Final answer:
The value of Kw at 30°C with a pH of 6.92 is calculated using the concentrations of hydronium and hydroxide ions and is approximately 1 x 10^-14 mol^2 dm^-6, closest to option a) 1.008 x 10^-14.
Step-by-step explanation:
To find the value of the autoionization constant of water, Kw, at a temperature of 30°C and a pH of 6.92, we must first calculate the concentration of the hydronium ions, [H3O+]. The pH is given as 6.92, hence [H3O+] is 10-6.92. We can determine the concentration of hydroxide ions, [OH-], using the formula pOH = 14 - pH, which then gives us [OH-] = 10-7.08. Using the ion product for water, Kw = [H3O+][OH-], we multiply the concentrations together to find Kw.
Calculating, we get:
- [H3O+] = 10-6.92 M
- [OH-] = 10-7.08 M
- Kw = (10-6.92)(10-7.08)
Therefore:
Kw = 10-(6.92+7.08)
Kw = 10-14
The correct value of Kw at 30°C with a pH of 6.92 is approximately 1 x 10-14 mol2 dm-6, matching closest to option a) 1.008 x 10-14.