Question

A weak mono acidic base is $5\%$ ionized in $0.01{\text{M}}$ solution. The hydroxide ion concentration in the solution is
(A) $5 \times {10^{ - 2}}$
(B) $5 \times {10^{ - 4}}$
(C) $5 \times {10^{ - 10}}$
(D) $2 \times {10^{ - 11}}$

Answer 1

To determine the hydroxide ion concentration, we need to know the species in which the weak monoacidic base will dissociate. We also need to know the concentration in terms of given concentration and degree of dissociation for the reactants and products at the beginning and at the equilibrium state of the reaction.

Complete step by step solution: To calculate the concentration of hydroxide ion in the solution produced by the dissociation of a weak mono acidic base, let us first take ${\text{XOH}}$as our weak monoacidic base.
So, ${\text{XOH}}$upon dissociation will produce ${{\text{X}}^ + }$ion and ${\text{O}}{{\text{H}}^ - }$ion.
$XOH \to {X^ + } + O{H^ - } - - - (i)$
Now, according to the question, initial concentration (c) of ${\text{XOH}}$is given as $0.01{\text{M}}$ and the degree of dissociation($\alpha$) as $5\%$.
Here, the degree of dissociation is the fraction of the given acid or base that has dissociated into its respective ions. For weak acid or base, its value is always less than 1.
So, now we can write reaction (i) as,

| $XOH$| ${X^ + }$| $O{H^ - }$
---|---|---|---
Initial Concentration| c| 0| 0
Equilibrium Concentration| $c - c\alpha$| $c\alpha$| $c\alpha$

Hence, the concentration of hydroxide ion produced is given by ${\text{c}}\alpha$ which can be represented as, $\left[ {O{H^ - }} \right] = {\text{c}}\alpha$ Since, $c = 0.01M$ and $\alpha = 5\%$or $\dfrac{5}{{100}}$
So,

$${\text{ }}\left[ {O{H^ - }} \right] = 0.01 \times \dfrac{5}{{100}} \\\ \Rightarrow \left[ {O{H^ - }} \right] = 5 \times {10^{ - 4}}{\text{M}} \\\$$

Therefore, when a weak monoacidic base dissociates with a degree of dissociation of $5\%$ in a $0.01{\text{M}}$ solution, concentration of hydroxide ion produced is $5 \times {10^{ - 4}}{\text{M}}$.

Hence, option (B) $5 \times {10^{ - 4}}{\text{M}}$ is the correct answer.

Additional Information: If the question asks us to calculate the concentration value at equilibrium of ${{\text{X}}^ + }$ or ${\text{XOH}}$, same concept has to be used for its calculation. Here, we can write the concentration of ${{\text{X}}^ + }$as ${\text{c}}\alpha$ and concentration of ${\text{XOH}}$ as ${\text{c}} - {\text{c}}\alpha$.

Note: During the calculation of concentration of ions so produced or reactant as mentioned in the question, students should remember to properly write the ionic species in which the reactant is dissociating with proper concentration terms. Sometimes the initial concentration of the given acid or base is not given, in that case we can take its concentration as $1{\text{M}}$.