For the reaction of ammonium carbonate to produce carbon dioxide and ammonia, an experiment was devised and the results were plotted as in the following diagram:

Which one of the following is consistent with these results?

Options

A. `Delta H ^(@) =- 455 kJ mol ^(-1) , Delta S ^(@) = 156 J mol ^(-1) K ^(-1)`
B. `Delta H ^(@) = 156 xx 103 mol ^(-1), Delta S ^(@) =0 455 J mol ^(-1) K ^(-1)`
C. `Delta H ^(@) = 170 kJ mol ^(-1) , Delta S ^(@) = 500 J mol ^(-1) K ^(-1)`
D. `Delta H ^(@)=156 xx 103 kJ mol ^(-1) , Delta S ^(@) = 455 kJ mol ^(-1) K ^(-1)`

Explanation

Slope of the line `(- Delta S ^(@))` can be determined approximaltely as
`- Delta S ^(@) = ( 20, 000 - 15 000)/( 300 - 310 ) =- 500 implies Delta S ^(@) = 500 JK ^(-1) mol ^(-1)`
Sustituting `Delta S ^(@)` in `Delta G ^(@) = Delta H ^(@) - T Delta S ^(@) at 300 K ` gives :
`Delta H ^(@) = 2000 + 300 xx 500 = 170, 000 J ~~ 170 KJ // mol`