Consider the following reaction between oxides of nitrogen: NO₂(g) + N₂O(g) → 3 NO(g) (b) Calculate ΔG at 800 K, assuming that ΔH° and ΔS° do not change with temperature. Under standard conditions is the reaction spontaneous at 800 K?

Verified step by step guidance

1. Identify the given values: \( \Delta H^\circ \) (standard enthalpy change) and \( \Delta S^\circ \) (standard entropy change) for the reaction. These values are typically found in thermodynamic tables.
2. Use the Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \), where \( T \) is the temperature in Kelvin. Substitute the given temperature (800 K) into the equation.
3. Calculate \( \Delta G \) using the values of \( \Delta H^\circ \) and \( \Delta S^\circ \) along with the temperature. Remember to convert \( \Delta S^\circ \) from J/mol·K to kJ/mol·K if necessary, to match the units of \( \Delta H^\circ \).
4. Determine the spontaneity of the reaction by analyzing the sign of \( \Delta G \). If \( \Delta G < 0 \), the reaction is spontaneous under standard conditions at 800 K. If \( \Delta G > 0 \), the reaction is non-spontaneous.
5. Conclude whether the reaction is spontaneous at 800 K under standard conditions based on the calculated \( \Delta G \).

Key Concepts

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates that a reaction is spontaneous under the given conditions.

Enthalpy (ΔH) and Entropy (ΔS)

Enthalpy (ΔH) is the total heat content of a system, reflecting the energy required to break and form bonds during a reaction. Entropy (ΔS) measures the degree of disorder or randomness in a system. Both ΔH and ΔS are crucial for determining the spontaneity of a reaction through their influence on ΔG, particularly at varying temperatures.

Spontaneity of Reactions

The spontaneity of a reaction refers to whether a reaction can occur without external intervention. A reaction is spontaneous if ΔG is negative, indicating that the products are favored at equilibrium. Factors such as temperature, enthalpy, and entropy changes play significant roles in determining spontaneity, especially in reactions involving gases and temperature variations.