#### The self-ionization constant for pure formic acid $\mathrm{K=\left[\mathrm{HCOOH}_{2}^{+}\right]\left[\mathrm{HCOO}^{-}\right]}$ has been estimated as $10^{-7}$ room temperature. What percentage of formic acid molecules in pure formic acid is converted to formate ions? The density of formic acid is $\mathrm{1.25\ g/cm^{3}}$Option: 1 0.01%Option: 2 0.001%Option: 3 0.02%Option: 4 0.002%

The density of HCOOH  is given as $\mathrm{1.25\ g/cm^{3}}$

$\therefore$ Mass of HCOOH in 1 litre  solution $\mathrm{= 1.25 \times 10^{3}\ g}$

The concentration of HCOOH ,

$\mathrm{c = \frac{1.25\times 10^{3}}{46} = 27.17\: M}$

As it is given the HCOOH goes to auto-ionization, so $\left[\mathrm{HCOOH}_{2}^{+}\right]=\left[\mathrm{HCOO}^{-}\right]$

Also, $\left[\mathrm{HCOOH}_{2}^{+}\right]\left[\mathrm{HCOO}^{-}\right]= 10^{-7}$

$\therefore \left[\mathrm{HCOO}^{-}\right]= \sqrt{10^{-7}} =3.16\times 10^{-4}$

$\text{\% dissociation of HCOOH = }\frac{\left[\mathrm{HCOO}^{-}\right] \times 100}{[\mathrm{HCOOH}]}$

$\Rightarrow \alpha = \frac{3.16\times 10^{-4}\times 100}{27.17} = 0.001\%$

Hence, the correct answer is Option (2)