Question

question 12 · 1 point
an aqueous solution at 25°c has a hydronium ion concentration of 9.7 × 10⁻⁵ m. what is the hydroxide ion concentration of the solution?
select the correct answer below:
9.7 × 10⁻¹⁹ m
9.7 × 10⁻¹² m
1.0 × 10⁻¹⁰ m
1.0 × 10⁻³ m

Explanation:

Step1: Recall the ion - product constant for water

At \(25^{\circ}\text{C}\), \(K_w=[\text{H}_3\text{O}^+][\text{OH}^-]=1.0\times 10^{-14}\)

Step2: Solve for \([\text{OH}^-]\)

Given \([\text{H}_3\text{O}^+]=9.7\times 10^{-5}\text{ M}\), we can rearrange the formula \(K_w=[\text{H}_3\text{O}^+][\text{OH}^-]\) to \([\text{OH}^-]=\frac{K_w}{[\text{H}_3\text{O}^+]}\)
Substitute the values: \([\text{OH}^-]=\frac{1.0\times 10^{-14}}{9.7\times 10^{-5}}\)
\([\text{OH}^-]\approx1.0\times 10^{-10}\text{ M}\) (after performing the division \(1.0\times 10^{-14}\div9.7\times 10^{-5}\approx1.0\times 10^{-10}\) considering significant - figure rules)

Answer:

\(1.0\times 10^{-10}\text{ M}\)