Question

A solution of formic acid (HCOOH, ${\mathbf{K}}_a=\mathbf{1}.\mathbf{8}\times {\mathbf{10}}^{-\mathbf{4}}$) has a pH of 2.70. Calculate the initial concentration of formic acid in this solution.

Short answer

The initial concentration of formic acid is $2.42\times {10}^{-2}$.

Step-by-step solution

 [H+] of HCOOH

H⁺ ion concentration can be calculated as:

${\text{[H}}^{+}\text{]}={10}^{-\text{pH}}={10}^{-2.70}=2\times {10}^{-3}$

Initial Concentration of HCOOH

HCOOH dissociates in water as:

$\begin{array}{l}{\text{HCOOH+H}}_{\text{2}}\text{O\hspace{1em}}\rightleftharpoons {\text{\hspace{1em}H}}_3{\text{O}}^{\text{+}}{\text{+HCOO}}^{\text{-}}\\ \mathrm{a}00\\ \mathrm{a}-\mathrm{x}2\times {10}^{-3}\mathrm{x}\end{array}$

$\begin{array}{l}{\mathrm{K}}_{\mathrm{a}}=\frac{{\mathrm{x}}^2}{\mathrm{a}-\mathrm{x}}=\frac{{(2\times {10}^{-3})}^2}{\mathrm{a}-(2\times {10}^{-3})}=1.8\times {10}^{-4}\\ 4\times {10}^{-6}=1.8\times {10}^{-4}\mathrm{a}-3.6\times {10}^{-7}\\ \mathrm{a}=\frac{4.36\times {10}^{-6}}{1.8\times {10}^{-4}}=2.42\times {10}^{-2}\end{array}$

As a is the initial concentration, the initial concentration of formic acid is$2.42\times {10}^{-2}$.