Question

question
at 100°c, the ion product of water is 5.13×10⁻¹³. what is the concentration of hydronium ions at this temperature?
select the correct answer below:
2.56×10⁻¹³ m
5.06×10⁻⁷ m
7.16×10⁻⁷ m
there is not enough information.

Explanation:

Step1: Recall the ion - product constant of water formula

For water, \(K_w=[H_3O^+][OH^-]\). In pure water, \([H_3O^+]=[OH^-]\). Let \(x = [H_3O^+]\), then \(K_w=x\times x=x^{2}\).

Step2: Solve for \(x\)

Given \(K_w = 5.13\times10^{-13}\), we have \(x^{2}=5.13\times 10^{-13}\). So \(x=\sqrt{5.13\times 10^{-13}}\).

$$x=\sqrt{5.13}\times\sqrt{10^{-13}}=\sqrt{5.13}\times10^{-6.5}$$

\(\sqrt{5.13}\approx2.26\), \(10^{-6.5}=\frac{10^{-7}}{\sqrt{10}}\approx3.16\times 10^{-7}\)
\(x = 2.26\times3.16\times10^{-7}\approx7.16\times 10^{-7}\)

Answer:

C. \(7.16\times 10^{-7}\text{ M}\)