Question

What concentration of $HCO{O^ - }$ is present in a solution of $0.01M$ $HCOOH$ $({K_a} = 1.8\, \times \,{10^{ - 4}})$ and $0.01M$ $HCl$ ?
A.$1.8 \times {10^{ - 3}}$
B.${10^{ - 2}}$
C.$1.8 \times {10^{ - 4}}$
D.${10^{ - 4}}$

Answer 1

Hint: The formic acid is a weak acid and for ionization if feebly possible, it means we have to apply the Ostwald law of dilution of weak electrolytes. Now as it is given that concentration of both hydrochloric acid. Put the value of both concentration as well as for dissociation constant in the Ostwald law and calculate the concentration of $HCO{O^ - }$ ion.

Complete step-by-step answer:When we react formic acid with hydrochloric acid, a reaction like this happens
$\,HCOOH\, \rightleftharpoons \,HCO{O^ - }\, + \,{H^ + }$
The hydrogen ion concentration will formed as (x) and same for the $HCO{O^ - }$ ion, now as we have given that $0.01M$ $HCl$ is added hence the total concentration of hydrogen ion will be-
${H^ + } = \,x + \,0.01M$
For the above equation, if we apply the Ostwald dilution law it will be written like this, ${K_a} = \,\dfrac{{\left[ {HCO{O^ - }} \right]\,\left[ {{H^ + }} \right]}}{{HCOOH}}$
Here, $\left[ {HCO{O^ - }} \right]$ represents the concentration of ion and $\left[ {{H^ + }} \right]$ as concentration of hydrogen ion. Now if we put the values of concentration of $\left[ {{H^ + }} \right]$ and value of dissociation constant ${K_a}$ in the above formula we will get $\left[ {HCO{O^ - }} \right] = \,\dfrac{{1.8\, \times {{10}^{ - 4}}\, \times \,0.01\,}}{{0.01\,}}$
As you have seen that the concentration of hydrogen ion and formic acid concentration are same, they will cancel and we will get the concentration of $HCO{O^ - }$ as $\left[ {HCO{O^ - }} \right] = \,1.8\, \times {10^{ - 4}}$

Thus our option C is correct.

Note: Keep in mind that as dilution increases here as we are dissolving the formic acid in hydrochloric acid we will get $HCO{O^ - }$ at last. So, on increasing the dilution when the solvent amount is increasing the degree of dissociation also increases. Ostwald law is only applicable to weak electrolyte while for strong electrolyte we have Debye Huckel law.