For reaction, `2K_((g))+L_((g))rarr2M_((g)),DeltaU^(@)=-"10.5 KJ and "DeltaS^(@)=-"44.1 J K"^(-1)`. Calculate `DeltaG^(@)` for the reaction and predict whether the reaction will be spontaneous or non-spontaneous?

Options

A. `DeltaG=+"0.16 kJ, non-spontaneous"`
B. `DeltaG=-"0.16 kJ, spontaneous"`
C. `DeltaG=+"26.12 kJ, non-spontaneous"`
D. `DeltaG=-"26.12 kJ, spontaneous"`

Answer

A

Explanation

`2K+L rarr 2M`
`Deltan_(g)=2-3=-1`
`DeltaH=DeltaU+Deltan_(g)RT=-10.5xx10^(3)+(-1xx8.314xx298)`
`=-10500+(-2477.572)=-12977.57J=-12.98kJ`
`DeltaG^(@)=DeltaH^(@)-TDeltaS^(@)=-12.98-298(-44.1xx10^(-3))`
`=-12.98+13.14=0.16kJ`
Since `DeltaG^(@)` is `+ve` hence it is non-spontaneous.