The dissociation constant of formic acid is 0.00024. The hydrogen ion concentration in solution is n — Ionic Equilibrium Chemistry Question

💡 Solution & Explanation

Given $K_a = 2.4 \times 10^{-4}$ and $C = 2 \times 10^{-3}\text{ M}$, the degree of dissociation is significant because $K_a$ is not negligibly small compared to $C$. We use the full quadratic equation: $[\text{H}^+]^2 + K_a[\text{H}^+] - K_aC = 0 \implies x^2 + (2.4 \times 10^{-4})x - (4.8 \times 10^{-7}) = 0$. Using the quadratic formula, $x = \frac{-2.4 \times 10^{-4} + \sqrt{(2.4 \times 10^{-4})^2 - 4(1)(-4.8 \times 10^{-7})}}{2}$. This evaluates to $x \approx 5.8 \times 10^{-4}\text{ M}$.