Question

Calculate the amount of ammonium chloride required to dissolved in $500\;mL$ water to have $pH = 4.5\left( {{K_b}\;{\rm{for}}\;N{H_4}OH = 1.8 \times {{10}^{ - 5}}} \right)$.

Answer 1

As we know that, ammonium chloride is a compound of ammonia and ammonium hydrogen chloride. We can determine the pH value by using the formula.
$pH = \dfrac{1}{2}\left( {p{K_W} - \log C - p{K_b}} \right)$

Complete step by step solution
According to the question ammonium chloride requires dissolving in $500\;ml$ and its pH value is given.
As we know that $N{H_4}Cl$ is a salt of weak base and strong acid. Using the formula, we can get the valve of ammonium chloride to dissolve. This formula represents the relation between the pH and $p{K_b}$.Here $p{K_w}$ is the water autoionization, and $p{K_b}$ is the base dissociation. On substituting these values, we can find the pH value.
$pH = \dfrac{1}{2}\left( {p{K_W} - \log C - p{K_b}} \right)\\\ \Rightarrow 4.5 = \dfrac{1}{2}\left[ {14 - \log C + \log \left( {1.8 \times {{10}^{ - 5}}} \right)} \right]\\\ \Rightarrow9 = 14 - \log C - 4.74\\\ \Rightarrow \log C = 0.26........................................(1)\\\ \Rightarrow C = \dfrac{x}{{26.25}},\;{\rm{where,}}\;\dfrac{{{\rm{Mass}}\;{\rm{of}}\;{\rm{ammonium}}\;{\rm{chloride}}}}{{\rm{2}}} = \dfrac{{52.5}}{2} = 26.25$
Where x is the amount of $N{H_4}Cl$ dissolved in $500\;ml$ of water. When we take both side log we get value of log C, putting the value of log C in equation 2 we get,
$\log \;c = \log \left( {\dfrac{x}{{26.25}}} \right)..........................................(2)$
Here we find the value of log c, on solving these we can find the value of x. Which is the amount of $N{H_4}Cl$ dissolved in $500\;ml$ of water.
$\Rightarrow \log \left( {\dfrac{x}{{26.25}}} \right) = 0.26\\\ \Rightarrow \log x - \log 26.25 = 0.26\\\ \log x = 0.26 + 1.4191 = 1.6791\\\ \Rightarrow x = Anti\log \left( {1.6791} \right)\\\ \Rightarrow x = 47.76$
Therefore, the amount of $N{H_4}Cl$ dissolved is $47.76\;g$.
$N{H_4}Cl$ Solution is acidic in nature because it reacts with water and produces ammonium hydroxide and hydrochloric acid. Ammonium hydroxide is a weak base. So it is partially ionized in aqueous solution and $HCl$ is a strong acid, As a result, in the solution the number of ${H^ + }$ ions are more than $O{H^ - }$ ions.
We know that the acidic and basic property of substances is measured in terms of pH. It is a measurement of the hydrogen ion concentration. And we know that it is a negative log of hydrogen ion concentration.

Note:
We know that when ammonium chloride is dissolved in water it decomposes in its ion like $N{H_4 }^+ \;and\;C{l^ - }$. It can back in crystallization form.