Question

The self ionisation constant for pure formic acid. $K=\left[HCOO{H}_2^{+}\right]\left[HCO{O}^{-}\right]$ has been estimated as ${10}^{-6}$ at room temperature. The percentage of formic acid molecules in pure formic acid are converted to formate ion is $0.00X$%. The density of formic acid is $1.22g/{cm}^3$. Value of X is:

Answer 1

Given density of formic acid $=1.22g/{cm}^3$
$\therefore$ Mass of formic acid in $1$ litre solution $=1.22\times {10}^{3}g$
Thus, $\left[HCOOH\right]=\frac{1.22\times {10}^3}{46\times 1}=26.5M$
since, in case of auto ionisation $\left[HCOO{H}_2^{+}\right]=\left[HCOO{H}^{-}\right]$
and $\left[HCOO{H}^{-}\right]\left[HCOO{H}_2^{+}\right]={10}^{-6}$
$\therefore$ $\left[HCOO{H}^{-}\right]={10}^{-3}$
Now, % dissociation of $HCOOH=\frac{\left[HCO{O}^{-}\right]\times 100}{\left[HCOOH\right]}=\frac{{10}^{-3}}{26.5}\times 100[\alpha =\frac{c\alpha }{c(1-\alpha )}]$
$0.004$%