Question

Hydrolysis of sucrose gives,
$Sucrose space plus space straight H subscript 2 straight O space rightwards harpoon over leftwards harpoon space space Glucose space plus space Fructose$
Equilibrium constant K_c for the reaction is $2 cross times 10 to the power of 13 space at space 300 space straight K.$ Calculate $increment straight G degree$ at 300K.

Solution

We know,
$increment straight G degree space equals space minus RT space ln space straight K subscript straight c space equals space minus 2.303 space straight R space straight T space log space straight K subscript straight c space space space... left parenthesis 1 right parenthesis$
$Here comma space space space space space straight K subscript straight c space equals space 2 space cross times space 10 to the power of 13 space space space space space space space space space space space space straight T space equals 300 space straight K comma space space space space space space space space space space space space straight R space equals space 8.314 space JK to the power of negative 1 end exponent space mol to the power of negative 1 end exponent$
Putting the values in expression (1), we have
$increment straight G degree equals space minus 2.303 space cross times space left parenthesis 8.314 space JK to the power of negative 1 end exponent space mol to the power of negative 1 end exponent right parenthesis space left parenthesis 300 space straight K right parenthesis space log space left parenthesis 2 cross times 10 to the power of negative 13 end exponent right parenthesis or space space space increment straight G to the power of 0 space equals space minus 7.64 space cross times space 10 to the power of 4 space straight J space mol to the power of negative 1 end exponent$