6. DISCUSSION
The molar excess volumes and heat capacities here can be described by the equation ,I -
Y,E=x,x*
c
of the mixtures
considered
1
a,(x, -x2)l
(5)
r=O
The coefficients a, in this equation, the fit 8, defined by
S2= C, [ Y,E(exp.) - Y,“(calc.)12/(
together
with the standard
deviation
of
N - n)
where N denotes the number of experimental points, are presented in Table 2. All experimental values were weighted equally. The values of a certain partial molar quantity for a compound in a mixture are often determined largely by the value for the pure compound, that at infinite dilution in the other compound, and the change of the latter with composition in the dilute region (limiting slope). For a preliminary examination of the present results consideration is confined to dilute regions. A compilation of the data for both ends of the mole-fraction scale is given in Table 3. Partial molar
volumes
Values of V, - V;” ( = V,“) for the dialkylacetamides are represented in Fig. 2. They are slightly negative for DMA and DEA, and positive for DBuA and DPeA. The curves for DPrA, DBuA and DPeA show maxima at x1 = 0.66, 0.93 and 0.96, respectively, so that in all cases negative slopes of VzE occur at x1 = 1. Not visible are shallow extrema in VzE for DBuA and DPeA between x1 = 0.10 and x1 = 0.25. Values of VzE at infinite dilution, V,“.“, increase with nearly equal increments from VIE., = -0.39 cm3 mol-’ for DEA to V,“,” = + 0.70 cm3 mol-’ for DPeA. The value for DMA, v2E+ = -0.06 cm3 mol-‘, deviates from this regularity. The partial molar volumes of DMF (see Fig. 3) differ only slightly from V,* in mixtures with DMA, DEA and DPrA. The differences are larger in mixtures with DBuA and DPeA. In these mixtures two characteristic extrema in V, are found, in the region 0.10 < x, < 0.25. Shallow minima are present in the curves for mixtures with DPrA, DBuA and DPeA, at x, = 0.66,
1.1860 4.8357 5.0372 5.7954 6.2970
;;’
a 93.12 127.97 162.01 195.95 229.56 mol-‘.
G* (cm3 mol- ‘)
b C;, =148.36 J K-’
77.43 77.20 77.60 78.00 78.34
DMA DEA DPrA DBuA DPeA
a V* = 77.49 cm3 mol-‘. 1
V? (cm3 mol-‘)
Acetamide
- 0.2170 0.9678 1.2359 1.6733
(J K mol-‘)
a2
0.01225 - 0.04580 0.00951 - 0.06743
a2 (cm3 mol-‘)
mol-‘)
0.8087 1.3503 0.8507
(J K-’
a3
- 0.07827 0.34056
a3 (cm3 mol-‘)
of fit for excess molar volumes
93.06 127.58 161.98 196.26 230.25
vz” (cm3 mol-‘)
a4
0.7806 1.4978
149.50 151.76 152.27 152.72 152.83
mol-‘)
b
a5
c;2
175.15 240.60 299.87 360.23 418.23
(J K-’
mol-‘)
mol-‘)
1.1314
(J K-’
acetamides
(J K-’ mol-‘)
- 0.45505
(cm3 molt ‘)
- 0.07958 0.03719
a5
(cm3 mol-‘)
of DMF with
mol-‘)
176.40 246.50 308.20 371.40 432.29
C” (f&l
mol-‘)
1.7x10~2 1.7x10~2 2.1 x 1o-2 1.4.X1o-2 1.5x10-*
(J K-’
6
6.0~10-~ 6.0 x 1O-4 1.3x 1o-3 l.ox10~3 1.2x10p3
(cm3 mol-‘)
6
of mixtures
a4
and excess molar heat capacities
of disubstituted C”P.1 (J K-’
in mixtures of DMF with a number
mol-‘)
1.2347 1.6331 1.9565 3.0669
K-’
0.05638 - 0.07942 0.00018 0.05731
a1 (cm3 mol-‘)
Partial molar volumes and heat capacities
TABLE 3
DMA DEA DPrA DBuA DPeA
a,
Acetamide
mo]-‘)
- 0.05517 - 0.32538 0.08001 0.47922 0.84154
DMA DEA DPrA DBuA DPeA
(J K-’
a, (cm3 mol-‘)
Acetamide
Coefficients of eqn. (5) and standard deviations several disubstituted acetamides at 298.15 K
TABLE 2
g
309
0.93 and 0.96, respectively, but these are hardly visible in the figure. The limiting slope of VI at x, = 0 decreases from positive values in DMA and DEA to negative ones in DBuA and DPeA. The values of V, at infinite dilution, Vim, change gradually from 77.20 cm3 mol-’ in DEA to 78.34 cm3 mol-’ in DPeA. Vim in DMA (77.43 cm3 mol- ‘) deviates from this trend. The deviating values of VIE.” for DMA and of V,* in DMA may be due to a relatively more efficient packing of DMA molecules in the pure liquid, as indicated by the ratio of the Van der Waals volumes (Bondi, 1964) and VI*. For DEA, DPrA, DBuA and DPeA, this ratio amounts to 0.6004, 0.6006, 0.6010 and 0.6021. The ratio for DMA (0.6055) is significantly larger. Partial molar heat capacities in mixtures with Values of Cp,2 - CpT,( = c;z, for all dialkylacetamides DMF are positive. As Fig. 5 shows, the Czl values increase steadily with increasing x1 towards a maximal value at X, = 1. Up to x1 = 0.75 the values for DEA, DPrA, DBuA and DPeA are nearly the same, and differences emerge only at higher x1. At infinite dilution, CpyiX ranges from 1.3 J K-r mol-’ for DMA to 14.1 J K”’ mol-’ for DPeA. The mean CH, increment in C,“;” is 1.6 + 0.4 J K-’ mol-r. For n-alkanols dissolved in DMF (Zegers and Somsen, 1984), C”yi” is always negative with a mean CH, increment of - 1.0 _t 0.4 J K-’ mol-‘. Such differences between two classes of compounds do not seem to occur in water. From the results of Nichols et al. (1976) and Shaw (1969), it can be concluded that the CH, increment in CEim is positive and constant at + 59 J K-r mol-l for a variety of organic compounds. This is probably due to the dominating influence of hydrophobic hydration in dilute aqueous systems. The partial molar heat capacities Cp,r of DMF all exceed Cp*, and increase with decreasing x,. In mixtures with the larger amides the values of Cpy, tend to level off around a value of 153 J K-’ mol-‘. The apparent molar heat capacities Cp.,,,+ and Cp,2,+ appear to be linear functions of the volume fractions in the mixtures defined by G, = 0L+,Y
(7)
+ -%v,)
Since C:, .+ = C/l?, and Cps;.+ = Cpy,, this means for component Cp,~,+ = cp”T~+ For component XICP:, + x&p
2 a similar equation
From eqns. (7)-(9), Cp.2.0
=
cz2
+
that (8)
92CpFi”
.2 . + =
1 (DMF)
XICp,l.qI
+
x2CpT2
applies. Also, (9)
it follows that
+lc~i”v2/v~
(W
310 TABLE
4
Values of Cp:(30/V,* for mixtures Acetamide
c;v: (J K-’ 0.0147 0.0439 0.0504 0.0562 0.0577
DMA DEA DPrA DBuA DPeA
Combination Cp,2.ql=
cme3)
CL2
of DMF with disubstituted CF;“/’ v; (JK-‘cm 0.0135 0.0460 0.051s 0.0570 0.0612
-3 )
acetamides
YJ K-’
cmp3)
0.014 0.045 0.051 0.057 0.060
with +
+,c,‘:;-
01)
gives
For the present mixtures V, and V, do not differ very much from VI* and V2*, so that Cpy;S/v* = u will also be a constant for each mixture. Table 4 shows that this is indeed a good approximation. The values of u can be used to calculate partial molar heat capacities according to
cp,;= c;, + (1
- +,)2q*0
(13)
The calculated values of CP., and CpT2 are in close agreement with those represented by the curves in Figs. 5 and 6. The magnitude of u tends to a constant value with increasing V,*. This behaviour parallels the observation that C’y values in the larger amides level off at 153 J K“ mol-‘. The linear dependence of the apparent molar hear capacities on volume fraction suggests that in the present mixtures preferential solvation effects are not present. The interactions between the molecules seem to be determined predominantly by their size ratio. Hence the temperature dependence of the different molecular interaction energies in the mixtures seems to be the same, and in this sense these aprotic dipolar mixtures may be regarded as suitable reference mixtures for other polar binary systems. REFERENCES Benson, SW., 1978. Heat capacity and structure in liquids: application to the structure water. J. Am. Chem. Sot., 100: 5640-5644. Bhattacharyya, S.M. and Patterson, D., 1979. Excess heat capacities of cyclohexane+alkane systems and orientational order of n-alkanes. J. Phys. Chem., 83: 2979-2985.
of
311
Bhattacharyya, S.N. and Patterson, D., 1980. Excess heat capacities and orientational order in systems containing hexadecane isomers of different molecular structure. J. Solut. Chem., 9: 247-258. Bondi, A., 1964. Van der Waals volumes and radii. J. Phys. Chem., 68: 441-451. Chute, W.J., Nunn, G.E., MacKenzie, J.C., Myers, G.S., Smart, G.N.R., Suggit, J.W. and Wright, G.F., 1948. Catalyzed nitration of amines. 111. The ease of nitration among aliphatic secondary amines. Can. J. Res., 26B: 114-137. Croucher. M.D. and Patterson, D., 1974. Thermodynamic effects of orientational order in chain-molecule mixtures. Part 2. Temperature-dependence of heats of mixing of branched and normal alkane mixtures. J. Chem. Sot., Faraday Trans. 2, 70: 1479- 1487. Croucher, M.D. and Patterson, D., 1975. Thermodynamic effects of orientational order in chain-molecule mixtures. Part 3. Heats of mixing of dimethylsiloxanes with normal and branched alkanes. J. Chem. Sot., Faraday Trans. 2, 71: 985-996. De Visser, C. and Somsen, G., 1979. Thermochemical behaviour of mixtures of N, N-dimethylformamide with dimethylsulfoxide, acetonitrile, and N-methylformamide: volumes and heat capacities. J. Solut. Chem., 8: 593-600. De Visser, C., Perron, G., Desnoyers, J.E., Heuvelsland, W.J.M. and Somsen, G., 1977. Volumes and heat capacities of mixtures of N,N-dimethylformamide and water at 298.15 K. J. Chem. Eng. Data, 22: 74-79. De Visser, C., Heuvelsland, W.J.M., Dunn, L.A. and Somsen, G., 1978. Some properties of binary aqueous liquid mixtures: apparent molar volumes and heat capacities at 298.15 K over the whole mole fraction range. J. Chem. Sot., Faraday Trans. 1, 74: 1159-1168. Fein, M.L. and Fisher, C.H., 1944. Acetylation of alkyl lactates: methyl and ethyl aacetoxypropionates. Ind. Eng. Chem., 36: 235-238. Giaquinto, A.R., Lindstrom, R.E., Swarbrick, J. and Lo-Surdo, A., 1977. Amide-water interactions in cosolvent systems. 1. Solubilities and apparent molar volumes of methyl paraben. J. Solut. Chem., 6: 687-701. Kell, G.S., 1967. Precise representation of volume properties of water at one atmosphere. J. Chem. Eng. Data, 12: 66-69. Lam, V.T., Picker, P., Patterson, D. and Tan&de, P., 1974. Thermodynamic effects of orientational order in chain-molecule mixtures. Part 1. Heats of mixing of globular and normal alkanes. J. Chem. Sot., Faraday Trans. 2, 70: 1465-1478. Mirejovsky, D. and Arnett, E.M., 1983. Heat capacities of solution for alcohols in polar solvents and the new view of hydrophobic effects. J. Am. Chem. Sot.. 105: 1112-1117. Nichols, N., Skiild, R., Spink, C., Suurkuusk, J. and Wads& I., 1976. Additivity relations for the heat capacities of non-electrolytes in aqueous solution. J. Chem. Thermodyn., 8: 1081-1093. Robson, J.H. and Reinhart, J., 1955. The infrared spectra of N-substituted trifluoroacetamides. J. Am. Chem. Sot., 77: 498-499. Shaw, R., 1969. Heat capacity of liquids: estimation of heat capacity at constant pressure and 25 ‘C, using additivity rules, J. Chem. Eng. Data, 14: 461-465. Verhoef, J.C. and Barendrecht, E., 1977. Mechanism and reaction rate of the Karl Fisher titration reaction. Part V. Analytical implications. Anal. Chim. Acta, 94: 395-403. Zegers, H.C. and Somsen, G., 1984. Partial molar volumes and heat capacities in (dimethylformamide+ n-alkanols). J. Chem. Thermodyn., 16: 225-235.
299 -
Printed
in The Netherlands
VOLUMES AND HEAT CAPACITIES OF MIXTURES OF DIMETHYLFORMAMIDE WITH SEVERAL DIALKYLACETAMIDES H.C. ZEGERS Department Netherlands) (Received
and G. SOMSEN of Chemistry,
February
Free
* University>
1, 1984; accepted
June
De Boelelaan
lOH3,
1081
H V Amsterdum
(The
25, 1984)
ABSTRACT Zegers, H.C. and Somsen, G., 1984. Volumes and heat capacities of mixtures of dimethylformamide with several dialkylacetamides. Fluid Phase Equilihriu, 18: 299-311.
and
Densities a series
and heat capacities per of di-n-alkylacetamides
unit volume of binary mixtures of dimethylformamide have been measured and converted into excess molar
volumes and heat capacities of the mixtures. In addition, the apparent and partial molar volumes and heat capacities of the various components have been evaluated. They vary smoothly with the mole fraction. The apparent molar heat capacities in the mixtures depend linearly on volume fraction, so that the partial molar heat capacities can be described using only one parameter for each mixture.
INTRODUCTION
As (higher) derivatives of the Gibbs energy, the heat capacities, volumes, expansivities and compressibilities of liquid solutions and mixtures show sensitivity to structural influences. This is illustrated by the importance of the heat capacity in recognizing a hydrophobic solute in water (Benson, 1978; Mirejovsky and Arnett, 1983). Also, Patterson and his group (Lam et al., 1974; Croucher and Patterson, 1974, 1975; Bhattacharyya and Patterson, 1979, 1980) have pointed out that even apparently simple mixtures, such as those of the alkanes, show local ordering of molecular orientations resulting in negative contributions to the excess heat capacity. If heat capacities are to be used as an indication of possible structural influences of solutes on solvents, it would be desirable to know the heat-capacity behaviour of solutes in a variety of solvents where structural influences will differ. Since we are interested in mixtures of polar compounds, we present in this paper the volumes and heat capacities of a number of aprotic solvent * Author
to whom
0378-3812/X4/$03.00
correspondence
should
0 1984 Elsevier
be addressed.
Science
Publishers
B.V.
300
mixtures in which structural influences are expected to be small. We have previously studied mixtures of N, N-dimethylformamide (DMF) with water (de Visser et al,, 1977), with dimethylsulphoxide, acetonitrile and N-methylformamide (de Visser and Somsen, 1979), and with a series of n-alkanols (Zegers and Somsen, 1984). Here we present results for mixtures of DMF with a series of aprotic dialkylacetamides, i.e., N, N-dimethylacetamide (DMA), N, N-diethylacetamide (DEA), N, N-di-n-propylacetamide (DPrA), N, N-di-n-butylacetamide (DBuA) and N, N-di-n-pentylacetamide (DPeA). EXPERIMENTAL
Materials
DMF (Baker, analyzed reagent), DMA (Aldrich, spectrophotometric grade) and DEA (Aldrich) were stored over molecular sieves (4 A) for at least one week and used without further purification. DPrA, DBuA and DPeA were synthesized (Chute et al., 1948; Robson and Reinhart, 1955) according to the reaction CH,COOH
+ RR’NH + CH,CONRR’
+ H,O
where R(R’) denotes an alkyl group. This reaction was made quantitative by adding acetic anhydride to the reaction mixture. Acetic acid and acetic anhydride were removed by azeotropic distillation with methylcyclohexane (Fein and Fisher, 1944). The dialkylacetamides were purified by azeotropic distillation with benzene (to remove the last traces of water and acetic acid) followed by fractional distillation under reduced pressure. The middle fraction was taken and stored over molecular sieves (4 A). The water contents of all compounds were determined by the modified Karl Fischer procedure of Verhoef and Barendrecht (1977). In all cases the volume fraction of water was less than 0.0001. Gas-liquid chromatography showed a mole-fraction purity of 0.995 or higher for each compound. Procedure
Liquid mixtures of DMF and the various dialkylacetamides were prepared by mass. Details of the procedure have been described previously (Zegers and Somsen, 1984). The usual precautions were taken to exclude water during all manipulations. The densities of the mixtures relative to the density of pure DMF were measured using a digital flow densimeter (Sodev, Model 03D, Sherbrooke, Quebec). Molar heat capacities were obtained from heat capacities per unit volume ( C,/ V) measured using a Picker flow microcalorimeter (Setaram, Model “chaleur specifique”, Lyon, France). The pro-
301
cedure was as reported previously (Zegers and Somsen, 1984) but modified in one respect. The microcalorimeter was fed from vials placed in closed boxes filled with nitrogen under pressure. For all mixtures a constant flow rate through the calorimeter cell was achieved by adjustment of the nitrogen pressure. The pressure needed to maintain a flow of - 0.010 cm3 SC’ never exceeded 0.6 bar. This modification makes the microcalorimeter more suitable for measuring rather viscous liquids such as DBuA and DPeA, and it avoids the use of pumps, which can be problematic with organic solvents. Measurements on mixtures with and without this modification gave the same results. RESULTS
Volumes
Densities d of the binary mixtures at 298.15 K relative to that of pure DMF (d,) are presented in Table 1 as function of the mole fraction x1 of DMF. The density of pure DMF as measured with respect to pure water (Kell, 1967) is 0.943289 g cme3 at 298.15 K, corresponding to a molar volume VI* = 77.489 cm3 mol-‘. The molar volumes of the pure dialkylacetamides DMA, DEA and DPrA, respectively V1*= 93.117, 127.972 and 162.012 cm3 mol-‘, compare reasonably with literature data. In our laboratory we found previously for DMA V,* = 93.07 cm3 mol-’ (de Visser et al., 1978), whereas Giaquinto et al. (1977) reported for DMA, DEA and DPrA, respectively, V, * = 92 .996, 127.831 and 161.83 cm mol-‘. The molar volumes of DBuA and DPeA are 195.948 and 229.555 cm3 mol-’ and have not been reported earlier. From the experimental densities the molar excess volumes of the mixtures can be calculated from v~=n,M,(d-‘-d,l)+x,M,rd-‘-di’) where M,, component ered here component
(1)
d, and
x, are the molar mass, density and mole fraction of i, with i = 1, 2. Smoothed values of V,” for the mixtures considare represented in Fig. 1. The apparent molar volumes y,, of i are obtained from
q/i,+ = K* + Q/Xi
(2)
For the present mixtures both V,,, and Vz.+ are smooth functions of X, and were used to calculate the partial molar volumes V, of the components according to vi = Y,+ + XIX2(W,,/ax,
I,.,-
(3)
TABLE
1
Experimental at 298.15 K X1
relative densities d - d, and changes in heat capacity per unit volume A(C,/V)
103(&d,) (g cm-‘)
Dimethylformamide
103A(CP/V) (J K-’ cmP3) (1) -I- dimethylacetamide
X,
103A( C,,‘V) (J K-’ cm-3)
0.54997
- 3.652
- 13.010
~ -
3.199 2.824 2.447 1.943 1.537 1.153 0.973
- 11.049
-0.819 - 0.368 - 0.310 0.000
- 2.386 - 1.109 - 0.802 0.000
- 6.760
0.00000
- 7.666
0.03514 0.04613 0.04941
- 7.425 - 7.341 -7.317
- 32.428 - 31.773 - 31.721
0.60887 0.65569 0.70389
0.11794 0.15054 0.19746 0.25214 0.30341 0.37263
-
-
0.76695 0.81647 0.86361 0.88454 0.90351 0.95678
28.907 27.544 25.503 23.274 21.742 18.968
- 17.406 0.39961 - 4.778 - 16.039 0.45657 - 4.353 - 14.059 0.51288 - 3.945 Dimethylformumide (I) + diethylucetamide
d,)
(2)
- 33.676
6.835 6.604 6.278 5.882 5.498 4.983
lO”(d(gem-‘)
0.96350 1 .ooooo
-
9.420 7.798 6.161 4.867 3.314 2.742
(2)
0.00000
- 43.272
- 34.494
0.53143
0.03361
-42.313
- 32.703
0.58694
- 24.903 - 22.499
0.05030 0.08421
-41.829 - 40.830
- 31.957 - 29.774
0.67928 0.69712
-18.211 - 17.341
0.10911 0.15233 0.19661
- 40.079 - 38.742 - 37.331
- 28.823 - 26.543 - 24.210
0.76747 0.79321 0.83373
.- 13.765
0.25816 0.29865
- 35.284 - 33.895
- 20.527 - 18.315
0.89494 0.92132
0.33867 0.40390 0.45067
- 32.452 - 30.044 - 28.214
- 15.977 - 13.150 - 10.465
0.94651 0.96700 1 .ooooo
- 8.470 0.49250 - 26.548 Dimethylformamide (1) + di -n-propyfacetamide - 63.720 0.00000 - 59.213 - 62.169 0.02940 - 58.385
(2) 0.55058 0.59849
- 12.390 -- 10.166 -6.618 - 5.031 - 3.470 - 2.160 0.000
- 37.466 - 34.712
- 4.608 - 1.244 - 0.722 0.846 1.333 1.493 1.595 1.315 7.137 0.858 0.000
- 29.711
- 32.072 - 28.085
- 25.849 - 22.615 - 18.403
0.80309 0.84916
- 24.301 - 20.085 - 16.037
- 14.358 - 10.438 - 7.306
- 48.723 - 46.351
0.90171 0.92657
- 10.973 - 8.400
- 47.229 - 44.835
- 42.895 - 39.567
0.95602 0.97207
- 5.180 - 3.347
- 4.235 - 2.679 - 1.522
0.45342
- 42.539
- 36.408
1.00000
0.000
0.51425
- 39.463
- 31.740
0.06081 0.06326 0.09288
- 57.471 - 57.400 - 56.502
- 60.546 - 60.320 - 58.826
0.64058 0.69942 0.75094
0.15254 0.20992
- 54.616 - 52.645
- 55.372 -51.917
0.25632 0.29606
- 50.961 - 49.432
0.35009 0.40537
- 0.839 0.000
303
Xl
103(d-
d,)
Dimethylformamide
0.00000 0.02951 0.04911 0.07488 0.07783 0.09880 0.12222 0.12989
xl
cm-‘)
10Z'(d-
d,)
103A(Cp/V)
(g cm-‘)
(J Km’ cmP3)
- 54.485 - 53.657
- 51.455 - 50.406 - 45.773 -41.911
(I) + di -n- butylacetamide (2)
- 69.153 - 68.397 - 67.876 -67.166 - 67.085 - 66.483
0.13737 0.14989
-
0.17232 0.20560
- 64.247 - 63.146
0.24477 0.25483 0.28863
- 61.772 -61.417 - 60.137 - 59.681 - 58.011
0.30050 0.34140
103Uc,,/V)
(J IV’
(gcme3)
65.794 65.562 65.339 64.951
- 76.219 - 74.794 - 73.820 - 72.468
0.41983 0.43648 0.49958 0.54832
-
72.305 71.216 69.897 69.542 69.192 68.457
0.60346 0.65069 0.70013 0.74380 0.80773 0.83836
-
- 67.197
0.85305 0.87052 0.90146
- 2.1.516 - 19.374 - 15.361
0.90270 0.92642 0.93058 0.95533
- 15.193 -11.861 - Il.257 - 7.490
- 11.312 - 8.129 - 8.087 - 5.623 - 5.426 - 3.171
0.96823 56.787 0.97601 53.441 52.905 1 .ooooo pent_placetamide (2)
- 5.427 - 4.141
- 2.118 - 1.583
0.000
0.000
- 57.260 - 54.416 - so.939
- 61.582 - 57.015
-
- 47.233 - 40.756
-
0.34480 - 57.865 0.39044 - 55.866 0.40147 - 55.334 Dimethylformamide (I) t di -n-
65.415 63.148 62.474 60.550 59.613 56.952
0.00000 0.02693
- 74.917 - 74.306
- 92.681 - 91.461
0.49938 0.54818
0.04711 0.06887 0.08105
- 73.824 - 73.287 - 72.977
- 90.546 - 89.474 - 88.882
0.60166 0.64841 0.70454
0.10277 0.13559 0.17145 0.21332
-
72.408 71.501 70.475 69.199
-
87.770 86.039 84.145 81.817
0.75383 0.79774 0.84076 0.87531
0.25175 0.29912 0.35405 0.39571 0.44609
-
67.948 66.280 64.152 62.364 60.032
-
79.489 76.703 73.016 70.057 66.043
0.90658 0.92893 0.96062 0.97818 1 .ooooo
50.350 47.529 43.994 40.640 36.743 32.947 26.640 23.233
47.513 42.856 38.144 :33.339 28.001 23.162
- 37.207 - 33.012 - 28.185 - 24.122 - 17.729 - 14.875 - 13.111
-- 51.959
---
34.375 28.380 22.615 17.626
- 18.277
- 12.652
- 14.443 -~ 8.464 -- 4.842 0.000
- 9.188 - 4.829 - 2.569 0.000
Values of 1/,+ and ( SV,.+P/SX,)~.~ were obtained by the local fitting procedure reported previously (Zegers and Somsen, 1984). This procedure allows calculation of the partial molar quantities without being dependent on the suitability of a particular analytical expression, such as the Redlich-Kister equation, for representing the excess quantities. The resulting partial molar volumes are shown in Figs. 2 and 3.
304
Heat
capacities
Changes in the heat capacities per unit volume with respect DMF, A( C,/V) = C,/V - C,T,/VI*, are also reported in Table 1. refer to a mean temperature of 298.15 ~frO.-l K. Adopting C,T,/V,* K-’ cm- 3 for DMF (Zegers and Somsen, 1984), we found for the
Fig. 1. Smoothed dialkylacetarnides.
excess molar volumes for mixtures
of dimethylformamide
to that of The results = 1.9146 J molar heat
with a series of
+0.6 L
-0.2
\( I
0.0
0.2
0.6
0.4
DEA I
0.8
1.0
Xl Fig. 2. Excess mamide.
partial
molar
volumes
of dialkylacetamides
in mixtures
with dimethylfor-
305
capacities of the pure compounds DMA, DEA, DPrA, DBuA and DPeA, c * = 175.15, 240.60, 299.87, 360.23 and 418.23 J K-’ mol-‘, respectively. O?ihese values, only the molar heat capacity of DMA can be compared with the value of 178.2 J K-’ mol-’ obtained earlier in our laboratory (de Visser et al., 1977). However, this value resulted from a different and less precise experimental procedure (static calorimetry) and its calculation was hampered by the fact that no precise densities of DMA at temperatures other than
Fig. 3. Partial molar volumes of dimethylformamide
0.0
0.2
Fig. 4. Smoothed excess series of dialkylacetamides.
0.4
0.6
0.8
Xl molar heat capacities
in mixtures with some dialkylacetamides.
1.0 for mixtures
of dimethylformamide
with a
305
298.15 K were available. Since the CP:l values for n-alkanols obtained by flow calorimetry in our previous paper (Zegers and Somsen, 1984) agreed excellently with literature data, we feel that the present value of CP,Tzfor DMA should be preferred. Excess molar heat capacities for the mixtures considered were calculated according to
and are represented
in Fig. 4. Apparent
and partial
molar heat capacities
of
IO 7
0 E -iY
-5 wd
6
0
0.0
0.2
0.4
0.6
0.8
Fig. 5. Excess partial molar heat capacities mamide.
I
0.0
I
0.2
I
1
I
0.4
I
0.6
I
1.0
of dialkylacetamides
I
0.8
in mixtures
with dimethylfor-
I
1.0
9 Fig.
6. Partial
kylacetamides.
molar
heat
capacities
of dimethylformamide
in mixtures
with
some
dial-
307
the components in the mixtures can be calculated following the same procedure as applied for the volumes. The partial molar heat capacities are shown in Figs. 5 and 6. DISCUSSION
The molar excess volumes and heat capacities here can be described by the equation ,I -
Y,E=x,x*
c
of the mixtures
considered
1
a,(x, -x2)l
(5)
r=O
The coefficients a, in this equation, the fit 8, defined by
S2= C, [ Y,E(exp.) - Y,“(calc.)12/(
together
with the standard
deviation
of
N - n)
where N denotes the number of experimental points, are presented in Table 2. All experimental values were weighted equally. The values of a certain partial molar quantity for a compound in a mixture are often determined largely by the value for the pure compound, that at infinite dilution in the other compound, and the change of the latter with composition in the dilute region (limiting slope). For a preliminary examination of the present results consideration is confined to dilute regions. A compilation of the data for both ends of the mole-fraction scale is given in Table 3. Partial molar
volumes
Values of V, - V;” ( = V,“) for the dialkylacetamides are represented in Fig. 2. They are slightly negative for DMA and DEA, and positive for DBuA and DPeA. The curves for DPrA, DBuA and DPeA show maxima at x1 = 0.66, 0.93 and 0.96, respectively, so that in all cases negative slopes of VzE occur at x1 = 1. Not visible are shallow extrema in VzE for DBuA and DPeA between x1 = 0.10 and x1 = 0.25. Values of VzE at infinite dilution, V,“.“, increase with nearly equal increments from VIE., = -0.39 cm3 mol-’ for DEA to V,“,” = + 0.70 cm3 mol-’ for DPeA. The value for DMA, v2E+ = -0.06 cm3 mol-‘, deviates from this regularity. The partial molar volumes of DMF (see Fig. 3) differ only slightly from V,* in mixtures with DMA, DEA and DPrA. The differences are larger in mixtures with DBuA and DPeA. In these mixtures two characteristic extrema in V, are found, in the region 0.10 < x, < 0.25. Shallow minima are present in the curves for mixtures with DPrA, DBuA and DPeA, at x, = 0.66,
1.1860 4.8357 5.0372 5.7954 6.2970
;;’
a 93.12 127.97 162.01 195.95 229.56 mol-‘.
G* (cm3 mol- ‘)
b C;, =148.36 J K-’
77.43 77.20 77.60 78.00 78.34
DMA DEA DPrA DBuA DPeA
a V* = 77.49 cm3 mol-‘. 1
V? (cm3 mol-‘)
Acetamide
- 0.2170 0.9678 1.2359 1.6733
(J K mol-‘)
a2
0.01225 - 0.04580 0.00951 - 0.06743
a2 (cm3 mol-‘)
mol-‘)
0.8087 1.3503 0.8507
(J K-’
a3
- 0.07827 0.34056
a3 (cm3 mol-‘)
of fit for excess molar volumes
93.06 127.58 161.98 196.26 230.25
vz” (cm3 mol-‘)
a4
0.7806 1.4978
149.50 151.76 152.27 152.72 152.83
mol-‘)
b
a5
c;2
175.15 240.60 299.87 360.23 418.23
(J K-’
mol-‘)
mol-‘)
1.1314
(J K-’
acetamides
(J K-’ mol-‘)
- 0.45505
(cm3 molt ‘)
- 0.07958 0.03719
a5
(cm3 mol-‘)
of DMF with
mol-‘)
176.40 246.50 308.20 371.40 432.29
C” (f&l
mol-‘)
1.7x10~2 1.7x10~2 2.1 x 1o-2 1.4.X1o-2 1.5x10-*
(J K-’
6
6.0~10-~ 6.0 x 1O-4 1.3x 1o-3 l.ox10~3 1.2x10p3
(cm3 mol-‘)
6
of mixtures
a4
and excess molar heat capacities
of disubstituted C”P.1 (J K-’
in mixtures of DMF with a number
mol-‘)
1.2347 1.6331 1.9565 3.0669
K-’
0.05638 - 0.07942 0.00018 0.05731
a1 (cm3 mol-‘)
Partial molar volumes and heat capacities
TABLE 3
DMA DEA DPrA DBuA DPeA
a,
Acetamide
mo]-‘)
- 0.05517 - 0.32538 0.08001 0.47922 0.84154
DMA DEA DPrA DBuA DPeA
(J K-’
a, (cm3 mol-‘)
Acetamide
Coefficients of eqn. (5) and standard deviations several disubstituted acetamides at 298.15 K
TABLE 2
g
309
0.93 and 0.96, respectively, but these are hardly visible in the figure. The limiting slope of VI at x, = 0 decreases from positive values in DMA and DEA to negative ones in DBuA and DPeA. The values of V, at infinite dilution, Vim, change gradually from 77.20 cm3 mol-’ in DEA to 78.34 cm3 mol-’ in DPeA. Vim in DMA (77.43 cm3 mol- ‘) deviates from this trend. The deviating values of VIE.” for DMA and of V,* in DMA may be due to a relatively more efficient packing of DMA molecules in the pure liquid, as indicated by the ratio of the Van der Waals volumes (Bondi, 1964) and VI*. For DEA, DPrA, DBuA and DPeA, this ratio amounts to 0.6004, 0.6006, 0.6010 and 0.6021. The ratio for DMA (0.6055) is significantly larger. Partial molar heat capacities in mixtures with Values of Cp,2 - CpT,( = c;z, for all dialkylacetamides DMF are positive. As Fig. 5 shows, the Czl values increase steadily with increasing x1 towards a maximal value at X, = 1. Up to x1 = 0.75 the values for DEA, DPrA, DBuA and DPeA are nearly the same, and differences emerge only at higher x1. At infinite dilution, CpyiX ranges from 1.3 J K-r mol-’ for DMA to 14.1 J K”’ mol-’ for DPeA. The mean CH, increment in C,“;” is 1.6 + 0.4 J K-’ mol-r. For n-alkanols dissolved in DMF (Zegers and Somsen, 1984), C”yi” is always negative with a mean CH, increment of - 1.0 _t 0.4 J K-’ mol-‘. Such differences between two classes of compounds do not seem to occur in water. From the results of Nichols et al. (1976) and Shaw (1969), it can be concluded that the CH, increment in CEim is positive and constant at + 59 J K-r mol-l for a variety of organic compounds. This is probably due to the dominating influence of hydrophobic hydration in dilute aqueous systems. The partial molar heat capacities Cp,r of DMF all exceed Cp*, and increase with decreasing x,. In mixtures with the larger amides the values of Cpy, tend to level off around a value of 153 J K-’ mol-‘. The apparent molar heat capacities Cp.,,,+ and Cp,2,+ appear to be linear functions of the volume fractions in the mixtures defined by G, = 0L+,Y
(7)
+ -%v,)
Since C:, .+ = C/l?, and Cps;.+ = Cpy,, this means for component Cp,~,+ = cp”T~+ For component XICP:, + x&p
2 a similar equation
From eqns. (7)-(9), Cp.2.0
=
cz2
+
that (8)
92CpFi”
.2 . + =
1 (DMF)
XICp,l.qI
+
x2CpT2
applies. Also, (9)
it follows that
+lc~i”v2/v~
(W
310 TABLE
4
Values of Cp:(30/V,* for mixtures Acetamide
c;v: (J K-’ 0.0147 0.0439 0.0504 0.0562 0.0577
DMA DEA DPrA DBuA DPeA
Combination Cp,2.ql=
cme3)
CL2
of DMF with disubstituted CF;“/’ v; (JK-‘cm 0.0135 0.0460 0.051s 0.0570 0.0612
-3 )
acetamides
YJ K-’
cmp3)
0.014 0.045 0.051 0.057 0.060
with +
+,c,‘:;-
01)
gives
For the present mixtures V, and V, do not differ very much from VI* and V2*, so that Cpy;S/v* = u will also be a constant for each mixture. Table 4 shows that this is indeed a good approximation. The values of u can be used to calculate partial molar heat capacities according to
cp,;= c;, + (1
- +,)2q*0
(13)
The calculated values of CP., and CpT2 are in close agreement with those represented by the curves in Figs. 5 and 6. The magnitude of u tends to a constant value with increasing V,*. This behaviour parallels the observation that C’y values in the larger amides level off at 153 J K“ mol-‘. The linear dependence of the apparent molar hear capacities on volume fraction suggests that in the present mixtures preferential solvation effects are not present. The interactions between the molecules seem to be determined predominantly by their size ratio. Hence the temperature dependence of the different molecular interaction energies in the mixtures seems to be the same, and in this sense these aprotic dipolar mixtures may be regarded as suitable reference mixtures for other polar binary systems. REFERENCES Benson, SW., 1978. Heat capacity and structure in liquids: application to the structure water. J. Am. Chem. Sot., 100: 5640-5644. Bhattacharyya, S.M. and Patterson, D., 1979. Excess heat capacities of cyclohexane+alkane systems and orientational order of n-alkanes. J. Phys. Chem., 83: 2979-2985.
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