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Will the pH of pure water at 20^(@)C be ...

Will the pH of pure water at `20^(@)C` be lower or higher than that at `50^(@)C`?

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Ionic product of water `(K_(w))` increases with rise in temperature. Hence, `K_(w)(50^(@)C) gt K_(w)(20^(@)C)` or, `pK_(w)(50^(@)C) lt pK_(w)(20^(@)C)." "(because pK_(w)=-log_(10)K_(w))`. Now, for pure water, `pH=(1)/(2)pK_(w)`. Therefore, `pH(50^(@)C) lt pH(20^(@)C)`.
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