Given the following data:

Determine at what temperature the following reaction is spontaneous?
`Fe O (s) + C ` (Graphite) `to Fe (s) + CO (g)`

Options

A. 298 K
B. 668 K
C. 966 K
D. `Delta G ^(@) ` is + ve, hence the reaction will never be spontaneous

Explanation

`Delta H _("reaction") = sum { Delta H _(f Fe(s))^(@) + Delta H _(fCO(g)) ^(@) } - {Delta H _(f Fe O (s)) ^(@) + Delta H _(f C("graphite"))^(@) }`
`= (0- 110.5) - (-266.3+ 0) = 155.8 kJ mol ^(-1) , Delta S _("reaction") = sum [S _(Fe(s)) ^(@) + S _(CO (g)) ^(@) ] -[ S _(Fe O (s)) ^(@) + S _(c ("graphite"))^(@)]`
`= (27.28 + 197.6) - (59. 49 + 5. 74) = 161.65 JK ^(-1) mol ^(-1)`
For spontaneous reaction, `T gt ( Delta H)/( Delta S) , T gt ( 155 8 xx 1000)/(161 . 65) therefore T gt 694 K`