Open Question
How is K_w defined, and what is its numerical value at 25 °C?
10. Acids and Bases
Auto-Ionization
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Calculate the Kw of pure water given the pH = 6.34.
A
4.57 × 10−7
B
6.76 × 10−4
C
2.09 × 10−13
D
4.57 × 10−14
Verified step by step guidance1
Understand that the pH of a solution is related to the concentration of hydrogen ions [H⁺] in the solution. The formula to find [H⁺] from pH is: [H⁺] = 10^{-pH}.
Substitute the given pH value into the formula: [H⁺] = 10^{-6.34}. This will give you the concentration of hydrogen ions in the water.
In pure water, the concentration of hydrogen ions [H⁺] is equal to the concentration of hydroxide ions [OH⁻]. Therefore, [OH⁻] = [H⁺].
The ion product of water (Kw) is defined as the product of the concentrations of hydrogen ions and hydroxide ions: Kw = [H⁺] × [OH⁻].
Substitute the value of [H⁺] (which is equal to [OH⁻]) into the expression for Kw: Kw = [H⁺]². Calculate this to find the value of Kw for pure water at the given pH.
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