What is Kc for the following equilibrium when the equilibrium concentration of each substance
is: $open square brackets SO subscript 2 close square brackets space equals space 0.60 space straight M comma space space open square brackets straight O subscript 2 close square brackets space equals space 0.82 space straight M space and space open square brackets SO subscript 3 close square brackets space equals space 1.90 space straight M ?$
$2 SO subscript 2 left parenthesis straight g right parenthesis space plus space straight O subscript 2 space space rightwards harpoon over leftwards harpoon space space 2 SO subscript 3 left parenthesis straight g right parenthesis$

Solution

The reversible reaction is
$space 2 SO subscript 2 plus straight O subscript 2 left parenthesis straight g right parenthesis space space rightwards harpoon over leftwards harpoon space space space 2 SO subscript 3 left parenthesis straight g right parenthesis$
The equilibrium constant K_c is given by
$space straight K subscript straight c space equals space fraction numerator open square brackets SO subscript 3 close square brackets squared over denominator open square brackets SO subscript 2 close square brackets squared space open square brackets straight O subscript 2 close square brackets end fraction space space space space space space space space space space space... left parenthesis 1 right parenthesis$
Putting the values in expression (1), we have

$straight K subscript straight c space equals space fraction numerator left parenthesis 1.90 space straight M right parenthesis squared over denominator left parenthesis 0.60 space straight M right parenthesis squared space left parenthesis 0.82 space straight M right parenthesis end fraction space space space equals space 12 space cross times space 229 space straight M to the power of negative 1 end exponent space space or space space space 12.229 space straight L space mol to the power of negative 1 end exponent$