# What is the pH of a millimolar solution of ammonium hydroxide which is 20 % dissociated?(A) 3.699(B) 10.301(C) 4.691(D) 9.301

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Hint:. We know that ammonium hydroxide is the weak base, therefore $O{H^ - }$ ions will dissociate partially. From the data given in the question we can calculate the concentration and degree of dissociation of $O{H^ - }$ ions. Later by using the relationship to pH and pOH we can easily calculate pH of a millimolar solution of ammonium hydroxide which is 20% dissociated.

Complete step by step answer:
In the question they have asked us to find the pH of millimolar solution of ammonium hydroxide which is 20 % dissociated.
Let us start finding the concentration of the $N{H_4}OH$ solution. It has been shown that $N{H_4}OH$ is present in millimolar concentration.
$N{H_4}OH = 0.001M$……. (1)
The ammonium hydroxide is a weak base, so $N{H_4}OH$ will dissociate as $O{H^ - }$ ions partially.
The degree of dissociation of $N{H_4}OH$ is 20 %
degree of dissociation $= 20\% = \dfrac{{20}}{{100}} = 0.2$……. (2)
From the above value concentration of $O{H^ - }$ions can be calculated
${\text{Concentration of O}}{{\text{H}}^{\text{ - }}}{\text{ = Concentration of solution}} \times {\text{degree of dissociation}}$
$[O{H^ - }] = 0.001 \times 0.2 = 2 \times {10^{ - 4}}$…… (3)
We know that water has pOH = 7
Therefore, the concentration of $O{H^ - }$ ions will be
$pOH = - \log [O{H^ - }]$……... (4)
$7 = - \log [O{H^ - }]$
$[O{H^ - }] = {10^{ - 7}}$….…... (5)

- To find the total concentration of $O{H^ - }$ we should add equation (3) and (5)
$total [O{H^ - }] = (2 \times {10^{ - 4}}) + {10^{ - 7}}$
$total [O{H^ - }] = {10^{ - 4}}(2 + 0.001)$
$total [O{H^ - }] = 2.001 \times {10^{ - 4}}$
- Substituting $[O{H^ - }]$ in equation (4)
$pOH = - \log (2.001 \times {10^{ - 4}})$
$pOH = 3.6988$
pH can be calculated using the equation
$pH = 14 - pOH$…… (6)
$pH = 14 - 3.6988$
$pH = 10.301$
The pH of a millimolar solution of ammonium hydroxide which is 20 % dissociated is 10.301.
So, the correct answer is “Option B”.

Acids and bases are measured using pH or pOH scale. This scale provides the measure of ${H^ + }$ or $O{H^ - }$ ion concentration.