Question

At 700K, the equilibrium constant K_p, for the reaction
$2 SO subscript 3 left parenthesis straight g right parenthesis space space rightwards harpoon over leftwards harpoon space space space 2 SO subscript 2 left parenthesis straight g right parenthesis space plus space straight O subscript 2 left parenthesis straight g right parenthesis$ is $1.8 space cross times space 10 to the power of negative 3 end exponent space straight k space Pa.$ What is the chemical value in moles per litre of K_cfor this reaction at the same temperature?

Solution

The reversible reaction is

2 SO subscript 3 left parenthesis straight g right parenthesis space space rightwards harpoon over leftwards harpoon space space space space 2 SO subscript 2 left parenthesis straight g right parenthesis space plus space straight O 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

increment straight n space equals space left parenthesis 2 plus 1 right parenthesis space minus 2 space equals space 1 straight T space equals space 700 space straight K semicolon space space space straight K subscript straight p space equals space 1.8 space cross times space 10 to the power of negative 3 end exponent KP subscript straight a straight K subscript straight p space equals space fraction numerator 1.8 space cross times 10 to the power of negative 3 end exponent KP subscript straight a over denominator 101.3 space straight K space Pa space atm to the power of negative 1 end exponent end fraction space equals space 1.78 space cross times space 10 to the power of negative 5 end exponent atm

Now,

Now 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

Substituting the values, we have,

straight K subscript straight c space equals space fraction numerator 1.78 space cross times space 10 to the power of negative 5 end exponent atm over denominator 0.082 space straight L space atm space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent space cross times space 700 space straight K end fraction

equals 3.09 cross times 10 to the power of negative 7 end exponent mol space straight L to the power of negative 1 end exponent

For Daily Free Study Material Join wiredfaculty