Question

Find out the value of K_c for each of the following equilibrium from the value of K_p:

$left parenthesis straight a right parenthesis space 2 space NOCl left parenthesis straight g right parenthesis space space space rightwards harpoon over leftwards harpoon space space space space 2 NO left parenthesis straight g right parenthesis space plus space Cl subscript 2 left parenthesis straight g right parenthesis semicolon space space straight K subscript straight p space equals space 1.8 space cross times space 10 to the power of negative 2 end exponent space at space 500 straight K left parenthesis straight b right parenthesis space CaCO subscript 3 left parenthesis straight s right parenthesis space space space space leftwards harpoon over rightwards harpoon space space CaO left parenthesis straight s right parenthesis space plus space CO subscript 2 left parenthesis straight g right parenthesis comma space straight K subscript straight p space equals space 167 space at space 1073 space straight K$

Solution

(a) The reversible reaction is

2 NOCl left parenthesis straight g right parenthesis space space rightwards harpoon over leftwards harpoon space space space space 2 NO left parenthesis straight g right parenthesis space plus space Cl subscript 2 left parenthesis straight g right parenthesis

We know,

straight K subscript straight p space equals space straight K subscript straight c left parenthesis RT right parenthesis to the power of increment straight n end exponent

or space space space space straight K subscript straight c space equals space fraction numerator straight K subscript straight p over denominator left parenthesis RT right parenthesis to the power of increment straight n end exponent end fraction

...(1)
Here,

straight K subscript straight p space equals space 1.8 space cross times space 10 to the power of negative 2 end exponent semicolon

straight R space equals space 0.00831 space straight L space bar space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent straight T space equals space 500 space straight K semicolon increment straight n space equals space left parenthesis 2 plus 1 right parenthesis minus 2 space equals space 1

Substituting the values in (1), we have,

straight K subscript straight c space equals fraction numerator 1.8 space cross times 10 to the power of negative 2 end exponent over denominator 0.0831 space cross times 500 end fraction space equals space 4.33 space cross times space 10 to the power of 4

(b) The reversible reaction is

CaCO subscript 3 left parenthesis straight s right parenthesis space space space rightwards harpoon over leftwards harpoon space space space space CaO left parenthesis straight s right parenthesis space plus space CO subscript 2 left parenthesis straight g right parenthesis

We know,

straight K subscript straight p space equals space straight K subscript straight c left parenthesis RT right parenthesis to the power of increment straight n end exponent

or space space space space straight K subscript straight c space equals space fraction numerator straight K subscript straight p over denominator left parenthesis RT right parenthesis to the power of increment straight n end exponent end fraction

...(1)

Here space straight K subscript straight p space equals space 167 semicolon space space straight R space equals space 0.0831 space straight L space bar space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent straight T space equals space 1073 space straight K semicolon space space increment straight n space equals space 1

Substituting the values in (1), we have,

straight K subscript straight c space equals space fraction numerator 167 over denominator 0.0831 space cross times space 1073 space end fraction space equals space 1.87

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