Question

1M $\text{N}{{\text{H}}_{4}}\text{OH}$ and 1M $\text{HCl}$ are mixed to make a total volume of 300 ml. If the pH of the mixture is 9.26 and $\text{p}{{\text{K}}_{a}}(\text{NH}_{4}^{+})$= 9.26 then volume ratio of $\text{N}{{\text{H}}_{4}}\text{OH}$ and $\text{HCl}$ will be:
A. 1: 1
B. 1: 2
C. 2: 1
D. 3: 1

Answer 1

To solve this problem first we have to write the balanced chemical reaction between the $\text{N}{{\text{H}}_{4}}\text{OH}$ and $\text{HCl}$ and after it by applying the formula of pH we can measure the ratio of $\text{N}{{\text{H}}_{4}}\text{OH}$ and$\text{HCl}$.

Complete step by step answer:
- In the given, we have to find the correct ratio of $\text{N}{{\text{H}}_{4}}\text{OH}$ and $\text{HCl}$which makes the total volume of 300 ml when mixed.
- Firstly we have to write the balanced chemical reaction between $\text{N}{{\text{H}}_{4}}\text{OH}$ and $\text{HCl}$ that is:
$\text{N}{{\text{H}}_{4}}\text{OH + HCl }\to \text{ N}{{\text{H}}_{4}}\text{Cl}$

- Now, as we know that 1 M of $\text{N}{{\text{H}}_{4}}\text{OH}$ and $\text{HCl}$ are present so, let the concentration of hydrochloric acid at time zero is x and the concentration of $\text{N}{{\text{H}}_{4}}\text{OH}$ is $\text{(300 - x)}$.
- Now, after sometime when the product is formed, the concentration of $\text{N}{{\text{H}}_{4}}\text{Cl}$ and $\text{HCl}$ will be $\text{(300 - 2x)}\text{ and x}$ and the concentration of $\text{N}{{\text{H}}_{4}}\text{OH}$ is x.

- Now, we will apply the formula of pH that is:
$\text{pH = p}{{\text{K}}_{\text{a }}}+\text{ log }\dfrac{(\text{N}{{\text{H}}_{4}}\text{Cl)}}{(\text{N}{{\text{H}}_{4}}\text{OH})}$ …… (1)

- It is given in the question, that the value of pH and $\text{p}{{\text{K}}_{\text{a }}}$ is 9.26. So, by putting the value in the equation (1) we will get:
$\text{9}\text{.26 = 9}\text{.26}+\text{ log }\dfrac{(\text{x)}}{(300\text{ - 2x)}}$
$\text{log }\dfrac{(\text{x)}}{(300\text{ - 2x)}}\text{ = 0}$ or
$\dfrac{(\text{x)}}{(300\text{ - 2x)}}\text{ = 1}$ as log 10 = 1.
So, the value of x will be:
$\begin{aligned} & \text{x = 300 - 2x} \\\ & \text{x = 100} \\\ \end{aligned}$
- Thus, if the concentration of acid is 100ml then the concentration of base will be 300 - 100 = 200 ml.
So, the correct answer is “Option C”.

Note: The reaction between $\text{N}{{\text{H}}_{4}}\text{OH}$ and $\text{HCl}$ forms the product $\text{N}{{\text{H}}_{4}}\text{Cl}$ and the solution formed is known as a buffer solution. Because the buffer solution is a solution in which the weak base ( $\text{N}{{\text{H}}_{4}}\text{OH}$) and its weak salt that is ($\text{N}{{\text{H}}_{4}}\text{Cl}$) is present.