[HC03-1. Hence, using eqn. (1)
letters
[HCOI-][lO-o."
+ 1 + 10°.O"
=
[OH-]
(3)
Also, from the graph [H2C03]= [HCOa-] X 10-0.70 and [C032-] < [HC03-1, giving the mass balance of carbonate
Calculation of Hydrogen Ionic Concentrations
T o the Editor:
C = 10-7.D= IHCOa-][10-07 + 1 + 10-$1 (4 I would like to bring to the attention of the JOURNAL readership misimpressions concerning the so-called from which [HCOa-] = lO-'J/l.20 = 10-7J8. Ingraphical method for estimating [H+l contained in the serting this value in eqn. (3) article by F. S. Nakayama [J. CHEM.EDUC.,47, 67 10-7 08(2.3) = 10-14/[H+l (5) (1970)l. Proper application of the graphical method' to the or pH = 7.28 (computer value 7.23). problem is rapid, convenient, reliable, and rich in A few further moments of examination of the graphiinsight. ~ h u s : cal display of the Na,C03 system serves to reveal these The pH of a solution of C M Na2C03is rigorously additional insights. defined by the equation (proton balance) In solutions of concentrated NazCOa (C-1M) the extent of 2[H,CO,]
+ [HCO,-I + /Hi]
=
[OH-I
(1)
Graphical examination of this system as C varies, i.e., as the log a versus pH curves for carbonic acid is moved down along a log C versus pH grid2 quickly shows that for C equal to or greater than eqn. (1) can be simplified to IHC0.-1 = IOH-1
At 10-8 M r\Ta2COa,the graph shows log [H2COs]and log [H+] to be 1.6 and 2.0 logarithm units below log [HCOa-1, respectively. Hence theomission of [HzCo3] [H+]from eqn, (2) results in 5 and 10/,, or a total of 6% error. At M NazC03,a moment's perusal of the graph shows that log 2 [HzC03]is 0.5 log units below and log [H+] is 0.0 units below log
-
12.1). Tho extent of hydrolysis hydrolysis is about 1% (pH T h ~ srelainoreaws with the muare root of the dilution (C-'1. tionship starts to faiiat C 0.02 M (10% error). At eoncentrations of 4 X lW4M and lower, the predominant species of the system is HC0.-.
-
I t may be concluded, therefore, that the graphical technique, particularly when used in conjunction with the algebraic approach, is a rapid, convenient, and re-
' SILLEN,L. G., in "Treatise on Analytical Chemistry" (Editors: KOLTNOFF. I. M.. AND ELVING. P. .I.). Interscience (division of John Wiley & sons, Inc. j, ~ e ~wo r k ;1959, part I,' Vol, 1, chap. 8. FRF.ISER,H., A N D FERN.
