What is the hydroxide ion concentration and the pH for a hydrochloric acid solution that has a hydronium ion concentration of $1.50 \times 10 ^{- 2 }\mathrm {~mol} \mathrm {~L}^{ - 1 }?$ A)6.67 × 10^-¹² mol L^-1,2.82 B)6.67 × 10^-¹² mol L^-1,11.18 C)6.67 × 10^-¹³ mol L^-1,1.82 D)6.67 × 10^-¹³ mol L^-1,12.17

Question

Quizplus · Accepted Answer

First, we can write the chemical equation for the reaction between hydrochloric acid and water:
HCl + H2O ⇌ H3O+ + Cl-
Since we are given the hydronium ion concentration, we can use the equilibrium constant expression to find the hydroxide ion concentration:
Kw = [H3O+][OH-] = 1.0 × 10^-14 mol^2 L^-2
[H3O+] = 1.50 × 10^-2 mol L^-1 (given)
[OH-] = Kw/[H3O+] = 1.0 × 10^-14 mol^2 L^-2 / (1.50 × 10^-2 mol L^-1) = 6.67 × 10^-13 mol L^-1
Now we can use the definition of pH to find the pH:
pH = -log[H3O+] = -log(1.50 × 10^-2) = 1.82
Therefore, the answer is (C) 6.67 × 10^-13 mol L^-1, 1.82.

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