Question

The weak acid, HA has a ${{K}_{a}}$ of $1\times {{10}^{-5}}$ . If 0.1 mol of this acid is dissolved in
one litre of water, the percentage of acid dissociated at equilibrium is closest to:
a.) 1%
b.) 99.9%
c.) 0.1%
d.) 99%

Answer 1

Hint: An acid is a substance which dissociates in aqueous solution. We can write the equation of dissociation as- \[HA={{H}^{+}}+{{A}^{-}}\] .
For calculating the percentage of an acid dissociated you can divide the mass of dissociated ions by the total mass of dissociated and undissociated species and then multiply by 100 percent and thus you will get the required percentage.

Complete step by step answer:
The acid dissociation constant $\left( {{K}_{a}} \right)$ or the ionization constant is the measure of the strength of acid in a solution.
The dissociation constant can be given by-
\[{{K}_{a}}=\dfrac{[{{H}^{+}}][{{A}^{-}}]}{[HA]}\]
Now in the given question, the initial concentration of HA is 0.1 mol/L, suppose the initial concentration of \[{{H}^{+}}\] and \[{{A}^{-}}\] is x. Therefore, we can write that-
\[\begin{align}
  & HA={{H}^{+}}+{{A}^{-}} \\
 & initial\,\,\,\,0.1\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,x \\
\end{align}\]

At equilibrium the concentration will be-
\[\begin{align}
 & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,HA={{H}^{+}}+{{A}^{-}} \\
 & equilibrium\,\,\,\,0.1-x\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,x \\
\end{align}\]
 $x=\dfrac{HA\,(dissociated)}{HA\,(undissociated)}$ = Degree of dissociation.

Given here, ${{K}_{a}}={{10}^{-5}}$
Using the relation, \[{{K}_{a}}=\dfrac{[{{H}^{+}}][{{A}^{-}}]}{[HA]}\] , we can write that-
\[{{10}^{-5}}=\dfrac{x\times x}{0.1-x}\]
Since, it’s a weak acid therefore dissociation is less and x <<< 0.1 so it can be neglected. Therefore, we can write that-
\[\begin{align}
 & {{10}^{-5}}=\dfrac{{{x}^{2}}}{0.1} \\
 & {{10}^{-4}}={{x}^{2}} \\
 & x={{10}^{-2}} \\
\end{align}\]

Therefore, we can see from the above calculation that dissociation is ${{10}^{-2}}$ .
So, percentage of dissociation will be ${{10}^{-2}}\times 100=1%$

So, the correct answer is “Option A”.

Note: Dissociation is basically the separation of ions that occurs when a solid ionic compound dissolves. Strong acids and strong bases are the species that completely dissociate to form ions in solution whereas weak acids and bases ionize only partially, and the ionization reaction is reversible. Thus, weak acid and base solutions contain multiple charged and uncharged species in dynamic equilibrium.