For the reaction
`CO (g) + (1)/(2) O_(2) (g) rarr CO_(2) (g)`
`Delta H` and `Delta S` are `283 kJ` and `-87 J K^(-1)`, respectively. It was intended to carry out this reaction at 1000,1500,3000, and 3500 K. At which of these temperatures would this reaction be thermodynamically spontaneous?

Options

A. 3000 and 3500 K
B. 1500 and 3000 K
C. 1500 , 3000, and 3500 K
D. 1000, 1500, and 3000 K

Answer

D

Explanation

According to thermodynamics,
`Delta G = Delta H - T Delta S`
Since both `Delta H` and `Delta S` are negative, the reaction will be spontaneous at a temperature below equilibrium temperature so that the `Delta H` term prdominates.
At equilibrium, `Delta G = 0`. Thus,
`T = (Delta H)/(Delta S) = (- 283 xx 10^(3) J)/(- 87 xx 10 J K^(-1)) = 3252 K`
This implies that the reaction will be spontaneous at any temperature below `3252 K`.