Textbook Question
Like all equilibrium constants, the value of Kw depends on temperature. At body temperature (37 °C), Kw = 2.4×10–14. What are the [H3O+] and pH of pure water at body temperature?
17. Acid and Base Equilibrium
Auto-Ionization
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At 60°C, the ion product constant of water, Kw, is 9.61 x 10^-14. What is the pH of pure water at this temperature?
A
7.20
B
6.81
C
7.00
D
6.50
Verified step by step guidance1
Understand that the ion product constant of water, Kw, is the product of the concentrations of hydrogen ions [H⁺] and hydroxide ions [OH⁻] in water: Kw = [H⁺][OH⁻]. At 60°C, Kw is given as 9.61 x 10^-14.
In pure water, the concentrations of hydrogen ions [H⁺] and hydroxide ions [OH⁻] are equal. Therefore, we can set [H⁺] = [OH⁻] = x.
Substitute x for both [H⁺] and [OH⁻] in the expression for Kw: Kw = x * x = x².
Solve for x by taking the square root of Kw: x = √(9.61 x 10^-14). This will give you the concentration of hydrogen ions [H⁺] in pure water at 60°C.
Calculate the pH using the formula pH = -log[H⁺]. Substitute the value of [H⁺] obtained from the previous step into this formula to find the pH of pure water at 60°C.
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