Using the following data, calculate the value of equilibrium constant for the following reaction at `298K`
`underset("Acetylene")(3HC-=CH)hArr underset("Benzene")(C_(6)H_(6)(g))`
Assuming ideal behaviour
`Delta_(f)G^(Theta) (HC-= CH) = 2.09 xx 10^(5) J mol^(-1)`
`Delta_(f)G^(Theta) (C_(6)H_(6)) = 1.24 xx 10^(5) J mol^(-1)`,
`R = 8.314 J K^(-1) mol^(-1)`
Can the reaction be recommended for the synthesis of benzene?

Explanation

To calculate the equilibrium constant for the reaction \(3 \text{HC} \equiv \text{CH} \rightleftharpoons \text{C}_6\text{H}_6\) at 298 K, we will follow these steps:

### Step 1: Calculate the Gibbs Free Energy Change (\( \Delta G^\circ \)) for the reaction

The Gibbs free energy change for the reaction can be calculated using the standard Gibbs free energies of formation (\( \Delta_f G^\circ \)) of the products and reactants. The formula is:

\[
\Delta G^\circ = \sum (\Delta_f G^\circ \text{ of products}) - \sum (\Delta_f G^\circ \text{ of reactants})
...