Question

Addition of sodium hydroxide to a weak acid $\left( {HA} \right)$ results in a buffer of $pH6$. If the ionization constant of $HA$ is ${10^{ - 5}}$, the ratio of salt to acid concentration in buffer solution will be?

Answer 1

Hint: Initially, this question gives us the knowledge about the buffers and how its solutions are related to the acidity and basicity of the compounds. Buffer solution is a solution which resists any change when a small amount of acid or bases are added to it.

Formula used: The formula used to determine the $pH$ of a solution containing salt and an acid is as follows:
$pH = p{K_a} + {\log _{10}}\dfrac{{\left[ S \right]}}{{\left[ A \right]}}$
Where $p{K_a}$ is the dissociation constant, $S$ is salt concentration and $A$ is the acid concentration.

Complete step-by-step answer:
Buffer solution is a solution which resists any change when a small amount of acid or bases are added to it. Basically a buffer solution is the mixture of weak acid and its conjugate base. Whenever a little amount of acid or a base is added to the solution its $pH$ doesn’t change much. $pH$ is defined as the negative logarithm of the hydronium ion. The $pH$ of acids is less than seven and for bases it is more than seven.
The ionization constant of $HA$ is ${10^{ - 5}}$.
Now, Convert ionization constant into the dissociation constant $p{K_a}$ as follows:
$ \Rightarrow p{K_a} = - \log {K_a}$
Substitute the value of ${K_a}$
$ \Rightarrow p{K_a} = - \log \left( {{{10}^{ - 5}}} \right)$
On solving, we have
$ \Rightarrow p{K_a} = 5$
Then, to determine the ratio of salt to acid concentration in buffer solution we will use the$pH$ and other given quantities as follows:
$ \Rightarrow pH = p{K_a} + {\log _{10}}\dfrac{{\left[ S \right]}}{{\left[ A \right]}}$
Where $pH$ is $6$, $p{K_a}$ is $5$
$ \Rightarrow 6 = 5 + {\log _{10}}\dfrac{{\left[ S \right]}}{{\left[ A \right]}}$
On solving, we have
$ \Rightarrow 1 = {\log _{10}}\dfrac{{\left[ S \right]}}{{\left[ A \right]}}$
On taking antilog on both sides, we have
$ \Rightarrow \dfrac{{\left[ S \right]}}{{\left[ A \right]}} = \dfrac{{10}}{1}$
Therefore, the ratio of salt to acid concentration in buffer solution is $10:1$.

Note: Basically buffer solution is the mixture of weak acid and its conjugate base or vice versa. Whenever a little amount of acid or a base is added to the solution its $pH$ doesn’t change much. The $pH$ of acids is less than seven, for bases it is more than seven and for neutral compounds it is always seven.