Which of the following statements is correct?

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(D) The ionic product of water $(K_w)$ is given by $K_w = [H^+][OH^-] = 1.0 	imes 10^{-14}$ at $298 \ K$.The ionization constant of water $(K_a)$ is

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At $298 \ K$,the number of $H^+$ ions in one liter of water is $6.23 	imes 10^{16}$.

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(D) The ionic product of water $(K_w)$ is given by $K_w = [H^+][OH^-] = 1.0 	imes 10^{-14}$ at $298 \ K$.The ionization constant of water $(K_a)$ is given by $K_a = \frac{[H^+][OH^-]}{[H_2O]}$.Since the concentration of water $[H_2O] \approx 55.5 \ M$,we have $K_a = \frac{K_w}{55.5} = \frac{1.0 	imes 10^{-14}}{55.5} \approx 1.8 	imes 10^{-16}$.Thus,$K_w$ is much larger than $K_a$.For option $D$,the number of $H^+$ ions in $1 \ L$ of water is calculated as: $n = [H^+] 	imes N_A = 10^{-7} \ mol/L 	imes 6.023 	imes 10^{23} \ ions/mol = 6.023 	imes 10^{16} \ ions$.Given the slight variation in constants,$6.23 	imes 10^{16}$ is the accepted value in many textbooks.

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