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Equilibrium

Question
CBSEENCH11006580
Wired Faculty App

Derive the relations:
pH space equals space minus log space square root of fraction numerator straight K subscript straight w. space straight K subscript straight a over denominator straight c end fraction end root
for a solution of a salt of weak acid and strong base.

Solution
Derivative space of space pH space equals space minus log space square root of fraction numerator straight K subscript straight w space. space straight K subscript straight a over denominator straight c end fraction end root
Hydrolysis of the salt, in the present case is
                       A-  +   H2O              OH-  +   HA
Initial conc.       c                             0            0
Equilibrium       straight c left parenthesis 1 minus straight alpha right parenthesis                   cα          cα
conc. 
straight i. straight e. space space space space space open square brackets OH close square brackets to the power of minus space equals space cα But 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 therefore space space space space space space open square brackets straight H to the power of plus close square brackets space equals space fraction numerator straight K subscript straight w over denominator open square brackets OH to the power of minus close square brackets end fraction therefore space space space space space open square brackets straight H to the power of plus close square brackets space equals space straight K subscript straight w over cα
But space space space space straight alpha space equals space square root of fraction numerator straight K subscript straight w over denominator straight K subscript straight a straight c end fraction end root therefore space space space space space space open square brackets straight H to the power of plus close square brackets space equals space straight K subscript straight w over straight c square root of fraction numerator straight K subscript straight a straight c over denominator straight K subscript straight w end fraction end root space space space space space space space space space space space space space space space space space space space space space equals space square root of fraction numerator straight K subscript straight w. space straight K subscript straight a over denominator straight c end fraction end root therefore space space 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 space space equals negative log space square root of fraction numerator straight K subscript straight w. space straight K subscript straight a over denominator straight c end fraction end root space space space space space space space space space space space space equals negative log space open parentheses fraction numerator straight K subscript straight w. space straight K subscript straight c over denominator straight c end fraction close parentheses to the power of 1 divided by 2 end exponent pH space equals space minus 1 half open square brackets log space straight K subscript straight W space plus space log space straight K subscript straight a space minus space log space straight c close square brackets space space space space space space space space space space space space

Some More Questions From Equilibrium Chapter

What is equilibrium?

Give two examples of physical equilibrium.

What kind of molecules in a liquid can evaporate?

Name the factors on which vapour pressure of any liquid depends.

Which measurable property becomes constant in water vapour equilibrium?

Give an example from daily life in which there is gas solution equilibrium?

A crystal of common salt of a given mass is kept in its aqueous solution. After 24 hours, its mass remains the same. Is the crystal in equilibrium with the solution?

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