Question

which statement is true for the reaction below?\\(\ce{n2o4(g) -> 2no2(g)}\\)\\(\delta h = +57.24\space kj/mol\\)\
the reaction will occur at all temperatures.\
the reaction will occur only at low temperatures.\
the reaction will never occur.\
the reaction will occur only at high temperatures.

Explanation:

1. First, analyze the enthalpy change ($\Delta H$) and entropy change ($\Delta S$) of the reaction:

• The reaction is $\ce{N_{2}O_{4}(g) -> 2NO_{2}(g)}$ (assuming a typo, should be $\ce{NO_{2}}$ instead of $\ce{NCO_{2}}$). The number of moles of gas increases from 1 to 2, so $\Delta S>0$ (positive entropy change as disorder increases).
• $\Delta H = + 57.24\space kJ/mol$ (endothermic, $\Delta H>0$).

1. Then, use the Gibbs free energy equation $\Delta G=\Delta H - T\Delta S$ to determine the spontaneity:

• For a reaction to be spontaneous, $\Delta G < 0$.
• Substitute $\Delta H>0$ and $\Delta S>0$ into the equation: $\Delta G=\Delta H - T\Delta S$.
• At low temperatures, $T\Delta S$ is small (since $T$ is small). So $\Delta H - T\Delta S>0$ (because $\Delta H$ is positive and large enough compared to $T\Delta S$), so the reaction is non - spontaneous at low temperatures.
• At high temperatures, $T\Delta S$ becomes large (since $T$ is large). So $\Delta H - T\Delta S$ can be less than 0 (because $T\Delta S$ is large enough to overcome the positive $\Delta H$), so the reaction is spontaneous at high temperatures.
• The reaction is endothermic ($\Delta H>0$) and has an increase in entropy ($\Delta S>0$). Reactions with $\Delta H>0$ and $\Delta S>0$ are spontaneous only at high temperatures (when $T\Delta S>\Delta H$ to make $\Delta G < 0$).
• The option "The reaction will occur at all temperatures" is wrong because at low $T$, $\Delta G$ is positive. "The reaction will occur only at low temperatures" is wrong because at low $T$, $\Delta G$ is positive. "The reaction will never occur" is wrong because at high $T$, $\Delta G$ can be negative.

Answer:

D. The reaction will occur only at high temperatures.