Calculate the pH of an aqueous solution containing 1.3 * 10^-2 M HCl, 3.0 * 10^-2 M H2SO4, and 2.0 * 10^-2 M HCN.
To calculate the pH of an aqueous solution, we need to determine the concentration of the hydronium ion (H3O+), which is responsible for acidic properties.
Step 1: Write down the dissociation equations for each acid:
HCl → H+ + Cl-
H2SO4 → 2H+ + SO4^2-
HCN → H+ + CN-
Step 2: Calculate the concentration of H3O+ from each acid:
For HCl: Since HCl is a strong acid, it dissociates completely, so the concentration of H3O+ is equal to the concentration of HCl.
[H3O+] = [HCl] = 1.3 * 10^-2 M
For H2SO4: Since H2SO4 is a strong acid, it dissociates completely, so the concentration of H3O+ is twice the concentration of H2SO4.
[H3O+] = 2 * [H2SO4] = 2 * 3.0 * 10^-2 M
For HCN: HCN is a weak acid, so it only partially dissociates. We need to use the acid dissociation constant (Ka) to calculate the concentration of H3O+.
Ka = [H3O+] * [CN-] / [HCN]
Assuming that [CN-] is negligible compared to [HCN] since it is a weak base, we can approximate the equation as:
Ka ≈ [H3O+] * [CN-] / [HCN]
[H3O+] ≈ Ka * [HCN]
Ka for HCN is 6.2 * 10^-10 at 25°C (constant value), so:
[H3O+] ≈ 6.2 * 10^-10 * 2.0 * 10^-2 M
[H3O+] ≈ 1.24 * 10^-11 M
Step 3: Add up the concentrations of H3O+ from each acid:
[H3O+]total = [H3O+] from HCl + [H3O+] from H2SO4 + [H3O+] from HCN
[H3O+]total = 1.3 * 10^-2 M + 2 * 3.0 * 10^-2 M + 1.24 * 10^-11 M
Step 4: Calculate the pH using the formula pH = -log[H3O+]:
pH = -log([H3O+]total)
pH = -log(1.3 * 10^-2 + 2 * 3.0 * 10^-2 + 1.24 * 10^-11)
Using a calculator, the pH of the solution is determined to be approximately 1.52.