Consider the reaction 2 NO₂(g) → N₂O₄(g). (a) Using data from Appendix C, calculate ΔG° at 298 K. (b) Calculate ΔG at 298 K if the partial pressures of NO₂ and N₂O₄ are 0.40 atm and 1.60 atm, respectively.

Verified step by step guidance

1. Step 1: To calculate ΔG° at 298 K, we need to use the formula ΔG° = ΔH° - TΔS°. The values for ΔH° and ΔS° can be found in Appendix C for NO₂ and N₂O₄. Remember that ΔH° and ΔS° for the reaction are calculated as the difference between the products and reactants, taking into account their stoichiometric coefficients.
2. Step 2: After finding the values for ΔH° and ΔS°, substitute them into the formula along with the temperature in Kelvin (298 K) to calculate ΔG°.
3. Step 3: To calculate ΔG at 298 K with the given partial pressures, we need to use the formula ΔG = ΔG° + RTlnQ, where R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and Q is the reaction quotient.
4. Step 4: The reaction quotient Q is calculated as the ratio of the product of the concentrations (or pressures) of the products to the product of the concentrations (or pressures) of the reactants, each raised to the power of their stoichiometric coefficients. In this case, Q = [N₂O₄]/[NO₂]² = (1.60 atm)/(0.40 atm)².
5. Step 5: Substitute the values for ΔG°, R, T, and Q into the formula to calculate ΔG.

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 a crucial concept in predicting the spontaneity of a reaction; a negative ΔG indicates a spontaneous process, while a positive ΔG suggests non-spontaneity. The standard Gibbs free energy change (ΔG°) is calculated under standard conditions, typically at 1 atm and 298 K.

Standard Gibbs Free Energy Change (ΔG°)

The standard Gibbs Free Energy Change (ΔG°) is the change in Gibbs free energy for a reaction when all reactants and products are in their standard states (1 M concentration for solutions, 1 atm pressure for gases) at a specified temperature, usually 298 K. It is derived from the standard enthalpy and entropy changes of the reaction using the equation ΔG° = ΔH° - TΔS°. This value helps in determining the favorability of a reaction under standard conditions.

Reaction Quotient (Q) and its Relation to ΔG

The reaction quotient (Q) is a measure of the relative amounts of products and reactants present in a reaction at any point in time, calculated using the partial pressures or concentrations of the species involved. It is used to determine the direction in which a reaction will proceed to reach equilibrium. The relationship between ΔG and Q is given by the equation ΔG = ΔG° + RT ln(Q), where R is the gas constant and T is the temperature in Kelvin. This equation allows for the calculation of ΔG under non-standard conditions.