Question

Calculate the amount of $N{H_3}$ and $N{H_4}Cl$ required to prepare a buffer Solution of $pH$ $9.0$ when total concentration of buffering reagents is $0.6mol{L^{ - 1}}$. $p{K_b}$ for $N{H_3} = 4.7,\log 2 = 0.30$

Answer 1

Hint: $pOH + pH = 14$. Therefore, if we know the value of one, the other can be found out just by subtracting it from 14. Ammonium chloride is the salt of the reaction between ammonium hydroxide, a base, and hydrochloric acid, an acid. A buffer Solution, also commonly referred to as a $pH$ buffer or hydrogen ion buffer, is an aqueous Solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. The $pH$ change in a buffer Solution is very negligible when a small amount of strong acid or base is added to it.

Formulae used: $pOH = p{K_b} + \log \dfrac{{[Salt]}}{{[Base]}}$
Where $pOH$ is the negative log of the concentration of hydroxyl ions, $p{K_b}$ is the negative log of the base dissociation constant and $[Salt],[Base]$ are the respective concentrations of the salt and the base present in the buffer Solution.

Complete step by step answer:
From the following equation, we have a relation between $pOH$ and $pH$:
$pOH + pH = 14 \Rightarrow pOH = 14 - pH$
As we know that the buffer Solution should have a $pH$ of 9, its $pOH$ value is:
$pOH = 14 - 9 = 5$
Substituting this in our equation for $pOH$, we get:
$5 = 4.7 + \log \dfrac{{\left[ {Salt} \right]}}{{[Base]}}$
Simplifying the above result, we get:
$\log \dfrac{{[Salt]}}{{[Base]}} = 5 - 4.7 = 0.3$
But we have already been given that $0.3 = \log 2$
$ \Rightarrow \dfrac{{[Salt]}}{{[Base]}} = 2 \Rightarrow [Salt] = 2 \times [Base]$ (1)
The total concentration of the buffering reagents, as given in the question is $0.6$. Therefore,
$[Salt] + [Base] = 0.6$ (2)
Substituting equation 1 in equation 2, we get:
$3 \times [Base] = 0.6 \Rightarrow [Base] = 0.2$
Substituting this value in equation 1, we get:
$[Salt] = 2 \times 0.2 = 0.4$
Thus, the concentrations required are:
$
 N{H_3} = 0.2mol/L \\
 N{H_4}Cl = 0.4mol/L \\
 $

Additional Information: ${K_a},p{K_a},{K_b}$and $p{K_b}$ help us to predict whether a given species will accept or donate protons at the specified $pH$ level. They give us information about the degree of dissociation of an acid or base. ${K_a}$ and $p{K_a}$ relate to acids, while ${K_b}$ and $p{K_b}$ deal with bases. They give us relationships between the concentrations of hydrogen ions and hydroxyl ions, which are measurable quantities. Finding out these values can be of great importance in industries, where even a slight change in these quantities can lead to a drastic change in output.

Note: Buffer Solutions have the tendency to resist the changes in $pH$. Acidic buffers are made from weak acids, and a corresponding salt, while basic buffers, like in this question, are made from a weak base and its corresponding salt. Always remember that we have to take the negative logarithm. Like the $pOH$ equation, many others are there which describe various interdependencies. And it is important to identify in each question, which is the base and salt, so that the right concentration terms (whether to use acid concentration or base concentration) can be applied.