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(D) To determine the maximum $pH$,we need to find the solution with the highest concentration of hydroxide ions $[OH^-]$.$A$. $10^{-3} \ M \ NH_4OH$:

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$10^{-3} \ M \ Ba(OH)_2$

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(D) To determine the maximum $pH$,we need to find the solution with the highest concentration of hydroxide ions $[OH^-]$.$A$. $10^{-3} \ M \ NH_4OH$: This is a weak base. $[OH^-] = \sqrt{K_b 	imes C} $B$. $10^{-1} \ M \ NH_4OH$: This is a weak base. $[OH^-] = \sqrt{K_b 	imes 10^{-1}} \approx 10^{-3} \ M$ (assuming $K_b \approx 10^{-5}$).$C$. $10^{-3} \ M \ NaOH$: This is a strong base. $[OH^-] = 10^{-3} \ M$.$D$. $10^{-3} \ M \ Ba(OH)_2$: This is a strong base. $[OH^-] = 2 	imes 10^{-3} \ M$.Comparing the $[OH^-]$ concentrations: $2 	imes 10^{-3} \ M > 10^{-3} \ M > 	ext{weak base concentrations}$.Since $Ba(OH)_2$ provides the highest $[OH^-]$ concentration,it will have the highest $pOH$ and consequently the highest $pH$.

Which of the following solutions will have the maximum $pH$?

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