Question of equilibrium

Question

Answer with proper explanation

Answer 1

To calculate the equilibrium molar ratio of trans and cis isomers, you can use the relationship between Gibbs free energy change (ΔG°) and the equilibrium constant (K) given by:     \(Δ ∘ = − ln ⁡K\)

1. Find  \( Δ reaction ∘ = Δ trans ∘ − Δ cis\)\( reaction ∘ = 41.549  kJ/mol − 33.235  kJ/mol = 8.314  kJ/mol = 8314  J/mol \)

     2. Use ΔGreaction to calculate K (equilibrium constant):\(K=e−ΔG∘/RTK = e^{-\Delta G^\circ / RT}\)   

​​​​​​​\(− Δ ∘ / = − 8314 / 2478.572 = − 3.353 \)

1. \( = − 3.353 ≈ 0.035\)
2. This equilibrium constant K represents the ratio of trans to cis isomer. The ratio is approx 0.035:1. This indicates the cis isomer is significantly favored at equilibrium due to its lower free energy.