Aqueous acidity–basicity: what is the hydroxide-ion concentration [OH−] in a solution with pH = 3 (at 25 °C)?

Introduction / Context:
In water at 25 °C, the autoionization equilibrium defines the ion product Kw = [H+][OH−] = 1.0 × 10^-14. Using pH and pOH relationships enables rapid interconversion of hydrogen- and hydroxide-ion concentrations for acid–base calculations in environmental, biochemical, and process applications.

Given Data / Assumptions:

• Temperature is 25 °C (so pH + pOH = 14 holds).
• pH = 3 (strongly acidic solution).
• Activity coefficients taken as unity (dilute solution approximation).

Concept / Approach:
Use the relations pH = −log10[H+] and pOH = −log10[OH−], with pH + pOH = 14 at 25 °C. From pH we first get [H+], then compute pOH and [OH−].

Step-by-Step Solution:

Verification / Alternative check:
Directly from Kw: [OH−] = Kw/[H+] = 1.0 × 10^-14 / 10^-3 = 10^-11 M, identical to the pOH method.

Why Other Options Are Wrong:

• 10^-3 M is [H+], not [OH−].
• 10^-10 M and 10^-13 M do not satisfy the Kw product with pH = 3.
• 10^-7 M corresponds to neutrality at 25 °C, not an acidic solution with pH 3.

Common Pitfalls:
Forgetting the temperature dependence of Kw; at temperatures other than 25 °C, pH + pOH ≠ 14 exactly, though the qualitative approach remains valid.

Final Answer:
10^-11 M