Final answer:
To determine if a reaction is spontaneous, one considers the Gibbs free energy change (ΔG), which is the difference between enthalpy (ΔH) and the product of temperature and entropy (ΔS). For the reaction N₂ + 3H₂ → 2NH₃, ΔH° and ΔS° are both negative, indicating spontaneity at low temperatures. The reaction becomes nonspontaneous at a temperature of 463.3 K.
Step-by-step explanation:
To determine whether a chemical reaction is spontaneous, one can use Gibbs free energy change (ΔG), which is defined as ΔG = ΔH - TΔS. If ΔG is negative, the reaction is spontaneous; if it is positive, the reaction is not spontaneous. The spontaneity of a reaction can change with temperature, as ΔH and ΔS are often temperature independent but T is not.
Given the values of ΔH° and ΔS° for the reaction N₂(g) + 3H₂(g) → 2NH₃(g), where ΔH° is -91.8 kJ/mol and ΔS° is -198.1 J/K per mole of N₂, we see that both values are negative. Thus, according to the formula ΔG = ΔH° - TΔS°, at low temperatures TΔS° will be small and ΔG will most likely be negative, indicating that the reaction is spontaneous. However, as temperature increases, TΔS° grows and may eventually cause ΔG to become positive, indicating non-spontaneity.
The temperature at which the reaction changes from being spontaneous to nonspontaneous is found by setting ΔG equal to zero and rearranging the equation: T = ΔH° / ΔS°. In this case, the temperature would be T = 91.8 kJ/mol / 198.1 J/K⋅mol = 463.3 K.