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=1.24×105−3×2.09×105Calculate:
∆G‌reaction ‌0=1.24×105−6.27×105=−5.03×105J∕mol3. Use the relationship between the Gibbs free energy change and the equilibrium constant:
∆G0=−RT‌ln‌K Rearrange to solve for
K :
K=exp(−‌)Given the temperature
T=27∘C=300K, and the gas constant
R=8.314J∕K‌mol, substitute these values along with
∆G0.
K=exp(‌)Calculate exponent:
‌K=exp(‌)‌K=exp(201.71)‌K≈1.429×1088Thus, the correct option is:
Option C:
1.429×1088