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# At a certain temperature, dissociation constant of formic acid and acetic acid are $1.8 \times 10^{-4}$ and $1.8 \times 10^{-5}$ respectively. At what concentration of acetic solution, the $H_3O^+$ ion concentration is same as that in 0.001 M fromic acid solution

(a) 0.01 M

(b) $1 \times 10^{-3}$ M

(c) $1 \times 10^{-1}$ M

(d) $1 \times 10^{-4}$ M

$[H_3O^+] = \sqrt{K_a \times C}$

Let concentration of acetic acid is $C_1$ and that of formic acid is $C_2$

$\Rightarrow \sqrt{1.8 \times 10^{-5} \times C_1} = \sqrt{1.8 \times 10^{-4} \times 0.001}$
or $C_1 = \frac{1.8 \times 10^{-4} \times 0.001}{1.8 \times 10^{-5}} = 0.01$