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Equilibrium

Question
CBSEENCH11006550

How many grammes of NaOH must be dissolved in one litre of the solution to give it a pH value of 12?

Solution
By definition,
open square brackets straight H to the power of minus close square brackets space equals space 10 to the power of negative pH end exponent space equals 10 to the power of negative 12 end exponent space mol space straight L to the power of negative 1 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
or space space open square brackets OH to the power of minus close square brackets space equals space fraction numerator straight K subscript straight w over denominator open square brackets straight H to the power of plus 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 10 to the power of negative 12 end exponent end fraction
space space space space space space space space space space space space space space space space space equals 1 space cross times space 10 to the power of negative 2 end exponent space mol space straight L to the power of negative 1 end exponent
Since NaOH is a strong electrolyte, it gets completely ionised. So we have
NaOH space plus space straight H subscript 2 straight O space space rightwards arrow space space space Na to the power of plus left parenthesis aq right parenthesis space plus space OH to the power of minus left parenthesis aq right parenthesis
therefore space space space open square brackets OH close square brackets to the power of minus space equals space open square brackets NaOH close square brackets space equals space 1 space cross times space 10 to the power of negative 2 end exponent space mol space straight L to the power of negative 1 end exponent
therefore space space space Molarity space of space NaOH space solution space equals space 1 space cross times space 10 to the power of negative 2 end exponent straight M
therefore space space space space space Molecular space mass space of space NaOH space equals space 40
therefore space space Amount space of space NaOH space present space in space one space litre
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space Molar space mass space cross times space molarity
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 40 cross times 10 to the power of negative 2 end exponent space equals 0.4 space straight g