The pH of the solution is 1.
In aqueous solutions, the concentration of hydronium ions ([H₃O+]) and hydroxide ions ([OH-]) are related by the ion product constant of water (Kw) at a specific temperature:
Kw = [H₃O+][OH-] = 1.0 x 10⁻¹⁴ at 25°C
We are given that the [OH-] value is 10⁻¹³. We can use the Kw expression to calculate the [H₃O+] concentration:
[H₃O+] = Kw / [OH-]
[H₃O+] = (1.0 x 10⁻¹⁴) / (10⁻¹³)
[H₃O+] = 1.0 x 10⁻¹
Now that we know the [H₃O+] concentration, we can calculate the pH of the solution using the following equation:
pH = -log([H₃O+])
pH = -log(1.0 x 10⁻¹)
pH = 1
Therefore, the pH of the solution is 1.