I
U. S. Water Conservation
Laboratory Agricultural Research Service, USDA Phoenix, Arizona 85040
Hydrolysis of Sodium Carbonate
Estimation of the pH of sodium carbonate solution is frequently used to demonstrate the principle and concepts of salt hydrolysis. The ion concentrations are determined by mathematical or graphical approximatioll (1-5) using appropriate simplifying assumptions so that only straightforward arithmetical manipulations are necessary. One is left with the impression, however, that an exact method cannot be applied to the hydrolysis of sodium carbonate to solve the concentrationof the various component species in solution. I n this presentation, a procedure for obtaining the ion concentrations will be presented and compared with the other approximation methods. The analysis of Na2C03hydrolysis requires a combination of the following relationships for C moles of material, depending on the method of solution used
for
-
& - K=, KPA
[OH-] [HCOa-1 [OH-Is [COa'-I - [C0s2-I
(11)
Substituting the relationship for [OH-] from (7) into ( n ) , and assuming negligible hydrolysis, i e . , implying that [COa2-] = C, a new relationship is obtained such that [Ht]
=
(K%*K,/C)'h
(12)
for which the pH can be readily estimated as Method 8. If hydrolysis occurs to any significant extent, the original concentration of carbonate cannot he used as it stands. The concentration of COaZ- will be less than C and in this case [COsZ-] = [C - HCO3-] or since we are assuming [HCOa-] = [OH-], [C0a2-] = C - [OH-]. Substituting this improved C - [OH-] instead of [C03-] and also [OH-] relation from (7) into ( l l ) , the new estimate for [H+]is obtained as
Charge Balance
[Na+]
+ [ H C ] = [HCOs-I + 2[COsn-I + [OH-]
(3)
Proton Balance
[H+]
+ 2[H&Oa1 + [HCOs-I
=
[OH-]
(4)
Equilibrium Constants (5)
(6) (7)
(8) Hydrolysis Reaction
CO? HCOs-
+ H 2 0 = HCOI- + O H + HzO = H E O s + O H -
This relation appears more formidable than (12), but nevertheless solvable in a straightforward manner. Method 3. The graphical technique for resolving equilibrium data (6) provides another method for estimating [Hf]. Complete details are also presented by Bard (I), Butler (Z), Freiser and Fernando (3), and Margolis (4), so they will not be repeated here. With this technique, an essential consideration is that we assume that [HCOa-] = [OH-]. It thus follows from the proton balance eqn. (4),that H + and H2C03concentrations must be negligible in relation to [HC03-] and [OH-]. Consequently, the pH of the NapCOasolution is estimated at the intersection of the [OH-] and [HCOs-] curves in the graphical analysis. Atethod 4. The three preceding methods are reliable for the wH of the more concentrated Na2C03 - ~ calculatin~ -~~ solution. However, with less concentrated solutions, the percent of hydrolysis will increase, the pH will decrease, and the hydrolysis reaction represented by (10) cannot then be ignored. Furthermore, the estimate of the component concentrations (HC03-, C0a2-, HzCOa) is less reliable because of the simplifying assumptions made in order to calculate [H+]. To overcome these shortcomings, and to check on the accuracy of the preceding methods, the digital computer technique for chemical equilibrium calculations proposed by Bard and Icing (6) was adapted for Na2CO3 hydrolysis with the necessary transposition from their Fortran language to one compatible to the General Electric 235 digital computer. I n brief, eqns. (1) and (3) are rewritten as ~~
(9)
(10)
I n all cases to follow, it has been assumed that: total carbonate is constant; K values remain constant; concentrations and activities are the same; and complexes such as NaC03- are absent. Procedure
Method 1. I n this method, which is the simplest and most frequently used example in elementary textbooks, it is assumed that the reaction described by eqn. (9) is dominant and (10) is negligible, and also that [HCOa-] = [OH-]. The equilibrium describing eqn. (9) is
~
- .
Volume 47, Number 1, January 1970
~
/
67
Y ( l ) = [H,COsI Y(2) = [HCOI-]
+ [HCOa-I + [COs2-I - C
(15)
+ 2[COaa-] + [OH-] - [Nat1 - [H+l
(16)
The method involves initial guesses of [H+] and the least concentrated species to get the computational process started. I n this case, at the high pH's a guess of the HZC03concentration instead of [HCOg-I and [C032-]is appropriate, whereas at the low pH's a guess of the COa2-in place of [HC08-] and [HzCO~] is made. By using the mass and charge balance equations together with the dissociation constants (KIA,K ~ AK,w ) , the computer is programmed to minimize the difference between Y(l) and Y(2) by an appropriate and systematic change in [H2C031or [C032-] and [ H f ] by an iteration procedure. Details for the technique involving a hypothetical acid dissociation are adequately discussed by Bard and King (6). Results and Discussion
The pH's of Na2CO3solutions at diierent concentrations estimated by the four methods are compared in Table 1. Table 1. OH Values of Various NonCOa Solution ~oncentro'tionsObtained by Different Methods
Conc. NalCOa (M)
Method 1
2
vH
pH
3 VH
4 pH
centrations are compared for Methods 2 and 4. The greater hydrolysis of Na2C03a t lower concentrations will affect Method 1 because its derivation requires the assumption that hydrolysis is negligible and not corrected for. On the other hand, Methods 2 and 3 agree well with 4, because the assumption that [OH-] = [HC03-I holds throughout most of the Na2COaconcentration ranges as shown by the [OH-] and [HC03-] values calculated from Method 4 in Table 2. At the very low concentrations of Na?C08 (lo-' M), the dissociation of water will affectthe calculation procedure in all cases. Methods 2 and 4 are more convenient than the graphical technique (Method 3), since they provide a direct method for estimating concentrations of carbonate components. Thus, in essence, Methods 2 and 3 provide suitable means for predicting hydrolysis of salts, but the digital computer analysis of hydrolysis used in conjunction with these methods provides us with a better insight into the hydrolysis process and into the reliability of the assumptions made for simplifying some of the computational procedures. Furthermore, it is apparent that this numerical method gives concentration relations of the different components that are more reliable than the others since assumptions on the degree of hydrolysis, equality of OH- and HC03-, and single estimates of [COs2-I or [HZC03Jare not made. Of course, the method cannot be used in many undergraduate courses, but its results may he used as a standard for comparison. Literature Cited (1) BARD,A. J., "Chemical Equilibrium," Harper & Row, New York, 1966, p. 134. (2) BUTLER,J. N., "Ionic Equilibrium-A Mathematictical A p proitch," Addison-Wesley, Reading, Mass., 1964, p. 221.
The pH values estimated by Methods 2, 3, and 4 are comparable at all N&COa concentrations. Values estimated by Method 1 are in good agreement with those estimated by the other methods at the higher NapCOaconcentrations, but not a t the lower concentrations. The reason for the poor agreement between Method 1 and the others is illustrated in Table 2 , where the concentrations of the different components and the degree of hydrolysis of Na2C03at various solution conTable 2.
Cone.
NaCOa
(3) FREISER,IT., AND FERNANDO, Q., "Ionic Equilibria in Analytical Chemist,ry," John Wiley & Sons, Inc., New York, 1966, p. 101. (4) MARGOLIS, E. J., "Chemical Principles in Ca.lculations of Ionic Equilibria," MacMillan, New York, 1966, p., 42. 15) , , SILLBN.L. G.. in "Treatise on Anahtical Chemistrv." ~ d i l d r s : KO~THOFF, I. M., ELVINO,P, J., AND SANDEL, E. B., Part 1,Vol. 1,Interscience Publishers (division of John Wiley & Sons, Inc.), New York, 1964, Chap. 8. (6) B ~ R DA. , J., A N D KING,D. M., J. CAEM.EDUC.,42, 127 (1965).
Carbonates and Hydroxyl Concentrations, and Degree Hydrolysis of Na2C03 Estimated by Methods 2 and 4
--
2
[COa>-1-
4
68 / Journal of Chemicol Education
-[HCOI-12
4
PHICOI-
2
4
-----[OH-]2
Hydrolysis 4
2
(%I4
