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°_rxnand ΔS°_rxnfor the reaction.

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Identify the relationship between the equilibrium constant \( K \) and temperature \( T \) using the van 't Hoff equation: \( \ln K = -\frac{\Delta H^\circ}{R} \left( \frac{1}{T} \right) + \frac{\Delta S^\circ}{R} \).

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 \( \frac{\Delta S^\circ}{R} \).

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).

Determine the y-intercept of the line from the plot. Use the y-intercept to calculate \( \Delta S^\circ \) by rearranging the equation: \( \Delta S^\circ = \text{y-intercept} \times R \).

Summarize the calculated values of \( \Delta H^\circ \) and \( \Delta S^\circ \) for the reaction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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).