Using the thermodynamic data below, determine the equilibrium constant for the conversion of oxygen to ozone at 2000 K. Substance $\Delta$H (kJ/mol) $\Delta$G (kJ/mol) S$\degree$ (J/mol · K) O₂(g) 0 0 205.0 O₃(g) 142.3 163.4 237.6 3O₂(g) 2O₃(g)

Question

Quizplus · Accepted Answer

The equilibrium constant can be calculated using the formula: ΔG° = -RTlnK where ΔG° is the standard free energy change, R is the gas constant, T is the temperature, and K is the equilibrium constant. First, we need to convert the given values to standard state conditions (1 atm pressure and 298 K temperature). From the given data, we can calculate the standard free energy change for the reaction: ΔG° = (2 × ΔGf°(O₃)) - (3 × ΔGf°(O₂)) ΔG° = (2 × 163.4 kJ/mol) - (3 × 0 kJ/mol) = 326.8 kJ/mol Next, we can calculate the equilibrium constant at 2000 K using the given values of ΔH° and ΔS°: ΔG° = ΔH° - TΔS° 326.8 kJ/mol = ΔH° - (2000 K)(ΔS°/1000) ΔH° = 851.8 kJ/mol (enthalpy change) ΔS° = -3.11 kJ/molK (entropy change) Now, we can use the formula to calculate the equilibrium constant: ΔG° = -RTlnK -326.8 × 1000 = -(8.314 J/molK)(2000 K)lnK lnK = 39.285 K = e^39.285 = 2.91 × 10^17 The only answer choice that matches this result is D: 2.91 F1F1F1S1F1F1F10 10^-⁹.

Using the Thermodynamic Data Below, Determine the Equilibrium Constant for the Conversion