Explanation:
The given reaction will be as follows.
[tex]2H_{2}O + Br_{2} + SO_{2} \rightarrow 2Br^{-} + SO^{2-}_{4} + 4H^{+}[/tex]
Hence, expression that represents relation between given reaction and Q will be as follows.
Q = [tex]\frac{[Br^{-}]^{2}[SO^{2-}_{4}][H^{+}]^{4}}{[Br_{2}]P_{SO_{4}}}[/tex]
[tex]1.4 \times 10^{-26}[/tex] = [tex]\frac{(11.85)^{2} \times (8.35) \times [H^{+}]^{4}}{(2.5 \times 10^{4}) \times 2.50 \times 10^{5}}[/tex]
[tex][H^{+}]^{4} = 7.46 \times 10^{-34}[/tex]
[tex][H^{+}]= 5.22 \times 10^{-10}[/tex]
As relation between pH and [tex][H^{+}][/tex] is as follows.
pH = -log [tex][H^{+}][/tex]
= -log [tex]5.22 \times 10^{-10}[/tex]
= -(0.717 - 10)
= 9.28
Thus, we can conclude that the pH needed to produce the given value of Q is 9.28.
