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Equilibrium

Question
CBSEENCH11006537

Assuming complete dissociation, calculate the pH of the following solution:
0.005M NaOH

Solution

0.005 M NaOH:
Since NaOH is completely dissociated,
therefore space space space space open square brackets OH to the power of minus close square brackets space equals space 0.005 space straight M space equals space 5 space cross times space 10 to the power of negative 3 end exponent straight M
Also space space 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 1 space cross times space 10 to the power of negative 14 end exponent
therefore space space space space space open square brackets straight H to the power of plus close square brackets space equals space fraction numerator 1 space cross times space 10 to the power of negative 14 end exponent over denominator open square brackets OH to the power of minus close square brackets end fraction space equals space fraction numerator 1 space cross times space 10 to the power of negative 14 end exponent over denominator 5 space cross times space 10 to the power of negative 3 end exponent end fraction
space space space space space space space space space space space space space space space space equals space 2 space cross times space 10 to the power of negative 12 end exponent straight M
therefore space space space 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 space space space space space space equals space minus log space open square brackets 2 space cross times space 10 to the power of negative 12 end exponent close square brackets
space space space space space space space space space space space equals space minus open square brackets log space 2 space plus space log space 10 to the power of negative 12 end exponent close square brackets
space space space space space space space space space space space equals negative open square brackets 0.3010 space minus space 12 close square brackets
space space space space space space space space space space space equals space 11.6990 space asymptotically equal to space 11.70 space space space space space space space space space space space space space space space space space space space space space