# The self ionisation constant for pure formic acid,$K=[HCOOH_{2}^{+}] [HCOO^{-}]$ has been estimated as 10-6 at 1.22g/cm3.The percentage of formic acid molecules in pure formic acid converted to formate ion is Option 1) 0.002 percentage  Option 2) 0.004 percentage  Option 3) 0.006 percentage  Option 4) 0.008 percentage

As we learned in concept

Ionization constant of weak acids -

Consider

$HX(aq)+H_{2}O(l)\rightleftharpoons H_{3}O^{+}(aq)+\bar{X}(aq)$

$K_{a}=dissociation\:or\:ionization\:constant$

- wherein

$K_{a}=\frac{C^{2}\:\alpha ^{2}}{C(1-\alpha )}$

$K_{a}=\frac{C\alpha ^{2}}{1-\alpha }$

$C=initial\:concentration\:of\:undissociated\:acid$

$\alpha =extent\:upto\:which\:HX\:is\:ionized\:into\:ions.$

No. of moles of formic acid in one L of solution =$1.22\times 1000\times \frac{1}{46}= 26.5 mol$

$2HCOOH\rightleftharpoons HCOO^- +HCOOH_2^+$

$K= 10^{-6}= [HCOO^-][HCOOH_2^+]$

$[HCOO^-]=[HCOOH_2^+]=10^{-3}M$

% dissociation =  $\frac{10^{-3}}{26.5}\times 100 =0.004 \%$

Option 1)

0.002 percentage

Incorrect

Option 2)

0.004 percentage

Correct

Option 3)

0.006 percentage

Incorrect

Option 4)

0.008 percentage

Incorrect

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