Use data from Appendix C to calculate the equilibrium constant, K, and ΔG° at 298 K for each of the following reactions: (a) H2(g) + I2(g) ⇌ 2 HI(g) (b) C2H5OH(g) ⇌ C2H4(g) + H2O(g) (c) 3 C2H2(g) ⇌ C6H6(g)

Verified step by step guidance

Step 1: Identify the standard Gibbs free energy of formation (ΔG°f) for each reactant and product from Appendix C for each reaction at 298 K.

Step 2: Calculate the standard Gibbs free energy change (ΔG°) for each reaction using the formula: ΔG° = Σ(ΔG°f of products) - Σ(ΔG°f of reactants).

Step 3: Use the relationship between ΔG° and the equilibrium constant (K) given by the equation: ΔG° = -RT ln(K), where R is the universal gas constant (8.314 J/mol·K) and T is the temperature in Kelvin (298 K).

Step 4: Rearrange the equation from Step 3 to solve for the equilibrium constant (K): K = e^(-ΔG°/RT).

Step 5: Substitute the calculated ΔG° from Step 2 into the equation from Step 4 to find the equilibrium constant (K) for each reaction.

Key Concepts

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

Equilibrium Constant (K)

The equilibrium constant, K, is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is calculated using the formula K = [products]^[coefficients] / [reactants]^[coefficients]. A large K value indicates that products are favored at equilibrium, while a small K value suggests that reactants are favored.

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 universal gas constant and T is the temperature in Kelvin. A negative ΔG° value suggests that the reaction is spontaneous in the forward direction.

Standard Conditions

Standard conditions refer to a set of specific conditions (usually 1 atm pressure and 298 K temperature) under which thermodynamic measurements are made. These conditions are essential for calculating standard Gibbs free energy changes and equilibrium constants, ensuring consistency and comparability of data across different reactions and studies.

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Related Practice

Textbook Question

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.

Textbook Question

Consider the reaction 3 CH₄(g) → C₃H₈(g) + 2 H₂(g). (a) Using data from Appendix C, calculate ΔG° at 298 K.

Textbook Question

Consider the reaction 3 CH₄(g) → C₃H₈(g) + 2 H₂(g). (b) Calculate ΔG at 298 K if the reaction mixture consists of 40.0 atm of CH₄, 0.0100 atm of C₃H₈(g), and 0.0180 atm of H₂.

Textbook Question

Using data from Appendix C, write the equilibrium-constant expression and calculate the value of the equilibrium constant and the free-energy change for these reactions at 298 K: (a) NaHCO₃(s) ⇌ NaOH(s) + CO₂(g)

Textbook Question

Consider the decomposition of barium carbonate: BaCO₃(s) ⇌ BaO(s) + CO₂(g) Using data from Appendix C, calculate the equilibrium pressure of CO₂ at (a) 298 K.

Textbook Question

Consider the decomposition of barium carbonate: BaCO₃(s) ⇌ BaO(s) + CO₂(g) Using data from Appendix C, calculate the equilibrium pressure of CO₂ at (b) 1100 K.