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A simple method for determining the neutralization point in Boehm titration regardless of the CO2 effect
CARBON
5 0 ( 2 0 1 2 ) 3 3 1 5 –3 3 2 3
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A simple method for determining the neutralization point in Boehm titration regardless of the CO2 effect Yern Seung Kim, Seung Jae Yang, Hyeong Jun Lim, Taehoon Kim, Chong Rae Park
*
Carbon Nanomaterials Design Laboratory, Global Research Laboratory, Research Institute of Advanced Materials, and Department of Materials Science and Engineering, Seoul National University, Seoul 151-744, Republic of Korea
A R T I C L E I N F O
A B S T R A C T
Article history:
We report a simple method by which the neutralization point in the Boehm titration can be
Received 23 November 2011
easily determined without going through a pre-screening process to remove the effect of
Accepted 15 December 2011
atmospheric carbon dioxide (CO2). The proposed method is based on the principle that
Available online 24 December 2011
the equivalence and the corresponding neutralization point of the reaction bases remains unchanged regardless of the dissolution of CO2 in the reaction bases. This method was used to measure the surface functionality of acid-treated multi-walled carbon nanotubes with high precision. 2011 Elsevier Ltd. All rights reserved.
1.
Introduction
The Boehm titration has been generally adopted to characterize [1–14] and analyze the reactivity [15–17] of the surface functionality of various carbonaceous materials. In the method, three reaction bases with different basicities, such as sodium hydroxide (NaOH), sodium carbonate (Na2CO3) and sodium bicarbonate (NaHCO3), have been used to discern the kinds and amounts of surface functionalities among carboxylic, lactonic, and phenolic groups [1]. The amount of a specific surface functionality is calculated from the neutralization point usually determined as the point at pH 7 in the Boehm titration curve corresponding to a specific base [7,10,11]. However, the neutralization point as judged at pH 7 does not always mean a precise equivalence of the given surface functionality because of the effect of atmospheric carbon dioxide (CO2) that dissolves easily into the reaction base during the filtration of the carbonaceous samples or the titration process. In fact, when atmospheric CO2 dissolves into aqueous solution, it becomes carbonic acid (H2CO3), which is a weak acid [11,18]. The presence of H2CO3 in the reaction base has been known to distort the titration curve and make it
difficult to get an exact neutralization point from the curve, hence, the exact amount of a specific surface functionality, which is defined as the CO2 effect. To remove the CO2 as completely as possible, the reaction base has to be acidified [1,10,11] since CO2 is driven out from the solution by acidic conditions with additional processes such as heating [1,10,11] or degasification with an inert gas [11]. To prevent the dissolution of CO2 into the reaction base during titration, sealing, degasification of the reaction base with an inert gas [11,13], and titration in an N2 gas filled glove box [14] have been adopted. However, the introduction of these CO2 removal processes makes the Boehm titration complicated and inaccessible, although the Boehm titration method is an easier method for the determination of the surface functionality of carbonaceous materials than the direct titration method [19–21] whereby rather complicated analysis tools should be used. Having considered this situation, in this study, we tried to find a much easier method for determining the neutralization point in the Boehm titration, which does not need any additional processes to remove the CO2 effect from the titration process. To achieve this goal, the dissolution behavior of CO2 into each reaction base, and hence its influence on the
* Corresponding author: Fax: +82 2 885 1748. E-mail address: [email protected] (C.R. Park). 0008-6223/$ - see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2011.12.030
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CARBON
5 0 ( 2 0 1 2 ) 3 3 1 5 –3 3 2 3
titration curve, was systemically and quantitatively analyzed. The results obtained from the proposed method, which allows the dissolution of CO2 throughout the whole titration process (denoted in-CO2-titration), were comparatively discussed with those of the earlier typical method in which the reaction base is acidified to remove the CO2 effect (denoted ex-CO2-titration).
2.
Experimental
2.1.
Chemicals and materials
Chemicals for the titration such as NaOH, NaHCO3, Na2CO3, and HCl solutions (0.01 M) were purchased from Daejung (Korea). To prepare the samples of oxidized carbon nanotubes (CNTs) in which the functionality was to be analyzed, 1.00 g of multi-walled CNTs (MWCNTs; JEIO, Korea, ca. 96% purity) was treated with 300 mL of mixed acid (mixture of 14.2 M HNO3, 75 mL and concentrated H2SO4, 225 mL) in 60 C silicon oil for 3 h. After the treatment, the sample was refluxed in 1 M NaOH for 1 h to eliminate the acidic carbon compounds, which might disturb the accuracy of the results [7]. The MWCNT dispersion in aqueous NaOH solution was filtered and treated with 1 M HCl for 1 h until the pH of the filtrate became neutral. The obtained MWCNTs were vacuum-dried at 105 C for 1 day (denoted ox-MWCNT).
2.2.
In-CO2-titration of pre-reaction bases
In this study, the general reaction bases, NaOH, Na2CO3, and NaHCO3, were used for the Boehm titration. The concentration of each reaction base was limited to 0.01 M in this study. The amount of the reaction bases used in the titrations was 10.00 mL for the reaction bases NaOH and NaHCO3, and 5.00 mL for the reaction base Na2CO3. In the case of Na2CO3, a half volume of the other reaction bases was used to make the solution in the same equivalence of the base. To reduce the confusion, the reaction bases before and after the reaction with ox-MWCNTs were denoted pre- and post-reaction bases, respectively. Potentiometric titration behaviors of each reaction base were monitored with an 888 Titrando (Metrohm, Swiss). To find out the CO2 effects on the titration behaviors of the pre-reaction bases, the reaction bases were exposed to air for different periods of time (0, 1, 3, 6, and 12 h) and then titrated using 0.01 M HCl standard solution (20.00 mL) as the titrant (here, the titrant is a solution of known concentration that was added to the solution and analyzed in the titration procedure). The titration system allows the dissolution of CO2 throughout the whole titration process. To determine the neutralization point (NP) to obtain the equivalence of the reaction base (denoted base equivalence), the inflection points in each titration curve were detected with the installed program, Tiamo (Metrohm, Swiss), which is defined as the inflection measurement.
for 4 h to expel the dissolved CO2 from the solutions. The acidified reaction base was titrated with 0.01 M NaOH standard solution as the titrant to determine the equivalence of the remaining H+ ions (denoted acid equivalence) [11], and kept purged with N2 gas to minimize the dissolution of CO2 during the titration. Each titration was done in triplicate. In addition to the inflection measurement, the pH-7-measurement was done to determine the NP and the acid equivalence, where the titration of the acid is considered complete at pH 7. The NP determined by the pH-7-measurement is denoted as NP7. The differences between the in- and ex-CO2-titration systems are summarized in Table 1.
2.4.
In- and ex-CO2-titration of ox-MWCNTs
To examine the CO2 effect on an actual titration of carbonaceous samples, the in-CO2-titration was first applied to the ox-MWCNTs in which ca. 60 mg of ox-MWCNTs dispersed for 48 h with stirring in a specified aqueous reaction base solution (0.01 M NaOH, 60.00 mL; 0.01 M Na2CO3, 30.00 mL; and 0.01 M NaHCO3, 60.00 mL) was filtered through a 0.2 lm PTFE syringe filter, and then, 10.00 mL of the filtrates (5.00 mL in the case of Na2CO3) was titrated with 0.01 M HCl standard solution (20.00 mL). As described in Section 2.2, the filtrate of the reaction base after the reaction is denoted as the post-reaction base. Each titration was repeated three times in order to show the reproducibility of the result. In the ex-CO2-titration of the ox-MWCNTs, which was a comparative titration with the in-CO2-titration, the same amount of post-reaction base acidified with 20.00 mL of 0.01 M HCl was titrated with 0.01 M NaOH following the same procedures described in Section 2.3.
2.5. Determination of the surface functionality of the oxMWCNTs The amount of surface functional groups on the ox-MWCNTs was determined by the uptake of the reaction base calculated from the difference between the base equivalence of the pre(eqB,pre) and post-(eqB,post) reaction base B (B specifies NaOH, Na2CO3, and NaHCO3). In the case of the in-CO2-titration of each reaction base, the amount of functional groups, nFG,B, is calculated as follows: nFG;B ¼
cHCl ðVHCl B;pre VHCl mox-MWCNT;B
¼
eqB;pre eqB;post mox-MWCNT;B
;
ð1Þ
where cHCl is the concentration of the HCl titrant; VHCl_B,pre and VHCl_B,post are the volume of the HCl at the base equivalence for each of the pre- and post-reaction bases, respectively, and mox-MWCNT,B is the effective mass of the ox-MWCNTs corresponding to each post-reaction base. Therefore, the number of carboxylic groups nc, lactonic groups nl, and phenolic groups np, was calculated, respectively, as follows: nc ¼ nFG;NaHCO3 ¼
2.3.
B;post Þ
eqNaHCO3 ;pre eqNaHCO3 ;post mox-MWCNT;NaHCO3
;
ð2-1Þ
Ex-CO2-titration of the pre-reaction bases
The same amount of pre-reaction bases acidified with 20.00 mL of 0.01 M HCl as prepared in Section 2.2 were stirred
nl ¼ nFG;Na2 CO3 nFG;NaHCO3 eqNa2 CO3 ;pre eqNa2 CO3 ;post eqNaHCO3 ;pre eqNaHCO3 ;post ¼ ; mox-MWCNT;Na2 CO3 mox-MWCNT;NaHCO3
ð2-2Þ
CARBON
3317
5 0 ( 20 1 2 ) 3 3 1 5–33 2 3
Table 1 – Summary of each titration system. Titration system
In-CO2-titration
Ex-CO2-titration
CO2 exclusion process before the titration CO2 prevention process during the titration Kind of the titrant Determination of NP
None None 0.01 M HCl Inflection point
Acidification Purging with N2 gas 0.01 M NaOH Inflection point, the point at pH 7
np ¼ nFG;NaOH nFG;Na2 CO3 eqNaOH;pre eqNaOH;post eqNa2 CO3 ;pre eqNa2 CO3 ;post ¼ : mox-MWCNT;NaOH mox-MWCNT;Na2 CO3
ð2-3Þ
The reproducibility of the results was determined by the standard deviation in the number of each functional group as follows: 2 2 31=2 SeqNaHCO ;pre þ S2eqNaHCO ;post 3 3 5 ; Snc ¼ 4 ð3-1Þ m2ox-MWCNT;NaHCO3 2 2 31=2 SeqNa CO ;pre þ S2eqNa CO ;post S2eqNaHCO ;pre þ S2eqNaHCO ;post 2 3 2 3 3 3 5 ; þ Snl ¼ 4 m2ox-MWCNT;Na2 CO3 m2ox-MWCNT;NaHCO3 ð3-2Þ
Snp
2 31=2 2 2 S2eqNaOH;pre þ S2eqNaOH;post SeqNa CO ;pre þ SeqNa CO ;post 2 3 2 3 4 5 ; ¼ þ m2ox-MWCNT;NaOH m2ox-MWCNT;Na2 CO3
ð3-3Þ
where Sa is the standard deviation of the factor a. The standard deviation or the error range in the amount for each functional group largely depends on that of the measured equivalence of each reaction base. In the case of the ex-CO2-titration system, eqB,pre and eqB,post should be previously calculated from the acid equivalence of the acidified reaction base (eqex_B,pre(post)) as follows: eqB;preðpostÞ ¼ cHCl;ex VHCl;ex cNaOH VNaOH ¼ cHCl;ex VHCl;ex eqex
ð6Þ
B;preðpostÞ
ð4Þ
B;preðpostÞ ;
where cHCl,ex and VHCl,ex are the concentration and input volume of the HCl for the acidification of the reaction base to expel the CO2 (VHCl,ex = 20.00 mL in these cases), respectively, and cNaOH is the concentration of the NaOH titrant; VNaOH_B,pre, and VNaOH_B,post, are the volume of the NaOH titrant at the acid equivalence for each of the pre- and post-reaction bases acidified with HCl (0.01 M, 20.00 mL), respectively. Therefore, nFG,B can be calculated as follows: nFG;B ¼
eqB;pre eqB;post mox-MWCNT;B
¼
eqex
B;post
eqex
mox-MWCNT;B
B;pre
:
ð5Þ
nc, nl, and np, and their standard deviations were derived similarly as described in Eqs. (2-1)–(2-3) and (3-1)–(3-3), respectively.
3.
Regardless of the exposure time, the quantity of H+ from the dose of the HCl titrant ðQ Hþ ;tit Þ at the second inflection point remained unchanged (straight gray dashed lines in Fig. 1) even though the specific shapes of the curves were distorted for all of the in-CO2-titration curves. These distortions most certainly resulted from the CO2 effect since each titration curve showed two distinct inflections, which are regarded as the neutralization points (NPs) at pH 8 (NP1) and 5 (NP2). The pH value at each NP is given as the pH at neutralization of CO2 3 and HCO3 , respectively [22], which is the product of the reaction between each reaction base and CO2 [23–25]. Theoretical titration curves for each reaction base at the equilibrium state with CO2 (equilibrium curves) are shown as red dashed curves. To predict the change in the composition of the reaction base during the interaction with CO2, first, the simplest model describing the chemical equilibrium of CO2 and the reaction base was utilized. In this model, it was assumed that the partial pressure of atmospheric CO2 did not change (0.00035 atm) by the reaction involved in the equilibrium; therefore, the concentration of CO2 is fixed as [CO2]0 (1.2 · 105 M) by Henry’s law [18]. Thus, the acid–base equilibrium equations are the following [18]: þ HCO 3 ½H þ ðaqÞ þ H ðaqÞ; K ¼ ; CO2 ðaqÞ þ H2 OðlÞ () HCO a1 3 ½CO2 0
Results and discussion
3.1. CO2 effect on the in-CO2-titration behavior of each reaction base Fig. 1 shows the titration curves of the reaction bases in the in-CO2-titration system (denoted in-CO2-titration curves) with different exposure times to air before the titrations.
2 þ HCO 3 ðaqÞ () CO3 ðaqÞ þ H ðaqÞ;
H2 OðlÞ () Hþ ðaqÞ þ OH ðaqÞ;
Ka2 ¼
2 þ CO3 ½H ; HCO 3
KW ¼ ½Hþ ½OH ;
ð7Þ ð8Þ
and the conservation of charge for the ions in an aqueous solution is as follows: 2 þ ½Hþ ½OH ½HCO 3 2½CO3 þ ½Na ¼ 0:
ð9Þ
[Na+] is conserved as the initial concentration [Na+]i because it is a spectator ion in the reaction. Since [H+] is negligible, [Na+]i is the same as the summation of the normality of the base ions at the initial state, –[OH]i [HCO 3 ]i 2 2[CO2 ] . Generally, [OH ] + [HCO ] + 2[CO ], the summai 3 3 3 tion of the normality of bases, is defined as the alkalinity (Alk), which is a measure of the ability of an aqueous solution to neutralize acids [22]. Therefore, Eq. (9) can be expressed as follows: 2 þ ½Hþ ½OH ½HCO 3 2½CO3 ¼ ½Na i ¼ Alki ;
ð90 Þ
where Alki is the initial alkalinity of the reaction base. Then, Eqs. (6)–(9 0 ) can be reduced into a cubic equation as follows: ½Hþ 3 þ Alki ½Hþ 2 ðKW þ Ka1 ½CO2 0 Þ½Hþ 2Ka1 Ka2 ½CO2 0 ¼ 0: ð10Þ
3318
CARBON
5 0 ( 2 0 1 2 ) 3 3 1 5 –3 3 2 3
Fig. 1 – (I) Experimental and theoretical in-CO2-titration curves and (II) their first order derivatives of different pre-reaction bases (a) NaOH, (b) Na2CO3, and (c) NaHCO3 with different exposure times. The gray arrows indicate an increase in the exposure time. Since Alki is given for each reaction base, the concentra tion of each ion ([OH ], [CO2 3 ], and [HCO3 ]) and the pH at the equilibrium with CO2 were calculated. If the Alki is the same regardless of the kind of reaction base (NaOH, Na2CO3, or NaHCO3), the equilibrium state with atmospheric CO2 would be the same.
Fig. 2 shows the calculated ratio variation of the equiva lence (or the normality) of CO2 3 and HCO3 ions in the reaction base at the equilibrium state with respect to an Alki from 0.001 to 0.1 N, which is the usual concentration range applied in the Boehm titration. At the equilibrium state, most of the base components remain in the form of CO2 3 and HCO3 ions
CARBON
5 0 ( 20 1 2 ) 3 3 1 5–33 2 3
and the equivalence (or normality) of OH is almost negligible regardless of the kind of reaction base. For example, if 0.01 M NaOH or NaHCO3, or 0.005 M Na2CO3 (Alki = 0.01 N) is exposed to air and reaches equilibrium with atmospheric CO2, the and HCO equilibrium normality of CO2 3 3 would be 0.0017 and 0.0083 N, respectively, at pH 9.22. The specific mechanisms to reach the equilibrium will be discussed below. To analyze the effects of these composition variations on the titration behaviors of the reaction bases, the theoretical titration curve of the reaction base with the influence of CO2 was calculated using the modified Henderson–Hasselbalch (H–H) equation, previously developed in our laboratory, which is described as follows [26]: P Q Hþ ;tit ¼
Q A i
1þ½OH =Kb;A i
1 þ vH
vH
VBase þ1=½OH
2O
1=cHCl þ1=½OH
2O
vH
2O
þ vH
2O
VBase þ½OH =KW
1=cHCl þ½OH =KW
;
ð11Þ
where Q Hþ ;tit is the amount of added HCl titrant (in mmol), Q A is the quantity of the specific base component, A i , (in i mmol) in the reaction base, Kb;Ai is the base ionization constant of a base Ai , KW is the self-ionization constant of water, VBase is the volume of the reaction base, vH2 O is the molar volume of water, and cHCl is the concentration of the HCl titrant. The base components (A i ) associated with this study were the OH, CO2 3 , and HCO3 ions listed in order of their base strength. Different from the conventional H–H equation [27], the modified H–H equation is useful to estimate a titration behavior in the whole range of the titration [26]. When the modified H–H equation was applied to CO2 3 , a diprotic base, it was assumed that CO2 was divided into independent base 3 components and proton binding sites (Q CO2 = Q HCO3 ) with 3 individual common pKb values [26]. Applying the modified H–H equation, the titration behaviors of the reaction base NaOH (0.01 M, 10 mL, Q OH = 0.1 mmol) were calculated with the dissolution of different amounts of CO2 (Q CO2 = 0, 0.025, 0.05, 0.075 and 0.1 mmol), denoted Base a–Base e in order of the CO2 amount. The theoretical titration curves of Base a–Base e were drawn as la–le, respectively, in Fig. 3. la (Q CO2 = 0) shows the typical titration curve of an NaOH solution, and only a single NP from the OH ions exist at pH 7. To calculate the titration curve of Base b, in which Q CO2 is 0.025 mmol, the composition of each base component should
2 Fig. 2 – The calculated equivalence ratio of HCO 3 and CO3 ions in the reaction base at the equilibrium state with CO2.
3319
be calculated to apply the modified H–H equation. Q OH and in Base b can be set as 0.05 and 0.025 mmol QCO2 3 (0.05 meq), respectively, according to the well-known absorption reaction of CO2 in NaOH [23,24] as follows: CO2 ðaqÞ þ OH ðaqÞ ! HCO 3 ðaqÞ 2 HCO 3 ðaqÞ þ OH ðaqÞ ! CO3 ðaqÞ þ H2 OðlÞ : 2 2OH ðaqÞ þ CO2 ðaqÞ ! CO3 ðaqÞ þ H2 OðlÞ
ðStep 1Þ
As the NaOH is reacted with CO2, the titration curve begins to be distorted and the initial NP at pH 7 splits to make two NPs at pH 8 (NP1) and 5 (NP2), which are generally attributed and HCO to the neutralization of CO2 3 3 , respectively [22]. These kinds of behaviors were also observed in the real titration curves as shown in Fig. 1a. Q Hþ ;tit at NP1 indicates the summation of Q OH and Q CO2 , which implies both the CO2 3 3 and OH ions are neutralized at the same time since the pKb difference between the two ions would be not large enough [26]. And then, the remaining HCO 3 ions from the neutralization of the CO2 3 ions are neutralized to make clear the NP at Q Hþ ;tit = 0.1 mmol, which is the original base equivalence of the NaOH solution. It is noteworthy that the difference between the Q Hþ ;tit values at NP1 and NP2 in lb is exactly the same as the Q CO2 and Q CO2 initially set in Base b. The in3 CO2-titration curves of NaOH exposed to air for 0, 1, and 3 h in Fig. 1a show the titration profiles of the reaction bases at Step (1). In Base c (Q CO2 = 0.05 mmol), Q OH is exhausted according to the reaction in Step (1), and the base becomes exactly 0.005 M (0.01 N) Na2CO3 solution. The titration curve lc also exhibits the titration behavior of Na2CO3. From the equilibrium diagram shown in Fig. 2, it is reasonable to estimate that the composition of Base c, or the Na2CO3 solution, will change when it is exposed to CO2. In this case, ions are reported to mainly react with CO2 instead of CO2 3 OH ions and produce HCO 3 ions [25] as follows: CO2 3 ðaqÞ þ H2 O ðlÞ ! HCO3 ðaqÞ þ OH ðaqÞ
CO2 ðaqÞ þ OH ðaqÞ ! HCO 3 ðaqÞ CO2 3 ðaqÞ þ H2 O ðlÞ þ CO2 ðaqÞ ! 2HCO3 ðaqÞ:
ðStep 2Þ
Therefore, most of the base components in the reaction and base are converted into CO2 3 and HCO3 ions, and Q CO2 3 Q HCO3 in Base d (Q CO2 = 0.075 mmol) were set as 0.025 mmol (0.05 meq) and 0.05 mmol, respectively, to yield the curve ld. In the titration of Base d, the stronger base, CO2 3 ions, would ions and NP1 appears at be neutralized prior to the HCO 3 Q Hþ ;tit = 0.025 mmol, of which the amount is the same as ions are neutralized into HCO Q CO2 . At this state, as CO2 3 3 3 ions, the quantity of the remaining HCO 3 ions is 0.075 mmol and would result in NP2 at Q Hþ ;tit = 0.01 mmol when they are completely neutralized. The in-CO2-titration curves of NaOH exposed to air for 6 and 12 h in Fig. 1a, and all of those of Na2CO3 in Fig. 1b show the titration profiles of each reaction base at Step (2). If Q CO2 becomes 0.01 mmol (Base e), only HCO 3 ions would remain to make a pure NaHCO3 solution (0.01 M) and the resultant theoretical titration curve is le. However, this is not a spontaneous reaction because the reaction base would reach the equilibrium state with CO2 when the normality of HCO 3 ions becomes 0.0083 N as described in Fig. 2. On the other hand, le would shift toward ld when Base e, or 0.01 M
3320
CARBON
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Fig. 3 – (I) Theoretical titration curves and (II) their first order derivatives of 0.01 M NaOH (10 mL) reacted with different amounts of CO2.
NaHCO3, is exposed to air because more HCO 3 ions exist in pure NaHCO3 solution than those in the solution at the equilibrium state. The change of the composition of each base component in this case is followed by CO2 desorption of HCO 3 ion [25] as follows: 2 þ HCO 3 ðaqÞ ! CO3 ðaqÞ þ H ðaqÞ þ HCO3 ðaqÞ þ H ðaqÞ ! CO2 ðaqÞ þ H2 OðlÞ 2 2HCO 3 ðaqÞ ! CO3 ðaqÞ þ CO2 ðaqÞ þ H2 OðlÞ:
ðStep 2-Þ
The overall reaction can be considered as the reverse reaction of the reaction in Step (2); therefore, this step is denoted Step (2-). All of the titration curves of NaHCO3 in Fig. 1c show the titration profiles of the reaction bases at Step (2-). Based on these considerations, the theoretical titration curve of each experimental in-CO2-titration curve was calculated and drawn as the black solid lines in Fig. 1 with good coincidence between each other. In addition, the theoretical titration curve of each reaction base in the equilibrium state with atmospheric CO2 (denoted equilibrium curve) was calculated and drawn as the red dashed curve in Fig. 1. The experimental titration curves of each reaction base reached the equilibrium curve with an increase in the exposure time, which implies our theoretical approach related to the CO2 interactions with the reaction bases and the estimation of the titration curves by the modified H–H equation would be valid in the real case. Further, it is shown form Steps (1)–(2-) that the total base equivalence (the summation of the equivalence of OH , CO2 3 , and HCO3 ions) of each reaction base remains unchanged with the interaction of CO2 since the equivalence of the base is the same in the reactants and products, respectively, in the reaction in each step. The conservation of the base equivalence (eqB,pre) is revealed in the conservation of Q Hþ ;tit at NP2 both theoretically (Fig. 3) and experimentally (Fig. 1) regardless of the exposure of the reaction base to CO2. From this conservation, the precise measurement of eqB,pre of each reaction base is possible in the in-CO2-titration
system regardless of the exposure to air as shown in Table 2, which implies the exclusion and prevention of CO2 would not be necessary in the Boehm titration.
3.2. Comparison of the in-CO2-titration behavior with the ex-CO2-titration behavior For comparison, the ex-CO2-titration [11] was applied to each reaction base. Fig. 4 shows the titration curve of the acidified reaction base NaHCO3 in the ex-CO2-titration system (denoted ex-CO2-titration curve) as a function of the amount of OH ions from the dosed NaOH titrant (Q OH ;tit ) (the other acidified reaction bases, NaOH and Na2CO3, showed similar titration behaviors). The ex-CO2-titration curve shows almost a single inflection peak around pH 7, which implies that CO2 was almost expelled from the reaction base by the acidification. However, a magnified view shows that this peak splits into two inflection peaks at pH 5 (NP1 0 ) and pH 8 (NP2 0 ), which would be attributed to the neutralization of H2CO3 and HCO 3 , respectively [22], which come from the remaining CO2 in the reaction base even though the removal and prevention of the CO2 effect were adopted. In this case, Q OH ;tit at NP1 0 shows the exact acid equivalence (eqex_B,pre) of the acidified reaction base [11]. However, as the Q OH ;tit difference between NP1 0 and NP2 0 is rather narrow, the measurements of these NPs by the inflection measurement may not always ensure accuracy. For this reason, the pH-7-measurement has been usually utilized to determine the NP (NP7) [10,11], in which the neutralization is assumed to be completed at pH 7. If a highly precise measurement is not necessary, Q OH ;tit at NP7 is regarded as the eqex_B,pre rather than the Q OH ;tit at NP1 0 [11]. After eqex_B,pre is determined either by the inflection or pH-7-measurements, the equivalence (eqB,pre) of each pre-reaction base was calculated by Eq. (4) and compared to the eqB,pre obtained by the inflection measurement from the in-CO2-titration system in Table 2.
CARBON
3321
5 0 ( 20 1 2 ) 3 3 1 5–33 2 3
Table 2 – The base equivalence of each pre-reaction base (eqB,pre) determined by the different measurement methods of NP from in- and ex-CO2-titration. Titration method
In-CO2-titration Ex-CO2-titration
NP measurement method
Inflection point Inflection point The point at pH 7
Equivalence of the reaction base (meq) NaOH
Na2CO3
NaHCO3
0.10128 ± 0.00009 0.10122 ± 0.00006 0.10008 ± 0.00030
0.09957 ± 0.00005 0.09970 ± 0.00018 0.09887 ± 0.00022
0.09964 ± 0.00004 0.09974 ± 0.00002 0.09866 ± 0.00013
Fig. 4 – (a) Ex-CO2-titration curve and its first order derivative of the pre-reaction base NaHCO3, and (b) the magnified view around the NPs (blue dotted box in (a)). The results imply that both inflection measurements from the in- and ex-CO2-titration provide eqB,pre with high precision, which is comparable to that of a previous report [11]. However, the pH-7-measurement following the ex-CO2-titration resulted in the underestimation of eqB,pre because of a slight amount of CO2 remaining in the acidified reaction base. It is noteworthy that the in-CO2-titration system provides a simple but precise determination of the base equivalence.
3.3. Surface functionality of ox-MWCNTs as determined by in- and ex-CO2-titration The amount of each functional group on ox-MWCNTs was determined by applying both the in- and ex-CO2-titrations. Fig. 5 shows the variations of the in- (Fig. 5a) and ex(Fig. 5c) CO2-titration curves of the reaction base NaOH as it is reacted with ox-MWCNTs (Fig. 5b and d show the magnified view of Fig. 5a and c, respectively). NaOH uptake (nFG,NaOH), which indicates the quantity of all the functional groups of ox-MWCNTs [1], is presented in the figure with different measurements of the base or acid equivalence. The in-CO2-titration curve shifted entirely to the left (Fig. 5a) as the base equivalence of the reaction base decreased after the reaction. In addition, all of the in-CO2-titration curves showed two NPs, which indicates the CO2 effect [22]. In these cases, Q Hþ ;tit at the second inflection point (NP2) should be regarded as the base equivalence of the reaction base regardless of the CO2 effect. Therefore, nFG,NaOH was determined from the difference between Q Hþ ;tit at NP2 of the pre- and post-reaction base as described in Eq. (1). In the case of the ex-CO2-titration of ox-MWCNTs, the whole curve shifted to the right. Since the amount of HCl
for the acidification of the reaction base was the same, the reaction base with the lower base equivalence (pre-reaction base) had the higher acid equivalence when it was acidified, as described in Eq. (4). The difference of the acid equivalence between the pre- and post-reaction base (eqex_NaOH,pre and eqex_NaOH,post, respectively) indicates the nFG,NaOH as described in Eq. (5). The nFG,NaOH determined from the inflection measurements from the ex- and in-CO2-titrations (0.786 ± 0.007 and 0.790 ± 0.006 meq/g, respectively) was almost the same. Meanwhile, it seems that the nFG,NaOH was slightly overestimated by the pH-7-measurement from the ex-CO2-titration system (0.812 ± 0.027 meq/g), which is a result of the different tendency of CO2 expulsion by the acidification of each reaction base. The uptake of the rest of the reaction bases Na2CO3 and NaHCO3 was obtained by similar methods. Additionally, the number of each functional group on the ox-MWCNTs was calculated by Eqs. (2-1)–(2-3) and the results are listed in Table 3. All of the results listed in Table 3 show similar tendencies. However, the results from the pH-7-measurement following the ex-CO2-titration were slightly different from those from the inflection measurements because the tendency of CO2 expulsion by the acidification of each reaction base was different. On the other hand, a relatively high precision in the Boehm titration results was achieved with the in-CO2titration method compared to that in the results of the ex-CO2-titration method even though no treatments for CO2 expulsion or prevention were applied before and during the titration. Therefore, additional procedures such as acidification or protection of the reaction base by an inert-gas blanket to exclude the CO2 effect are not certainly necessary for the Boehm titration of carbonaceous materials.
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Fig. 5 – (I) Titration curves and (II) their first order derivatives of the reaction base NaOH from (a) the in- and (b) ex-CO2titration systems before and after the reaction with the ox-MWCNTs. (b and d) The magnified view around the NP of the titrations (blue dotted box in (a) and (c), respectively).
Table 3 – The number of each functional group on the ox-MWCNTs determined by the different measurement methods of NP from the in- and ex-CO2-titrations. Titration method
In-CO2-titration Ex-CO2-titration
4.
NP measurement method
Inflection point Inflection Point The point at pH 7
Number of functional group (meq/g) Carboxylic
Lactonic
Phenolic
Total
0.498 ± 0.016 0.494 ± 0.006 0.508 ± 0.017
0.222 ± 0.018 0.239 ± 0.024 0.263 ± 0.027
0.066 ± 0.010 0.058 ± 0.024 0.041 ± 0.033
0.786 ± 0.007 0.790 ± 0.006 0.812 ± 0.027
Conclusions
Atmospheric CO2 has been considered to cause a negative effect on determining the exact neutralization point and equivalence of the reaction base in the Boehm titration, and was thought to be removed or prevented using various additional procedures, which makes the Boehm titration complicated and inaccessible. However, it turns out unnecessary to
exclude CO2 to determine the equivalence of the reaction base because the position of the second inflection point indicating the equivalence of the reaction base remains unchanged even though the reaction base interacts with CO2. In addition, the surface functionality of acid-treated MWCNTs was determined with high precision applying the titration method including the CO2 effect. We believe our findings will help to establish an effective and simple Boehm titration method.
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Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MEST) [No. 2011-0029865].
R E F E R E N C E S
[1] Boehm HP. Some aspects of the surface-chemistry of carbonblacks and other carbons. Carbon 1994;32(5):759–69. [2] Carrasco-Marin F, Mueden A, Centeno TA, Stoeckli F, MorenoCastilla C. Water adsorption on activated carbons with different degrees of oxidation. J Chem Soc Faraday T 1997;93(12):2211–5. [3] Hulicova-Jurcakova D, Seredych M, Jin YG, Lu GQ, Bandosz TJ. Specific anion and cation capacitance in porous carbon blacks. Carbon 2010;48(6):1767–78. [4] Grzyb B, Hildenbrand C, Berthon-Fabry S, Begin D, Job N, Rigacci A, et al. Functionalization and chemical characterisation of cellulose-derived carbon aerogels. Carbon 2010;48(8):2297–307. [5] Moreno-Castilla C, Carrasco-Marin F, Mueden A. The creation of acid carbon surfaces by treatment with (NH4)2S2O8. Carbon 1997;35(10–11):1619–26. [6] Horikawa T, Kitakaze Y, Sekida T, Hayashi J, Katoh M. Characteristics and humidity control capacity of activated carbon from bamboo. Bioresource Technol 2010;101(11):3964–9. [7] Wang Z, Shirley MD, Meikle ST, Whitby RLD, Mikhalovsky SV. The surface acidity of acid oxidised multi-walled carbon nanotubes and the influence of in-situ generated fulvic acids on their stability in aqueous dispersions. Carbon 2009;47(1):73–9. [8] Azadi P, Farnood R, Meier E. Preparation of multiwalled carbon nanotube-supported nickel catalysts using incipient wetness method. J Phys Chem A 2010;114(11):3962–8. [9] Lago RM, Tsang SC, Lu KL, Chen YK, Green MLH. Filling carbon nanotubes with small palladium metal crystallites: the effect of surface acid groups. J Chem Soc Chem Commun 1995:1355–6. [10] Hu H, Bhowmik P, Zhao B, Hamon MA, Itkis ME, Haddon RC. Determination of the acidic sites of purified single-walled carbon nanotubes by acid–base titration. Chem Phys Lett 2001;345(1–2):25–8. [11] Goertzen SL, Theriault KD, Oickle AM, Tarasuk AC, Andreas HA. Standardization of the Boehm titration. Part I. CO2 expulsion and endpoint determination. Carbon 2010;48(4):1252–61. [12] Le Leuch LM, Bandosz TJ. The role of water and surface acidity on the reactive adsorption of ammonia on modified activated carbons. Carbon 2007;45(3):568–78.
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[13] Shaffer MSP, Menzel R, Lee A, Bismarck A. Inverse gas chromatography of as-received and modified carbon nanotubes. Langmuir 2009;25(14):8340–8. [14] Rockstraw DA, Guo YP. Activated carbons prepared from rice hull by one-step phosphoric acid activation. Micropor Mesopor Mater 2007;100(1–3):12–9. [15] Vukovic´ GD, Obradovic´ MD, Marinkovic´ AD, Rogan JR, Uskokovic´ PS, Radmilovic´ VR, et al. Ethylenediaminemodified multiwall carbon nanotubes as a Pt catalyst support. Mater Chem Phys 2011;130(1–2):657–64. [16] Zhao C, Ji L, Liu H, Hu G, Zhang S, Yang M, et al. Functionalized carbon nanotubes containing isocyanate groups. J Solid State Chem 2004;177(12):4394–8. [17] Wang Z, Korobeinyk A, Whitby RLD, Meikle ST, Mikhalovsky SV, Acquah SFA, et al. Direct confirmation that carbon nanotubes still react covalently after removal of acidoxidative lattice fragments. Carbon 2010;48(3): 916–8. [18] Takemura F, Matsumoto Y. Dissolution rate of spherical carbon dioxide bubbles in strong alkaline solutions. Chem Eng Sci 2000;55(18):3907–17. [19] Biniak S, Szymanski G, Siedlewski J, Swiatkowski A. The characterization of activated carbons with oxygen and nitrogen surface groups. Carbon 1997;35(12):1799–810. [20] Bandosz TJ, Jagiello J, Contescu C, Schwarz JA. Characterization of the surfaces of activated carbons in terms of their acidity constant distributions. Carbon 1993;31(7):1193–202. [21] Contescu A, Contescu C, Putyera K, Schwarz JA. Surface acidity of carbons characterized by their continuous pK distribution and Boehm titration. Carbon 1997;35(1): 83–94. 2 [22] Verma MP. A revised analytical method for HCO 3 and CO3 determinations in geothermal waters: an assessment of IAGC and IAEA interlaboratory comparisons. Geostand Geoanal Res 2004;28(3):391–409. [23] Plummer LN, Busenberg E. The solubilities of calcite, aragonite and vaterite in CO2–H2O solutions between 0 and 90 C, and an evaluation of the aqueous model for the system CaCO3–CO2–H2O. Geochim Cosmochim Acta 1982;46(6):1011–40. [24] Pohorecki R, Moniuk W. Kinetics of reaction between carbon dioxide and hydroxyl ions in aqueous-electrolyte solutions. Chem Eng Sci 1988;43(7):1677–84. [25] Pohorecki R, Kucharski E. Desorption with chemical-reaction in the system CO2-aqueous solution of potassium carbonate. Chem Eng J Biochem Eng 1991;46(1):1–7. [26] Kim YS, Yang SJ, Lim HJ, Kim T, Lee K, Park CR. Effects of carbon dioxide and acidic carbon compounds on the analysis of Boehm titration curves. Carbon, in press. doi:10.1016/ j.carbon.2011.11.021. [27] Ritchie JD, Perdue EM. Proton-binding study of standard and reference fulvic acids, humic acids, and natural organic matter. Geochim Cosmochim Acta 2003;67(1):85–96.
5 0 ( 2 0 1 2 ) 3 3 1 5 –3 3 2 3
Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/carbon
A simple method for determining the neutralization point in Boehm titration regardless of the CO2 effect Yern Seung Kim, Seung Jae Yang, Hyeong Jun Lim, Taehoon Kim, Chong Rae Park
*
Carbon Nanomaterials Design Laboratory, Global Research Laboratory, Research Institute of Advanced Materials, and Department of Materials Science and Engineering, Seoul National University, Seoul 151-744, Republic of Korea
A R T I C L E I N F O
A B S T R A C T
Article history:
We report a simple method by which the neutralization point in the Boehm titration can be
Received 23 November 2011
easily determined without going through a pre-screening process to remove the effect of
Accepted 15 December 2011
atmospheric carbon dioxide (CO2). The proposed method is based on the principle that
Available online 24 December 2011
the equivalence and the corresponding neutralization point of the reaction bases remains unchanged regardless of the dissolution of CO2 in the reaction bases. This method was used to measure the surface functionality of acid-treated multi-walled carbon nanotubes with high precision. 2011 Elsevier Ltd. All rights reserved.
1.
Introduction
The Boehm titration has been generally adopted to characterize [1–14] and analyze the reactivity [15–17] of the surface functionality of various carbonaceous materials. In the method, three reaction bases with different basicities, such as sodium hydroxide (NaOH), sodium carbonate (Na2CO3) and sodium bicarbonate (NaHCO3), have been used to discern the kinds and amounts of surface functionalities among carboxylic, lactonic, and phenolic groups [1]. The amount of a specific surface functionality is calculated from the neutralization point usually determined as the point at pH 7 in the Boehm titration curve corresponding to a specific base [7,10,11]. However, the neutralization point as judged at pH 7 does not always mean a precise equivalence of the given surface functionality because of the effect of atmospheric carbon dioxide (CO2) that dissolves easily into the reaction base during the filtration of the carbonaceous samples or the titration process. In fact, when atmospheric CO2 dissolves into aqueous solution, it becomes carbonic acid (H2CO3), which is a weak acid [11,18]. The presence of H2CO3 in the reaction base has been known to distort the titration curve and make it
difficult to get an exact neutralization point from the curve, hence, the exact amount of a specific surface functionality, which is defined as the CO2 effect. To remove the CO2 as completely as possible, the reaction base has to be acidified [1,10,11] since CO2 is driven out from the solution by acidic conditions with additional processes such as heating [1,10,11] or degasification with an inert gas [11]. To prevent the dissolution of CO2 into the reaction base during titration, sealing, degasification of the reaction base with an inert gas [11,13], and titration in an N2 gas filled glove box [14] have been adopted. However, the introduction of these CO2 removal processes makes the Boehm titration complicated and inaccessible, although the Boehm titration method is an easier method for the determination of the surface functionality of carbonaceous materials than the direct titration method [19–21] whereby rather complicated analysis tools should be used. Having considered this situation, in this study, we tried to find a much easier method for determining the neutralization point in the Boehm titration, which does not need any additional processes to remove the CO2 effect from the titration process. To achieve this goal, the dissolution behavior of CO2 into each reaction base, and hence its influence on the
* Corresponding author: Fax: +82 2 885 1748. E-mail address: [email protected] (C.R. Park). 0008-6223/$ - see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2011.12.030
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titration curve, was systemically and quantitatively analyzed. The results obtained from the proposed method, which allows the dissolution of CO2 throughout the whole titration process (denoted in-CO2-titration), were comparatively discussed with those of the earlier typical method in which the reaction base is acidified to remove the CO2 effect (denoted ex-CO2-titration).
2.
Experimental
2.1.
Chemicals and materials
Chemicals for the titration such as NaOH, NaHCO3, Na2CO3, and HCl solutions (0.01 M) were purchased from Daejung (Korea). To prepare the samples of oxidized carbon nanotubes (CNTs) in which the functionality was to be analyzed, 1.00 g of multi-walled CNTs (MWCNTs; JEIO, Korea, ca. 96% purity) was treated with 300 mL of mixed acid (mixture of 14.2 M HNO3, 75 mL and concentrated H2SO4, 225 mL) in 60 C silicon oil for 3 h. After the treatment, the sample was refluxed in 1 M NaOH for 1 h to eliminate the acidic carbon compounds, which might disturb the accuracy of the results [7]. The MWCNT dispersion in aqueous NaOH solution was filtered and treated with 1 M HCl for 1 h until the pH of the filtrate became neutral. The obtained MWCNTs were vacuum-dried at 105 C for 1 day (denoted ox-MWCNT).
2.2.
In-CO2-titration of pre-reaction bases
In this study, the general reaction bases, NaOH, Na2CO3, and NaHCO3, were used for the Boehm titration. The concentration of each reaction base was limited to 0.01 M in this study. The amount of the reaction bases used in the titrations was 10.00 mL for the reaction bases NaOH and NaHCO3, and 5.00 mL for the reaction base Na2CO3. In the case of Na2CO3, a half volume of the other reaction bases was used to make the solution in the same equivalence of the base. To reduce the confusion, the reaction bases before and after the reaction with ox-MWCNTs were denoted pre- and post-reaction bases, respectively. Potentiometric titration behaviors of each reaction base were monitored with an 888 Titrando (Metrohm, Swiss). To find out the CO2 effects on the titration behaviors of the pre-reaction bases, the reaction bases were exposed to air for different periods of time (0, 1, 3, 6, and 12 h) and then titrated using 0.01 M HCl standard solution (20.00 mL) as the titrant (here, the titrant is a solution of known concentration that was added to the solution and analyzed in the titration procedure). The titration system allows the dissolution of CO2 throughout the whole titration process. To determine the neutralization point (NP) to obtain the equivalence of the reaction base (denoted base equivalence), the inflection points in each titration curve were detected with the installed program, Tiamo (Metrohm, Swiss), which is defined as the inflection measurement.
for 4 h to expel the dissolved CO2 from the solutions. The acidified reaction base was titrated with 0.01 M NaOH standard solution as the titrant to determine the equivalence of the remaining H+ ions (denoted acid equivalence) [11], and kept purged with N2 gas to minimize the dissolution of CO2 during the titration. Each titration was done in triplicate. In addition to the inflection measurement, the pH-7-measurement was done to determine the NP and the acid equivalence, where the titration of the acid is considered complete at pH 7. The NP determined by the pH-7-measurement is denoted as NP7. The differences between the in- and ex-CO2-titration systems are summarized in Table 1.
2.4.
In- and ex-CO2-titration of ox-MWCNTs
To examine the CO2 effect on an actual titration of carbonaceous samples, the in-CO2-titration was first applied to the ox-MWCNTs in which ca. 60 mg of ox-MWCNTs dispersed for 48 h with stirring in a specified aqueous reaction base solution (0.01 M NaOH, 60.00 mL; 0.01 M Na2CO3, 30.00 mL; and 0.01 M NaHCO3, 60.00 mL) was filtered through a 0.2 lm PTFE syringe filter, and then, 10.00 mL of the filtrates (5.00 mL in the case of Na2CO3) was titrated with 0.01 M HCl standard solution (20.00 mL). As described in Section 2.2, the filtrate of the reaction base after the reaction is denoted as the post-reaction base. Each titration was repeated three times in order to show the reproducibility of the result. In the ex-CO2-titration of the ox-MWCNTs, which was a comparative titration with the in-CO2-titration, the same amount of post-reaction base acidified with 20.00 mL of 0.01 M HCl was titrated with 0.01 M NaOH following the same procedures described in Section 2.3.
2.5. Determination of the surface functionality of the oxMWCNTs The amount of surface functional groups on the ox-MWCNTs was determined by the uptake of the reaction base calculated from the difference between the base equivalence of the pre(eqB,pre) and post-(eqB,post) reaction base B (B specifies NaOH, Na2CO3, and NaHCO3). In the case of the in-CO2-titration of each reaction base, the amount of functional groups, nFG,B, is calculated as follows: nFG;B ¼
cHCl ðVHCl B;pre VHCl mox-MWCNT;B
¼
eqB;pre eqB;post mox-MWCNT;B
;
ð1Þ
where cHCl is the concentration of the HCl titrant; VHCl_B,pre and VHCl_B,post are the volume of the HCl at the base equivalence for each of the pre- and post-reaction bases, respectively, and mox-MWCNT,B is the effective mass of the ox-MWCNTs corresponding to each post-reaction base. Therefore, the number of carboxylic groups nc, lactonic groups nl, and phenolic groups np, was calculated, respectively, as follows: nc ¼ nFG;NaHCO3 ¼
2.3.
B;post Þ
eqNaHCO3 ;pre eqNaHCO3 ;post mox-MWCNT;NaHCO3
;
ð2-1Þ
Ex-CO2-titration of the pre-reaction bases
The same amount of pre-reaction bases acidified with 20.00 mL of 0.01 M HCl as prepared in Section 2.2 were stirred
nl ¼ nFG;Na2 CO3 nFG;NaHCO3 eqNa2 CO3 ;pre eqNa2 CO3 ;post eqNaHCO3 ;pre eqNaHCO3 ;post ¼ ; mox-MWCNT;Na2 CO3 mox-MWCNT;NaHCO3
ð2-2Þ
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Table 1 – Summary of each titration system. Titration system
In-CO2-titration
Ex-CO2-titration
CO2 exclusion process before the titration CO2 prevention process during the titration Kind of the titrant Determination of NP
None None 0.01 M HCl Inflection point
Acidification Purging with N2 gas 0.01 M NaOH Inflection point, the point at pH 7
np ¼ nFG;NaOH nFG;Na2 CO3 eqNaOH;pre eqNaOH;post eqNa2 CO3 ;pre eqNa2 CO3 ;post ¼ : mox-MWCNT;NaOH mox-MWCNT;Na2 CO3
ð2-3Þ
The reproducibility of the results was determined by the standard deviation in the number of each functional group as follows: 2 2 31=2 SeqNaHCO ;pre þ S2eqNaHCO ;post 3 3 5 ; Snc ¼ 4 ð3-1Þ m2ox-MWCNT;NaHCO3 2 2 31=2 SeqNa CO ;pre þ S2eqNa CO ;post S2eqNaHCO ;pre þ S2eqNaHCO ;post 2 3 2 3 3 3 5 ; þ Snl ¼ 4 m2ox-MWCNT;Na2 CO3 m2ox-MWCNT;NaHCO3 ð3-2Þ
Snp
2 31=2 2 2 S2eqNaOH;pre þ S2eqNaOH;post SeqNa CO ;pre þ SeqNa CO ;post 2 3 2 3 4 5 ; ¼ þ m2ox-MWCNT;NaOH m2ox-MWCNT;Na2 CO3
ð3-3Þ
where Sa is the standard deviation of the factor a. The standard deviation or the error range in the amount for each functional group largely depends on that of the measured equivalence of each reaction base. In the case of the ex-CO2-titration system, eqB,pre and eqB,post should be previously calculated from the acid equivalence of the acidified reaction base (eqex_B,pre(post)) as follows: eqB;preðpostÞ ¼ cHCl;ex VHCl;ex cNaOH VNaOH ¼ cHCl;ex VHCl;ex eqex
ð6Þ
B;preðpostÞ
ð4Þ
B;preðpostÞ ;
where cHCl,ex and VHCl,ex are the concentration and input volume of the HCl for the acidification of the reaction base to expel the CO2 (VHCl,ex = 20.00 mL in these cases), respectively, and cNaOH is the concentration of the NaOH titrant; VNaOH_B,pre, and VNaOH_B,post, are the volume of the NaOH titrant at the acid equivalence for each of the pre- and post-reaction bases acidified with HCl (0.01 M, 20.00 mL), respectively. Therefore, nFG,B can be calculated as follows: nFG;B ¼
eqB;pre eqB;post mox-MWCNT;B
¼
eqex
B;post
eqex
mox-MWCNT;B
B;pre
:
ð5Þ
nc, nl, and np, and their standard deviations were derived similarly as described in Eqs. (2-1)–(2-3) and (3-1)–(3-3), respectively.
3.
Regardless of the exposure time, the quantity of H+ from the dose of the HCl titrant ðQ Hþ ;tit Þ at the second inflection point remained unchanged (straight gray dashed lines in Fig. 1) even though the specific shapes of the curves were distorted for all of the in-CO2-titration curves. These distortions most certainly resulted from the CO2 effect since each titration curve showed two distinct inflections, which are regarded as the neutralization points (NPs) at pH 8 (NP1) and 5 (NP2). The pH value at each NP is given as the pH at neutralization of CO2 3 and HCO3 , respectively [22], which is the product of the reaction between each reaction base and CO2 [23–25]. Theoretical titration curves for each reaction base at the equilibrium state with CO2 (equilibrium curves) are shown as red dashed curves. To predict the change in the composition of the reaction base during the interaction with CO2, first, the simplest model describing the chemical equilibrium of CO2 and the reaction base was utilized. In this model, it was assumed that the partial pressure of atmospheric CO2 did not change (0.00035 atm) by the reaction involved in the equilibrium; therefore, the concentration of CO2 is fixed as [CO2]0 (1.2 · 105 M) by Henry’s law [18]. Thus, the acid–base equilibrium equations are the following [18]: þ HCO 3 ½H þ ðaqÞ þ H ðaqÞ; K ¼ ; CO2 ðaqÞ þ H2 OðlÞ () HCO a1 3 ½CO2 0
Results and discussion
3.1. CO2 effect on the in-CO2-titration behavior of each reaction base Fig. 1 shows the titration curves of the reaction bases in the in-CO2-titration system (denoted in-CO2-titration curves) with different exposure times to air before the titrations.
2 þ HCO 3 ðaqÞ () CO3 ðaqÞ þ H ðaqÞ;
H2 OðlÞ () Hþ ðaqÞ þ OH ðaqÞ;
Ka2 ¼
2 þ CO3 ½H ; HCO 3
KW ¼ ½Hþ ½OH ;
ð7Þ ð8Þ
and the conservation of charge for the ions in an aqueous solution is as follows: 2 þ ½Hþ ½OH ½HCO 3 2½CO3 þ ½Na ¼ 0:
ð9Þ
[Na+] is conserved as the initial concentration [Na+]i because it is a spectator ion in the reaction. Since [H+] is negligible, [Na+]i is the same as the summation of the normality of the base ions at the initial state, –[OH]i [HCO 3 ]i 2 2[CO2 ] . Generally, [OH ] + [HCO ] + 2[CO ], the summai 3 3 3 tion of the normality of bases, is defined as the alkalinity (Alk), which is a measure of the ability of an aqueous solution to neutralize acids [22]. Therefore, Eq. (9) can be expressed as follows: 2 þ ½Hþ ½OH ½HCO 3 2½CO3 ¼ ½Na i ¼ Alki ;
ð90 Þ
where Alki is the initial alkalinity of the reaction base. Then, Eqs. (6)–(9 0 ) can be reduced into a cubic equation as follows: ½Hþ 3 þ Alki ½Hþ 2 ðKW þ Ka1 ½CO2 0 Þ½Hþ 2Ka1 Ka2 ½CO2 0 ¼ 0: ð10Þ
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Fig. 1 – (I) Experimental and theoretical in-CO2-titration curves and (II) their first order derivatives of different pre-reaction bases (a) NaOH, (b) Na2CO3, and (c) NaHCO3 with different exposure times. The gray arrows indicate an increase in the exposure time. Since Alki is given for each reaction base, the concentra tion of each ion ([OH ], [CO2 3 ], and [HCO3 ]) and the pH at the equilibrium with CO2 were calculated. If the Alki is the same regardless of the kind of reaction base (NaOH, Na2CO3, or NaHCO3), the equilibrium state with atmospheric CO2 would be the same.
Fig. 2 shows the calculated ratio variation of the equiva lence (or the normality) of CO2 3 and HCO3 ions in the reaction base at the equilibrium state with respect to an Alki from 0.001 to 0.1 N, which is the usual concentration range applied in the Boehm titration. At the equilibrium state, most of the base components remain in the form of CO2 3 and HCO3 ions
CARBON
5 0 ( 20 1 2 ) 3 3 1 5–33 2 3
and the equivalence (or normality) of OH is almost negligible regardless of the kind of reaction base. For example, if 0.01 M NaOH or NaHCO3, or 0.005 M Na2CO3 (Alki = 0.01 N) is exposed to air and reaches equilibrium with atmospheric CO2, the and HCO equilibrium normality of CO2 3 3 would be 0.0017 and 0.0083 N, respectively, at pH 9.22. The specific mechanisms to reach the equilibrium will be discussed below. To analyze the effects of these composition variations on the titration behaviors of the reaction bases, the theoretical titration curve of the reaction base with the influence of CO2 was calculated using the modified Henderson–Hasselbalch (H–H) equation, previously developed in our laboratory, which is described as follows [26]: P Q Hþ ;tit ¼
Q A i
1þ½OH =Kb;A i
1 þ vH
vH
VBase þ1=½OH
2O
1=cHCl þ1=½OH
2O
vH
2O
þ vH
2O
VBase þ½OH =KW
1=cHCl þ½OH =KW
;
ð11Þ
where Q Hþ ;tit is the amount of added HCl titrant (in mmol), Q A is the quantity of the specific base component, A i , (in i mmol) in the reaction base, Kb;Ai is the base ionization constant of a base Ai , KW is the self-ionization constant of water, VBase is the volume of the reaction base, vH2 O is the molar volume of water, and cHCl is the concentration of the HCl titrant. The base components (A i ) associated with this study were the OH, CO2 3 , and HCO3 ions listed in order of their base strength. Different from the conventional H–H equation [27], the modified H–H equation is useful to estimate a titration behavior in the whole range of the titration [26]. When the modified H–H equation was applied to CO2 3 , a diprotic base, it was assumed that CO2 was divided into independent base 3 components and proton binding sites (Q CO2 = Q HCO3 ) with 3 individual common pKb values [26]. Applying the modified H–H equation, the titration behaviors of the reaction base NaOH (0.01 M, 10 mL, Q OH = 0.1 mmol) were calculated with the dissolution of different amounts of CO2 (Q CO2 = 0, 0.025, 0.05, 0.075 and 0.1 mmol), denoted Base a–Base e in order of the CO2 amount. The theoretical titration curves of Base a–Base e were drawn as la–le, respectively, in Fig. 3. la (Q CO2 = 0) shows the typical titration curve of an NaOH solution, and only a single NP from the OH ions exist at pH 7. To calculate the titration curve of Base b, in which Q CO2 is 0.025 mmol, the composition of each base component should
2 Fig. 2 – The calculated equivalence ratio of HCO 3 and CO3 ions in the reaction base at the equilibrium state with CO2.
3319
be calculated to apply the modified H–H equation. Q OH and in Base b can be set as 0.05 and 0.025 mmol QCO2 3 (0.05 meq), respectively, according to the well-known absorption reaction of CO2 in NaOH [23,24] as follows: CO2 ðaqÞ þ OH ðaqÞ ! HCO 3 ðaqÞ 2 HCO 3 ðaqÞ þ OH ðaqÞ ! CO3 ðaqÞ þ H2 OðlÞ : 2 2OH ðaqÞ þ CO2 ðaqÞ ! CO3 ðaqÞ þ H2 OðlÞ
ðStep 1Þ
As the NaOH is reacted with CO2, the titration curve begins to be distorted and the initial NP at pH 7 splits to make two NPs at pH 8 (NP1) and 5 (NP2), which are generally attributed and HCO to the neutralization of CO2 3 3 , respectively [22]. These kinds of behaviors were also observed in the real titration curves as shown in Fig. 1a. Q Hþ ;tit at NP1 indicates the summation of Q OH and Q CO2 , which implies both the CO2 3 3 and OH ions are neutralized at the same time since the pKb difference between the two ions would be not large enough [26]. And then, the remaining HCO 3 ions from the neutralization of the CO2 3 ions are neutralized to make clear the NP at Q Hþ ;tit = 0.1 mmol, which is the original base equivalence of the NaOH solution. It is noteworthy that the difference between the Q Hþ ;tit values at NP1 and NP2 in lb is exactly the same as the Q CO2 and Q CO2 initially set in Base b. The in3 CO2-titration curves of NaOH exposed to air for 0, 1, and 3 h in Fig. 1a show the titration profiles of the reaction bases at Step (1). In Base c (Q CO2 = 0.05 mmol), Q OH is exhausted according to the reaction in Step (1), and the base becomes exactly 0.005 M (0.01 N) Na2CO3 solution. The titration curve lc also exhibits the titration behavior of Na2CO3. From the equilibrium diagram shown in Fig. 2, it is reasonable to estimate that the composition of Base c, or the Na2CO3 solution, will change when it is exposed to CO2. In this case, ions are reported to mainly react with CO2 instead of CO2 3 OH ions and produce HCO 3 ions [25] as follows: CO2 3 ðaqÞ þ H2 O ðlÞ ! HCO3 ðaqÞ þ OH ðaqÞ
CO2 ðaqÞ þ OH ðaqÞ ! HCO 3 ðaqÞ CO2 3 ðaqÞ þ H2 O ðlÞ þ CO2 ðaqÞ ! 2HCO3 ðaqÞ:
ðStep 2Þ
Therefore, most of the base components in the reaction and base are converted into CO2 3 and HCO3 ions, and Q CO2 3 Q HCO3 in Base d (Q CO2 = 0.075 mmol) were set as 0.025 mmol (0.05 meq) and 0.05 mmol, respectively, to yield the curve ld. In the titration of Base d, the stronger base, CO2 3 ions, would ions and NP1 appears at be neutralized prior to the HCO 3 Q Hþ ;tit = 0.025 mmol, of which the amount is the same as ions are neutralized into HCO Q CO2 . At this state, as CO2 3 3 3 ions, the quantity of the remaining HCO 3 ions is 0.075 mmol and would result in NP2 at Q Hþ ;tit = 0.01 mmol when they are completely neutralized. The in-CO2-titration curves of NaOH exposed to air for 6 and 12 h in Fig. 1a, and all of those of Na2CO3 in Fig. 1b show the titration profiles of each reaction base at Step (2). If Q CO2 becomes 0.01 mmol (Base e), only HCO 3 ions would remain to make a pure NaHCO3 solution (0.01 M) and the resultant theoretical titration curve is le. However, this is not a spontaneous reaction because the reaction base would reach the equilibrium state with CO2 when the normality of HCO 3 ions becomes 0.0083 N as described in Fig. 2. On the other hand, le would shift toward ld when Base e, or 0.01 M
3320
CARBON
5 0 ( 2 0 1 2 ) 3 3 1 5 –3 3 2 3
Fig. 3 – (I) Theoretical titration curves and (II) their first order derivatives of 0.01 M NaOH (10 mL) reacted with different amounts of CO2.
NaHCO3, is exposed to air because more HCO 3 ions exist in pure NaHCO3 solution than those in the solution at the equilibrium state. The change of the composition of each base component in this case is followed by CO2 desorption of HCO 3 ion [25] as follows: 2 þ HCO 3 ðaqÞ ! CO3 ðaqÞ þ H ðaqÞ þ HCO3 ðaqÞ þ H ðaqÞ ! CO2 ðaqÞ þ H2 OðlÞ 2 2HCO 3 ðaqÞ ! CO3 ðaqÞ þ CO2 ðaqÞ þ H2 OðlÞ:
ðStep 2-Þ
The overall reaction can be considered as the reverse reaction of the reaction in Step (2); therefore, this step is denoted Step (2-). All of the titration curves of NaHCO3 in Fig. 1c show the titration profiles of the reaction bases at Step (2-). Based on these considerations, the theoretical titration curve of each experimental in-CO2-titration curve was calculated and drawn as the black solid lines in Fig. 1 with good coincidence between each other. In addition, the theoretical titration curve of each reaction base in the equilibrium state with atmospheric CO2 (denoted equilibrium curve) was calculated and drawn as the red dashed curve in Fig. 1. The experimental titration curves of each reaction base reached the equilibrium curve with an increase in the exposure time, which implies our theoretical approach related to the CO2 interactions with the reaction bases and the estimation of the titration curves by the modified H–H equation would be valid in the real case. Further, it is shown form Steps (1)–(2-) that the total base equivalence (the summation of the equivalence of OH , CO2 3 , and HCO3 ions) of each reaction base remains unchanged with the interaction of CO2 since the equivalence of the base is the same in the reactants and products, respectively, in the reaction in each step. The conservation of the base equivalence (eqB,pre) is revealed in the conservation of Q Hþ ;tit at NP2 both theoretically (Fig. 3) and experimentally (Fig. 1) regardless of the exposure of the reaction base to CO2. From this conservation, the precise measurement of eqB,pre of each reaction base is possible in the in-CO2-titration
system regardless of the exposure to air as shown in Table 2, which implies the exclusion and prevention of CO2 would not be necessary in the Boehm titration.
3.2. Comparison of the in-CO2-titration behavior with the ex-CO2-titration behavior For comparison, the ex-CO2-titration [11] was applied to each reaction base. Fig. 4 shows the titration curve of the acidified reaction base NaHCO3 in the ex-CO2-titration system (denoted ex-CO2-titration curve) as a function of the amount of OH ions from the dosed NaOH titrant (Q OH ;tit ) (the other acidified reaction bases, NaOH and Na2CO3, showed similar titration behaviors). The ex-CO2-titration curve shows almost a single inflection peak around pH 7, which implies that CO2 was almost expelled from the reaction base by the acidification. However, a magnified view shows that this peak splits into two inflection peaks at pH 5 (NP1 0 ) and pH 8 (NP2 0 ), which would be attributed to the neutralization of H2CO3 and HCO 3 , respectively [22], which come from the remaining CO2 in the reaction base even though the removal and prevention of the CO2 effect were adopted. In this case, Q OH ;tit at NP1 0 shows the exact acid equivalence (eqex_B,pre) of the acidified reaction base [11]. However, as the Q OH ;tit difference between NP1 0 and NP2 0 is rather narrow, the measurements of these NPs by the inflection measurement may not always ensure accuracy. For this reason, the pH-7-measurement has been usually utilized to determine the NP (NP7) [10,11], in which the neutralization is assumed to be completed at pH 7. If a highly precise measurement is not necessary, Q OH ;tit at NP7 is regarded as the eqex_B,pre rather than the Q OH ;tit at NP1 0 [11]. After eqex_B,pre is determined either by the inflection or pH-7-measurements, the equivalence (eqB,pre) of each pre-reaction base was calculated by Eq. (4) and compared to the eqB,pre obtained by the inflection measurement from the in-CO2-titration system in Table 2.
CARBON
3321
5 0 ( 20 1 2 ) 3 3 1 5–33 2 3
Table 2 – The base equivalence of each pre-reaction base (eqB,pre) determined by the different measurement methods of NP from in- and ex-CO2-titration. Titration method
In-CO2-titration Ex-CO2-titration
NP measurement method
Inflection point Inflection point The point at pH 7
Equivalence of the reaction base (meq) NaOH
Na2CO3
NaHCO3
0.10128 ± 0.00009 0.10122 ± 0.00006 0.10008 ± 0.00030
0.09957 ± 0.00005 0.09970 ± 0.00018 0.09887 ± 0.00022
0.09964 ± 0.00004 0.09974 ± 0.00002 0.09866 ± 0.00013
Fig. 4 – (a) Ex-CO2-titration curve and its first order derivative of the pre-reaction base NaHCO3, and (b) the magnified view around the NPs (blue dotted box in (a)). The results imply that both inflection measurements from the in- and ex-CO2-titration provide eqB,pre with high precision, which is comparable to that of a previous report [11]. However, the pH-7-measurement following the ex-CO2-titration resulted in the underestimation of eqB,pre because of a slight amount of CO2 remaining in the acidified reaction base. It is noteworthy that the in-CO2-titration system provides a simple but precise determination of the base equivalence.
3.3. Surface functionality of ox-MWCNTs as determined by in- and ex-CO2-titration The amount of each functional group on ox-MWCNTs was determined by applying both the in- and ex-CO2-titrations. Fig. 5 shows the variations of the in- (Fig. 5a) and ex(Fig. 5c) CO2-titration curves of the reaction base NaOH as it is reacted with ox-MWCNTs (Fig. 5b and d show the magnified view of Fig. 5a and c, respectively). NaOH uptake (nFG,NaOH), which indicates the quantity of all the functional groups of ox-MWCNTs [1], is presented in the figure with different measurements of the base or acid equivalence. The in-CO2-titration curve shifted entirely to the left (Fig. 5a) as the base equivalence of the reaction base decreased after the reaction. In addition, all of the in-CO2-titration curves showed two NPs, which indicates the CO2 effect [22]. In these cases, Q Hþ ;tit at the second inflection point (NP2) should be regarded as the base equivalence of the reaction base regardless of the CO2 effect. Therefore, nFG,NaOH was determined from the difference between Q Hþ ;tit at NP2 of the pre- and post-reaction base as described in Eq. (1). In the case of the ex-CO2-titration of ox-MWCNTs, the whole curve shifted to the right. Since the amount of HCl
for the acidification of the reaction base was the same, the reaction base with the lower base equivalence (pre-reaction base) had the higher acid equivalence when it was acidified, as described in Eq. (4). The difference of the acid equivalence between the pre- and post-reaction base (eqex_NaOH,pre and eqex_NaOH,post, respectively) indicates the nFG,NaOH as described in Eq. (5). The nFG,NaOH determined from the inflection measurements from the ex- and in-CO2-titrations (0.786 ± 0.007 and 0.790 ± 0.006 meq/g, respectively) was almost the same. Meanwhile, it seems that the nFG,NaOH was slightly overestimated by the pH-7-measurement from the ex-CO2-titration system (0.812 ± 0.027 meq/g), which is a result of the different tendency of CO2 expulsion by the acidification of each reaction base. The uptake of the rest of the reaction bases Na2CO3 and NaHCO3 was obtained by similar methods. Additionally, the number of each functional group on the ox-MWCNTs was calculated by Eqs. (2-1)–(2-3) and the results are listed in Table 3. All of the results listed in Table 3 show similar tendencies. However, the results from the pH-7-measurement following the ex-CO2-titration were slightly different from those from the inflection measurements because the tendency of CO2 expulsion by the acidification of each reaction base was different. On the other hand, a relatively high precision in the Boehm titration results was achieved with the in-CO2titration method compared to that in the results of the ex-CO2-titration method even though no treatments for CO2 expulsion or prevention were applied before and during the titration. Therefore, additional procedures such as acidification or protection of the reaction base by an inert-gas blanket to exclude the CO2 effect are not certainly necessary for the Boehm titration of carbonaceous materials.
3322
CARBON
5 0 ( 2 0 1 2 ) 3 3 1 5 –3 3 2 3
Fig. 5 – (I) Titration curves and (II) their first order derivatives of the reaction base NaOH from (a) the in- and (b) ex-CO2titration systems before and after the reaction with the ox-MWCNTs. (b and d) The magnified view around the NP of the titrations (blue dotted box in (a) and (c), respectively).
Table 3 – The number of each functional group on the ox-MWCNTs determined by the different measurement methods of NP from the in- and ex-CO2-titrations. Titration method
In-CO2-titration Ex-CO2-titration
4.
NP measurement method
Inflection point Inflection Point The point at pH 7
Number of functional group (meq/g) Carboxylic
Lactonic
Phenolic
Total
0.498 ± 0.016 0.494 ± 0.006 0.508 ± 0.017
0.222 ± 0.018 0.239 ± 0.024 0.263 ± 0.027
0.066 ± 0.010 0.058 ± 0.024 0.041 ± 0.033
0.786 ± 0.007 0.790 ± 0.006 0.812 ± 0.027
Conclusions
Atmospheric CO2 has been considered to cause a negative effect on determining the exact neutralization point and equivalence of the reaction base in the Boehm titration, and was thought to be removed or prevented using various additional procedures, which makes the Boehm titration complicated and inaccessible. However, it turns out unnecessary to
exclude CO2 to determine the equivalence of the reaction base because the position of the second inflection point indicating the equivalence of the reaction base remains unchanged even though the reaction base interacts with CO2. In addition, the surface functionality of acid-treated MWCNTs was determined with high precision applying the titration method including the CO2 effect. We believe our findings will help to establish an effective and simple Boehm titration method.
CARBON
5 0 ( 20 1 2 ) 3 3 1 5–33 2 3
Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MEST) [No. 2011-0029865].
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