Question

Formic (or methanoic) acid is a weak acid secreted by ants as a defense mechanism. The acid has a ${K_a}$ value of $1.8 \times {10^{ - 4}}$ . What is the pH of a $1.65M$ solution of formic acid?

Answer 1

Formic acid is a weak organic acid that dissociates partially in an aqueous medium. The partial dissociation results in the formation of an equilibrium, the given concentration of acid is therefore only the initial concentration and not the concentration of hydrogen ions released.

Complete answer:
Partial dissociation of formic acid can be represented by an equilibrium between the ionized form and the unionized acid that exists in an aqueous medium. The equilibrium can be represented as follows:
$HCOOH + {H_2}O \rightleftharpoons {H^ + } + HCO{O^ - }$
The given concentration of acid is the initial concentration when the acid is only present in the unionized form and no amount of ions are produced. The stoichiometry of the reactants and products is to be taken into account when calculating the amount of acid that gets dissociated and the ions that are produced.
Let us assume that $x$ is the concentration of the acid that actually dissociates to give ions. The initial and equilibrium concentrations can be represented as follows:
${\text{ }}HCOOH + {H_2}O \rightleftharpoons {H^ + } + HCO{O^ - }$
$t = 0{\text{ 1}}{\text{.65M 0 0}}$
$t = eq{\text{ 1}}{\text{.65 - x x x}}$
Since, the expression of an equilibrium constant is the product of product concentration divided by the products of reactant concentrations. The expression for dissociation constant can be written as follows:
${K_a} = \dfrac{{{x^2}}}{{{\text{1}}{\text{.65 - x}}}} = 1.8 \times {10^{ - 4}}$
On solving the above expression for $x$ we get,
$x \approx 0.0172$
Thus, the concentration of hydrogen ions being released by formic acid is $0.0172M$ .
The formula for calculating pH is given as follows:
$pH = - \log [{H^ + }]$
On inserting the concentration of hydrogen ions in the above formula we get,
$pH = 1.76$
$\Rightarrow$ Thus, the pH of formic acid comes out to be $1.76$ .

Note:
Complete dissociation of a weak acid can only be observed at infinite dilution which is practically difficult to achieve. Different weak acids have different values of dissociation constants at different temperatures.