The self-ionization constant for pure formic acid, has been estimated as and the density of formic a — Ionic Equilibrium Chemistry Question
Question
The self-ionization constant for pure formic acid, $K = [\text{HCOOH}_2^+][\text{HCOO}^-]$ has been estimated as $10^{-6}\text{ M}^2$ and the density of formic acid is $1.15\text{ g/cm}^3$ at room temperature. If '$x$ %' of formic acid molecules in pure formic acid is converted to formate ions, then the value of '$1000x$' is
💡 Solution & Explanation
Density of formic acid = $1.15\text{ g/cm}^3 = 1150\text{ g/L}$. Molar mass of $\text{HCOOH} = 46\text{ g/mol}$. The molarity of pure formic acid is $C = 1150 / 46 = 25\text{ M}$. The self-ionization gives $[\text{HCOOH}_2^+] = [\text{HCOO}^-]$. From $K = 10^{-6}$, we have $[\text{HCOO}^-] = \sqrt{10^{-6}} = 10^{-3}\text{ M}$. The fraction converted is $10^{-3} / 25 = 4 \times 10^{-5}$. The percentage $x = 4 \times 10^{-5} \times 100 = 0.004$. The value of $1000x = 1000 \times 0.004 = 4$. Therefore, correct answer is 4.