The values of `DeltaH` and `DeltaS` for the reaction,
`C_("graphite")+CO_(2)(g)rarr2CO(g)`
are `170KJ` and `170JJK^(-)` respectively. This reaction will be spontaneous at

Options

A. 910 K
B. 1110K
C. 510K
D. 710 K

Answer

B

Explanation

`DeltaG =DeltaH - T DeltaS`. For reaction to be spontaneous `DeltaS` should be -ve, i.e.,`DeltaH-TDetlaS lt0 `or `DeltaHlt T DeltaS`
or `TDeltaS gt DeltaH ` or`Tgt ( DeltaH )/( DeltaS) , i.e.,T gt (170000J)/( 170 JK^(-1))` or `T gt 1000K`. Hence, options (b) iscorrect. This method can be applied only when `DeltaH` and`DeltaS` both are `+ve`.
Alternatively, for equilibrium , `DeltaG =0`
`i.e., T DeltaS = DeltaH` or `T= ( DeltaH )/( DeltaS) =( 170000)/( 170) =1000K`
For spontaneity , `DeltaG = -ve`which can be so if `T gt 1000 K` ( so that`T DeltaS gt DetalH` in magnitude ) .