Question

What is the acidity constant for the following reaction given that the hydronium ion concentration of a \[0.04\] M solution of $ N{i^{2 + }} $ solution of Nickel (II) perchlorate is\[4.5 \times {10^{ - 6}}\]?
\[N{i^{2 + }}(aq) + 2{H_2}O(I) \to Ni{(OH)^ + }(aq) + {H_3}{O^ + }(aq)\]
a) $ 2 \times {10^{ - 12}} $
b) $ 4 \times {10^{ - 6}} $
c) $ 5 \times {10^{ - 12}} $
d) $ 5 \times{10^{ - 10}} $

Answer 1

Hint: Here $ N{i^{2 + }} $ in aqueous form, $ {H_2}O $ is solvent and $ {H_3}{O^ + } $ is in aqueous form. So we will write the equilibrium equation then we will write the by taking $ x $ as dissociation amount and we will solve for $ x $.

Complete Step by step answer:
\[N{i^{2 + }}(aq) + 2{H_2}O(I) \to Ni{(OH)^ + }(aq) + {H_3}{O^ + }(aq)\]
We are given that the concentration of $ Ni $ is \[0.04\] M respectively.
Let at equilibrium $ x $ amount of reactant has been converted to product so $ x $ amount has been formed in the product side respectively.
So we will write the same equation for equilibrium
\[\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; N{i^{2 + }}(aq) + 2{H_2}O(I) \to Ni{(OH)^ + }(aq) + {H_3}{O^ + }(aq)\]
At equilibrium \[\left( {0.04 - x} \right)\] $ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; $ $ x $ + $ \;\;\;\;\;\;\;\;\;\;\;\;\; $ $ x $
So value of acidity constant $ {K_a} $ = ${\dfrac{concentration \; of \;product}{concentration \; of \;reactant}}$ = $ \dfrac{x^2}{0.04 - x} $
Here we are given that $ x = 4.5 \times {10^{ - 6}} $
Here the value is $ < < 0.04 $
Hence we will neglect this
So
 $ {K_a} = \dfrac{{{x^2}}}{{0.04}} $
 $ \Rightarrow {K_a} = \dfrac{{{{(4.5 \times {{10}^{ - 6}})}^2}}}{{0.04}} $
 $ \Rightarrow {K_a} = \dfrac{{20.25 \times {{10}^{ - 12}}}}{{0.04}} $
 $ \Rightarrow {K_a} = \dfrac{{20.25 \times {{10}^{ - 10}}}}{4} $
 $ \Rightarrow {K_a} \approx 5 \times {10^{ - 10}} $

Hence the answer is option ‘d’.

Note: While calculating the acidity constant we will keep in mind that the value of $ x $ is usually low so we can ignore this value. So that the calculation will get simple and we will get the answer easily. Also use all the given information in the question wisely in the formulas.