Consider the reaction: 2 NO(g) + O₂(g) ⇌ 2 NO₂(g) The following data show the equilibrium constant for this reaction measured at several different temperatures. Use the data to find ΔH°_rxn and ΔS°_rxn for the reaction.

Verified step by step guidance

1. Identify the relationship between the equilibrium constant \( K \) and temperature \( T \) using the van 't Hoff equation: \( \ln K = -\frac{\Delta H^\circ}{R} \left( \frac{1}{T} \right) + \frac{\Delta S^\circ}{R} \).
2. Plot \( \ln K \) versus \( \frac{1}{T} \) using the given data. This will yield a straight line where the slope is \( -\frac{\Delta H^\circ}{R} \) and the y-intercept is \( \frac{\Delta S^\circ}{R} \).
3. Determine the slope of the line from the plot. Use the slope to calculate \( \Delta H^\circ \) by rearranging the equation: \( \Delta H^\circ = -\text{slope} \times R \), where \( R \) is the ideal gas constant (8.314 J/mol·K).
4. Determine the y-intercept of the line from the plot. Use the y-intercept to calculate \( \Delta S^\circ \) by rearranging the equation: \( \Delta S^\circ = \text{y-intercept} \times R \).
5. Summarize the calculated values of \( \Delta H^\circ \) and \( \Delta S^\circ \) for the reaction.

Key Concepts

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It provides insight into the extent of the reaction and is temperature-dependent. For the reaction 2 NO(g) + O2(g) ⇌ 2 NO2(g), K can be used to determine how favorably the products are formed compared to the reactants.

Gibbs Free Energy (ΔG°)

Gibbs free energy (ΔG°) is a thermodynamic potential that indicates the spontaneity of a reaction at constant temperature and pressure. It is related to the equilibrium constant by the equation ΔG° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. A negative ΔG° suggests that the reaction is spontaneous in the forward direction.

Thermodynamic Parameters (ΔH° and ΔS°)

The standard enthalpy change (ΔH°) and standard entropy change (ΔS°) are key thermodynamic parameters that describe the heat and disorder changes during a reaction. They can be derived from the temperature dependence of the equilibrium constant using the van 't Hoff equation, which relates changes in K with temperature to ΔH° and ΔS°: d(ln K)/dT = ΔH°/(RT²).