Question

Ionic product of water at 310K is 2·7 × 10^–14. What is the pH of neutral water at this temperature?

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Solution

Ionic product of water (K_w)

equals 2.7 space cross times space 10 to the power of negative 14 end exponent

We space know comma space open square brackets straight H to the power of plus close square brackets space open square brackets OH to the power of minus close square brackets space equals space straight K subscript straight w For space pure space water comma space space space space space space space space space space open square brackets straight H to the power of plus close square brackets space equals space open square brackets OH to the power of minus close square brackets therefore space space space space space space open square brackets straight H to the power of plus close square brackets squared space equals space straight K subscript straight w space equals space 2.7 space space cross times space 10 to the power of negative 14 end exponent or space space space space space space open square brackets straight H to the power of plus close square brackets space equals space square root of 2.7 space cross times space 10 to the power of negative 14 end exponent end root space equals space 1.6 space cross times space 10 to the power of negative 7 end exponent space mol space straight L to the power of negative 1 end exponent

pH space equals space minus log space open square brackets straight H to the power of plus close square brackets space space space space space equals space minus log space open square brackets 1.6 space cross times space 10 to the power of negative 7 end exponent close square brackets space space space space space equals space minus open square brackets log space 1.6 space plus space log space 10 to the power of negative 7 end exponent close square brackets space space space space space equals space minus open square brackets 0.2041 space minus space 7 close square brackets space space space open square brackets because space log space 10 space equals space 1 close square brackets space space space space space equals space 7 minus 0.2041 space space space space space equals space 6.7959 space asymptotically equal to space 6.8

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