If solution A has a pH that is four pH units greater than that of solution B, the H₃O⁺ concentration in solution B is 10⁴ times greater than that of solution A.
The pH of a solution is given by:
[tex] pH = -log([H_{3}O^{+}]) [/tex]
Solution A has a pH that is four pH units greater than that of solution B, so:
[tex] pH_{A} = pH_{B} + 4 [/tex]
or
[tex] pH_{B} = pH_{A} - 4 [/tex]
The H₃O⁺ concentration of solution B is related to that of solution A as follows:
[tex] [H_{3}O^{+}]_{B} = 10^{-pH_{B}} [/tex]
[tex] [H_{3}O^{+}]_{B} = 10^{-(pH_{A} - 4)} [/tex]
[tex][H_{3}O^{+}]_{B} = 10^{-(-log[H_{3}O^{+}]_{A} - 4)}[/tex]
[tex][H_{3}O^{+}]_{B} = 10^{(log[H_{3}O^{+}]_{A} + 4)}[/tex]
[tex][H_{3}O^{+}]_{B} = 10^{4}[H_{3}O^{+}]_{A}[/tex]
Therefore, the H₃O⁺ concentration in solution B is 10⁴ times greater than that of solution A.
Learn more here:
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