The dissociation of water into H₃O⁺ and OH⁻ ions depends on temperature. At 0 °C the [H₃O⁺] = 3.38 x 10⁻⁸ M, at 25 °C the [H₃O⁺] = 1.00 x 10⁻⁷ M, and at 50 °C the [H₃O⁺] = 2.34 x 10⁻⁷ M.What is the value of K_w at 0 °C and 50 °C.

Verified step by step guidance

1. Understand that the ion-product constant for water, K_w, is defined as the product of the concentrations of H₃O⁺ and OH⁻ ions: K_w = [H₃O⁺][OH⁻].
2. Recognize that at any given temperature, the solution is neutral, meaning [H₃O⁺] = [OH⁻].
3. For 0 °C, use the given [H₃O⁺] = 3.38 \times 10^{-8} \text{ M} to find [OH⁻] since [H₃O⁺] = [OH⁻].
4. Calculate K_w at 0 °C by squaring the concentration of H₃O⁺: K_w = (3.38 \times 10^{-8} \text{ M})^2.
5. For 50 °C, use the given [H₃O⁺] = 2.34 \times 10^{-7} \text{ M} to find [OH⁻] since [H₃O⁺] = [OH⁻], and calculate K_w by squaring this concentration: K_w = (2.34 \times 10^{-7} \text{ M})^2.

Key Concepts

Dissociation of Water

Water (H₂O) can dissociate into hydronium (H₃O⁺) and hydroxide (OH⁻) ions. This process is essential for understanding acid-base chemistry and is represented by the equilibrium expression: H₂O ⇌ H₃O⁺ + OH⁻. The concentrations of these ions in pure water are equal at a given temperature, which is crucial for calculating the ion product constant, K_w.

Ion Product Constant (K_w)

The ion product constant for water, K_w, is the product of the concentrations of H₃O⁺ and OH⁻ ions in water at a specific temperature. It is defined as K_w = [H₃O⁺][OH⁻]. K_w varies with temperature, increasing as temperature rises, which reflects the temperature dependence of water's dissociation and is fundamental in acid-base equilibria.

Temperature Dependence of K_w

The value of K_w is temperature-dependent, meaning it changes with variations in temperature. As temperature increases, the dissociation of water becomes more favorable, leading to higher concentrations of H₃O⁺ and OH⁻ ions, thus increasing K_w. Understanding this relationship is vital for calculating K_w at different temperatures, such as 0 °C and 50 °C.