COMEDK 2024 Shift 1 Paper

To calculate the equilibrium constant K for the cyclic polymerization of ethyne to benzene at 27∘C, we need to follow these steps:
1. Write the balanced chemical equation for the reaction:
3C2H2(g)⟶C6H6(l)
2. Calculate the change in Gibbs free energy for the reaction (∆G0) using the given standard Gibbs free energies of formation (∆Gf0) :
The formula to calculate the Gibbs free energy change for the reaction is:
∆G‌reaction ‌0=∆Gf0(C6H6)−3×∆Gf0(C2H2)

Given:
∆Gf0(C2H2)‌=2.09×105J∕mol
∆Gf0(C6H6)‌=1.24×105J∕mol

Substitute these values into the formula:
∆G‌reaction ‌0=1.24×105−3×2.09×105
Calculate:

∆G‌reaction ‌0=1.24×105−6.27×105=−5.03×105J∕mol
3. Use the relationship between the Gibbs free energy change and the equilibrium constant:
∆G0=−RT‌ln‌K

Rearrange to solve for K :
K=exp(−‌

∆G0

RT

)
Given the temperature T=27∘C=300K, and the gas constant R=8.314J∕K‌mol, substitute these values along with ∆G0.

K=exp(‌

5.03×105

8.314×300

)
Calculate exponent:
‌K=exp(‌

5.03×105

2494.2

)
‌K=exp(201.71)
‌K≈1.429×1088
Thus, the correct option is:
Option C: 1.429×1088