Question

We can observe the common-ion effect in action by comparing how much a pure sample of acid dissociates to how much a sample of an acid dissociates when its conjugate base is in solution. Let's consider the oxoacid HIO, which has a Ka of 2.3×10⁻¹¹

Calculate the pH of an aqueous solution of 0.100 M HIO. (Due to the low Ka value, you may apply the 5% approximation to avoid the quadratic equation if you wish.)

Answer 1

To find the pH of a 0.100 M HIO solution, we use an ICE table, apply the 5% approximation, and solve the equation Ka = x²/0.100 to find the concentration of H+, then calculate pH = -log([H+]).

Step-by-step explanation:

To calculate the pH of a 0.100 M solution of the weak acid HIO with a Ka of 2.3×10⁻¹¹, we can use an ICE table (Initial, Change, Equilibrium) and apply the 5% approximation due to the low Ka value. Let's assume that the initial concentration of HIO ([HIO]i) is 0.100 M and that it dissociates by a small amount x, producing [H+] and [IO−] both equal to x. Set up the equilibrium expression using Ka and solve for x.

Ka = [H+][IO−]/[HIO] = x²/0.100. By simplifying and solving the equation Ka = x²/0.100, we find x = √(Ka × 0.100). Substitute Ka with 2.3×10⁻¹¹ to find x (∼[H+]). Finally, calculate the pH by taking the negative logarithm of [H+], thus pH = -log([H+]). This approximation is valid if x is less than 5% of the initial concentration of HIO, which is the case here.