[Single-digit Integer] The self-ionization constant for pure formic acid, K = [HCOOH2+][HCOO-] has been estimated as 10^-6 M^2 and the density of formic acid is 1.15 g/cm^3 at room temperature. If 'x

Question

[Single-digit Integer] The self-ionization constant for pure formic acid, K = [HCOOH2+][HCOO-] has been estimated as 10^-6 M^2 and the density of formic acid is 1.15 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

Prashant Kotian · Accepted Answer

Correct answer: 0004. 1. Molar mass of HCOOH = 46 g/mol.
2. Density = 1.15 g/cm^3 = 1150 g/L.
3. Concentration [HCOOH] = 1150 / 46 = 25 M.
4. Auto-ionization: 2 HCOOH ⇌ HCOOH2+ + HCOO-.
Since [HCOOH2+] = [HCOO-], [HCOO-]^2 = 10^-6 => [HCOO-] = 10^-3 M.
5. x % = ([HCOO-] / [HCOOH]) × 100% = (10^-3 / 25) × 100% = 0.004% = 4 × 10^-3 %.
Thus, x = 4 × 10^-3.
6. Value of 1000x = 1000 × (4 × 10^-3) = 4.

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