technically it is not homework, more like struggling with textbook material, but something tells me it would end up here anyway so here it is :(adsbygoogle = window.adsbygoogle || []).push({});

there's something about the method that gives me different results using different paths so i'm going to show both of them and see if you can spot the error in my thinking

let's say i want to find the pH of the solution of, say, 0.004 M HCOONa, given that for HCOOH [tex] K_a = 1.8\times10^{-4} [/tex]

For the reaction

[tex] HCOOH \rightleftharpoons H^+ + HCOO^- [/tex] the constant is [tex] K_a = \frac{[H^+][HCOO^-]}{[HCOOH]} [/tex]

standard procedure of writing the initial and final concentrations

[tex]

\begin{array}{| c|c|c |} \ [HCOOH]&[H^+]&[HCOO^-]\\

\hline

\0&10^{-7}&0.004\\

\hline

x&10^{-7}-x&0.004-x\\

\hline

\end{array}

[/tex] which gives [tex] K_a = \frac{(10^{-7}-x) (0.004-x)}{x} = 1.8 \times 10^{-4} [/tex]

solving for x gives [tex] x = 9.569 \times 10^{-8} [/tex] so [tex] [H^+] = 10^{-7} - x = 4.32 \times 10^{-9} [/tex] and [tex] pH = 8.366 [/tex] which sounds OK for HCOONa solution

the textbook, however, insists on treating the [tex] HCOO^- [/tex] as the conjugate base of HCOOH and using the following reaction

[tex] HCOO^- + H_2 O \rightleftharpoons HCOOH + OH^- [/tex] and its basicity constant [tex] K_b = \frac{[HCOOH][OH^-]}{[HCOO^-]} [/tex]

(noting that [tex] K_a \times K_b = \frac{[H^+][HCOO^-]}{[HCOOH]} \times \frac{[HCOOH][OH^-]}{HCOO^-]} = [H^+] [OH^-] = K_w [/tex] so [tex] K_b = \frac{10^{-14}}{1.8 \times 10^{-4}} = 5.56 \times 10^{-11} [/tex]

and once again the concentrations

[tex]

\begin{array}{| c|c|c |} \ [HCOO^-]&[HCOOH]&[OH^-]\\

\hline

\0.004&0&10^{-7}\\

\hline

0.004-x&x&10^{-7}+x\\

\hline

\end{array}

[/tex] from which [tex] K_b = \frac{x (10^{-7}+x)}{0.004-x} = 5.56 \times 10^{-11} [/tex]

here the x is found as [tex] x = 4.240 \times 10^{-7} [/tex], therefore [tex] [OH^-] = 10^{-7} + x = 5.24 \times 10^{-7} [/tex] so [tex] pOH = 6.281 [/tex] and [tex] pH = 14 - pOH = 7.719 [/tex]

as you notice the two results (8.366 and 7.719) are too different to call them equivalent

so

any ideas ?

-- o, and why does my LaTeX appear on white background ?

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# Homework Help: Finding pH using acidity/basicity constants

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