Question

Calculate ΔG° (in kJ/mol) for each of the following reactions from the equilibrium constant at the temperature given.

(a) H₂CrO₄(aq) + H₂O(l) equilibrium reaction arrow HCrO₄−(aq) + H₃O+(aq) T = 25.0°C K = 0.180
ΔG° = kJ/mol

(b) Cl₂(g) + Br₂(g) equilibrium reaction arrow 2 BrCl(g) T = 690.0°C K = 4.99
ΔG° = kJ/mol

(c) CaF₂(s) equilibrium reaction arrow Ca₂+(aq) + 2 F −(aq) T = 25.0°C K = 3.5 ✕ 10−11
ΔG° = kJ/mol

(d) CHCl₃(l) equilibrium reaction arrow CHCl₃(g) T = 17.0°C K = 0.181
ΔG° = kJ/mol

(e) CoO(s) + CO(g) equilibrium reaction arrow Co(s) + CO₂(g) T = 575.0°C K = 261
ΔG° = kJ/mol

(f) 2 NO(g) + Cl₂(g) equilibrium reaction arrow 2 NOCl(g) T = 485.0°C K = 0.132
ΔG° = kJ/mol

Answer 1

The ΔG° for each reaction can be calculated using the equation ΔG° = -RT ln K, where R is the gas constant, T is the temperature in Kelvin, and K is the equilibrium constant. We can use this equation to calculate the ΔG° for each given reaction.

Step-by-step explanation:

(a) To calculate the standard free energy change, ΔG°, we can use the equation ΔG° = -RT ln K, where R is the gas constant (8.314 J/molK), T is the temperature in Kelvin, and K is the equilibrium constant. In this case, the equilibrium constant, K, is given as 0.180. Plugging in the values, we get: ΔG° = -8.314 J/molK * (25.0 + 273.15)K * ln(0.180) = -365.671 J/mol. To convert this to kJ/mol, we divide by 1000, giving us a value of -0.366 kJ/mol.

(b) Following the same equation as above, ΔG° = -8.314 J/molK * (690.0 + 273.15)K * ln(4.99) = 4725.05 J/mol. Converting to kJ/mol, we get 4.725 kJ/mol.

(c) Using the same equation, ΔG° = -8.314 J/molK * (25.0 + 273.15)K * ln(3.5 * 10^(-11)) = -27581.0 J/mol. Converting to kJ/mol, we get -27.581 kJ/mol.

(d) Using the same equation, ΔG° = -8.314 J/molK * (17.0 + 273.15)K * ln(0.181) = -1192.78 J/mol. Converting to kJ/mol, we get -1.192 kJ/mol.

(e) Using the same equation, ΔG° = -8.314 J/molK * (575.0 + 273.15)K * ln(261) = 72681.1 J/mol. Converting to kJ/mol, we get 72.681 kJ/mol.

(f) Using the same equation, ΔG° = -8.314 J/molK * (485.0 + 273.15)K * ln(0.132) = -5963.67 J/mol. Converting to kJ/mol, we get -5.964 kJ/mol.