Question

What is the pH of a buffer system that contains 0.170 M hydrocyanic acid (HCN) and 0.140 M sodium cyanide (NaCN)? The$p{{K}_{a}}$of the hydrocyanic acid is 9.21.

Answer 1

As we know that a buffer solution is an aqueous solution that consists of a mixture of a weak acid and
its conjugate base or a mixture of weak base and its conjugate acid. Also the pH of buffer solution changes very little when a minute amount of strong acid or base is put in the solution.
Formula used:
We will use the following formula:-
$pH=p{{K}_{a}}+\log \dfrac{\text{ }\\!\\![\\!\\!\text{ salt or conjugate base }\\!\\!]\\!\\!\text{ }}{\text{ }\\!\\![\\!\\!\text{ weak acid }\\!\\!]\\!\\!\text{ }}$

Complete answer:
Let us first understand the concept of buffer solution followed by the calculation of pH of the buffer system:-
-We know that buffer solution is an aqueous solution that consists of a mixture of a weak acid and its conjugate base or a mixture of weak base and its conjugate acid. Also the pH of buffer solution changes very little when a minute amount of strong acid or base is put in the solution.
-As we can see that in the given information sodium cyanide (NaCN) is the salt and hydrocyanic acid (HCN) is the weak acid. So the values of their concentration present in the buffer system are as follows:-
Concentration of sodium cyanide (salt) = 0.140 M
Concentration of hydrocyanic acid (weak acid) = 0.170 M
It is given that $p{{K}_{a}}$of the hydrocyanic acid = 9.21
-Calculation of pH of the buffer system:-
$\begin{aligned} & \Rightarrow pH=p{{K}_{a}}+\log \dfrac{\text{ }\\!\\![\\!\\!\text{ salt or conjugate base }\\!\\!]\\!\\!\text{ }}{\text{ }\\!\\![\\!\\!\text{ weak acid }\\!\\!]\\!\\!\text{ }} \\\ & \Rightarrow pH=9.21+\log \dfrac{0.140M}{0.170M} \\\ & \Rightarrow pH=9.21+(-0.084) \\\ & \Rightarrow pH=9.13 \\\ \end{aligned}$
-Hence, 9.13 is the pH of a buffer system that contains 0.170 M hydrocyanic acid (HCN) and 0.140 M sodium cyanide (NaCN).

Note:
-For solving such types of questions you need to learn and understand the concept of buffer solutions and equilibrium.
-Remember to use the concentration terms carefully and along with the units so as to get the minimum error result.