What is the value of the ion-product constant for water (K_w) at 25 °C?

• A. 1.0 × 10^{-14}
• B. 1.0 × 10^{-10}
• C. 1.0 × 10^{-7}
• D. 1.0 × 10^{-4}

Answer: (A)

Verified step by step guidance

1. Understand that the ion-product constant for water, denoted as \(K_{\mathrm{w}}\), represents the equilibrium constant for the self-ionization of water: \(\mathrm{H_2O (l)} \rightleftharpoons \mathrm{H^+ (aq)} + \mathrm{OH^- (aq)}\).
2. Recall that \(K_{\mathrm{w}}\) is defined as the product of the molar concentrations of hydrogen ions and hydroxide ions in pure water: \(K_{\mathrm{w}} = [\mathrm{H^+}][\mathrm{OH^-}]\).
3. At 25 °C, pure water is neutral, meaning the concentrations of \(\mathrm{H^+}\) and \(\mathrm{OH^-}\) are equal. Each concentration is approximately \$1.0 \times 10^{-7}$ M.
4. Calculate \(K_{\mathrm{w}}\) by multiplying these concentrations: \(K_{\mathrm{w}} = (1.0 \times 10^{-7})(1.0 \times 10^{-7})\).
5. Recognize that this multiplication results in \(K_{\mathrm{w}} = 1.0 \times 10^{-14}\), which is the ion-product constant for water at 25 °C.