For each reaction, calculate ΔH°_rxn, ΔS°_rxn, and ΔG°_rxn at 25 °C and state whether or not the reaction is spontaneous. If the reaction is not spontaneous, would a change in temperature make it spontaneous? If so, should the temperature be raised or lowered from 25 °C? d. N₂(g) + 3 H₂(g) → 2 NH₃(g)

Verified step by step guidance

1. Identify the standard enthalpy change (ΔH°) for the reaction by using standard enthalpies of formation (ΔH°f) for each compound: ΔH°rxn = ΣΔH°f(products) - ΣΔH°f(reactants).
2. Determine the standard entropy change (ΔS°) for the reaction using standard molar entropies (S°) for each compound: ΔS°rxn = ΣS°(products) - ΣS°(reactants).
3. Calculate the standard Gibbs free energy change (ΔG°) using the equation: ΔG°rxn = ΔH°rxn - TΔS°rxn, where T is the temperature in Kelvin (298 K for 25 °C).
4. Assess the spontaneity of the reaction: if ΔG°rxn < 0, the reaction is spontaneous; if ΔG°rxn > 0, the reaction is non-spontaneous.
5. If the reaction is non-spontaneous, analyze the signs of ΔH°rxn and ΔS°rxn to determine if a change in temperature could make the reaction spontaneous. If ΔH°rxn > 0 and ΔS°rxn > 0, increasing the temperature may make the reaction spontaneous. If ΔH°rxn < 0 and ΔS°rxn < 0, decreasing the temperature may make the reaction spontaneous.

Key Concepts

Thermodynamic Functions (ΔH, ΔS, ΔG)

ΔH°rxn represents the change in enthalpy, indicating the heat absorbed or released during a reaction. ΔS°rxn denotes the change in entropy, reflecting the disorder or randomness of the system. ΔG°rxn, the Gibbs free energy change, determines the spontaneity of a reaction; a negative ΔG indicates spontaneity at constant temperature and pressure.

Spontaneity of Reactions

A reaction is spontaneous if it occurs without external intervention, which is determined by the sign of ΔG°rxn. If ΔG°rxn is negative, the reaction is spontaneous; if positive, it is non-spontaneous. The relationship between ΔH, ΔS, and temperature (T) is crucial, as it can influence the spontaneity of a reaction under different conditions.

Temperature's Effect on Spontaneity

The temperature can affect the spontaneity of a reaction through the Gibbs free energy equation: ΔG°rxn = ΔH°rxn - TΔS°rxn. If ΔS°rxn is positive, increasing temperature can make a non-spontaneous reaction spontaneous. Conversely, if ΔS°rxn is negative, lowering the temperature may be necessary to achieve spontaneity.