Question

Calculate the $pH$ of a 0.033 M ammonia solution, if 0.033M $N{H}_{4}Cl$ is introduced in this solution at the same temperature. ( $k_b$ for $N{H}_3=1.77\times {10}^{-5}$).

Answer 1

To calculate the pH of the solution containing ammonia and $N{H}_{4}Cl$, we will use the Handerson Hasselbach equation.

According to this equation,

$pOH=p{K}_b+log\frac{\left[salt\right]}{\left[base\right]}$

where, $p{K}_b$ is to be calculated from $K_b$.

$K_b$ for $N{H}_3$ $=1.77\times {10}^{-5}$

$p{K}_b=-log{K}_b=-log(1.77\times {10}^{-5})=4.75$

$\left[Salt\right]=\left[N{H}_{4}Cl\right]=0.033M$

$\left[Base\right]=\left[NH3\right]=0.033M$

When we put all these values in the equation,

$pOH=4.75+log\frac{\left[salt\right]}{\left[base\right]}$

$=4.75+log\left(1\right)=4.75+0=4.75$

$pOH=4.75$

$pH=14-4.75=9.25$

$pH=9.25$

$pH$ of the solution $=9.25$