For 2Zn + O2 -> 2ZnO, Delta H deg=-700 kJ and Delta S deg=-0.200 kJ K^-1; for 2C + O2 -> 2CO, Delta H deg=-221 kJ and Delta S deg=+0.180 kJ K^-1 (both per mole of O2, taken as temperature independent). The lowest temperature at which ZnO + C -> Zn + CO becomes spontaneous is closest to

JEE Advanced levelSingle correct optionDifficulty 3 of 3mt146

For $2 Zn + O X_{2} 2 ZnO$ , $Δ H^{\circ} = - 700 kJ$ and $Δ S^{\circ} = - 0.200 kJ K^{- 1}$ ; for $2 C + O X_{2} 2 CO$ , $Δ H^{\circ} = - 221 kJ$ and $Δ S^{\circ} = + 0.180 kJ K^{- 1}$ (both per mole of $O X_{2}$ , taken as temperature independent). The lowest temperature at which $ZnO + C Zn + CO$ becomes spontaneous is closest to

Subtract the zinc equation from the carbon equation and halve it:

Δ H^{\circ} = (- 221 + 700) /2 = + 239.5 kJ

and

Δ S^{\circ} = (0.180 + 0.200) /2 = 0.190 kJ K^{- 1}

. Spontaneity needs

Δ H^{\circ} - T Δ S^{\circ} < 0

, so

T > 239.5/0.190 \approx 1260 K