Like all equilibrium constants, the value of K_w depends on temperature. At body temperature (37 °C), K_w = 2.4×10^–14. What are the [H₃O⁺] and pH of pure water at body temperature?

Verified step by step guidance

1. Identify the given values: Kw (the ion-product constant of water) at 37 °C is 2.4 * 10^-14.
2. Recall that for pure water, the concentrations of hydrogen ions [H3O+] and hydroxide ions [OH-] are equal. Therefore, [H3O+] = [OH-].
3. Set up the equation for Kw at equilibrium: Kw = [H3O+][OH-]. Since [H3O+] = [OH-], this can be rewritten as Kw = [H3O+]^2.
4. Solve for [H3O+] by taking the square root of Kw: [H3O+] = sqrt(Kw).
5. Calculate the pH of the solution using the formula pH = -log([H3O+]).

Key Concepts

Ion Product of Water (Kw)

Kw, the ion product of water, is the equilibrium constant for the self-ionization of water, represented as Kw = [H3O+][OH-]. Its value changes with temperature; at 25 °C, Kw is 1.0 x 10^-14, but at 37 °C, it increases to 2.4 x 10^-14. This indicates that the concentrations of hydronium ions [H3O+] and hydroxide ions [OH-] in pure water are equal at any temperature.

Hydronium Ion Concentration

In pure water, the concentration of hydronium ions [H3O+] is equal to the concentration of hydroxide ions [OH-]. At 37 °C, since Kw = 2.4 x 10^-14, we can find [H3O+] by taking the square root of Kw, leading to [H3O+] = [OH-] = √(2.4 x 10^-14). This concentration is crucial for determining the pH of the solution.

pH Scale

The pH scale is a logarithmic scale used to measure the acidity or basicity of a solution, defined as pH = -log[H3O+]. A pH of 7 indicates neutrality, while values below 7 indicate acidity and above 7 indicate basicity. At body temperature, the calculated [H3O+] will yield a pH value that reflects the neutral nature of pure water at that temperature.