Question

question
at 10°c, the ion product of water is 2.93×10^{-15}. what is the concentration of hydroxide ions at this temperature?
select the correct answer below:
○ 5.41×10^{-8} m
○ 3.82×10^{-8} m
○ 1.46×10^{-15} m
○ there is not enough information.

Explanation:

Step1: Recall the ion - product constant of water formula

The ion - product constant of water is \(K_w=[H^+][OH^-]\). In pure water, \([H^+]=[OH^-]\). Given \(K_w = 2.93\times10^{-15}\).

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

Since \([H^+]=[OH^-]\), let \(x = [OH^-]\), then \(K_w=x\times x=x^{2}\). So \(x=\sqrt{K_w}\). Substitute \(K_w = 2.93\times10^{-15}\) into the formula: \(x=\sqrt{2.93\times 10^{-15}}\).

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Answer:

\(5.41\times 10^{-8}\text{ M}\)