What is the value of the equilibrium constant (K_w) for the autoionization of pure water at 25°C?

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

Answer: (C)

Verified step by step guidance

1. Understand that the equilibrium constant for the autoionization of water, denoted as \(K_w\), is defined by the reaction: \(\mathrm{H_2O (l) \rightleftharpoons H^+ (aq) + OH^- (aq)}\).
2. Write the expression for the equilibrium constant \(K_w\) as the product of the molar concentrations of the hydrogen ions and hydroxide ions: \(K_w = [H^+][OH^-]\).
3. Recall that at 25°C, pure water is neutral, meaning the concentration of hydrogen ions \([H^+]\) equals the concentration of hydroxide ions \([OH^-]\).
4. Use the known concentration of hydrogen ions in pure water at 25°C, which is \$1.0 \times 10^{-7}\( M, and substitute into the expression: \)K_w = (1.0 \times 10^{-7})(1.0 \times 10^{-7})$.
5. Multiply the concentrations to find \(K_w = 1.0 \times 10^{-14}\), which is the equilibrium constant for the autoionization of water at 25°C.