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Calculate the equilibrium constant, $$K$$ for the reaction $$\text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^-$$ at $$25^\circ\text{C}$$ temperature. Given that density of water is 1 gm/cc at $$25^\circ\text{C}$$.
Correct Answer: 0.00000000000000018
The molar concentration of water is $$\frac{1000}{18} \approx 55.6\text{ mol L}^{-1}$$. With $$[\text{H}^+][\text{OH}^-] = K_w = 10^{-14}$$, $$K = \frac{10^{-14}}{55.6} \approx 1.8 \times 10^{-16}$$.
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