Chapter 18, Problem 7STP

Interpretation Introduction

Interpretation:

$\mathrm{pH}$ of cyanoacetic acid is to be calculated for given concentration.

Concept introduction:

pH gives the concentration of hydrogen ion in a solution.

It tells about acidity and basicity of a solution.

It is given by:

$\begin{array}{l}pH=-\log \left[H^{+}\right]\\ \left[H^{+}\right]isconcentationofhydrogenions\end{array}$

Answer to Problem 7STP

D

Explanation of Solution

Cyanoacetic acid has one replaceable hydrogen ion.

Therefore,

$\begin{array}{l}CNC{H}_{2}COOH\rightleftharpoons CNC{H}_{2}CO{O}^{-}+H^{+}\\ Therfore,\\ k_a=\frac{\left[CNC{H}_{2}CO{O}^{-}\right]\left[H^{+}\right]}{\left[CNC{H}_{2}COOH\right]}\\ k_a=\frac{{\left[H^{+}\right]}^2}{\left[CNC{H}_{2}COOH\right]}\\ {\left[H^{+}\right]}^2=k_a\times \left[CNC{H}_{2}COOH\right]\end{array}$

Given data:

$\begin{array}{c}\left[CNC{H}_{2}COOH\right]=0.40\\ k_a=3.55\times {10}^{-3}\\ \left[H^{+}\right]=\sqrt{3.55\times {10}^{-3}\times 0.40}\\ =0.038M\end{array}$

$\begin{array}{c}pH=-\log 0.038\\ =1.42\end{array}$

Conclusion

Thus $pH$ is 1.42. So option D is correct.