Using the data given below, calculate the value of equilibrium constant for the reaction
`underset("acetylene")(3HC-= CH(g)) hArr underset("benzene")(C_6H_6)(g)`
at 298 K, assuming ideal behaviour.
`Delta_fG^@ HC -= CH(g) = 2.09 xx 10^5 J mol^(-1)`,
`Delta_fG^@ C_6H_6(g) = 1.24 xx 10^5 J mol^(-1)`
`R = 8.314 JK^(-1) mol^(-1)`

Explanation

To calculate the equilibrium constant (K) for the reaction:

\[ 3 \text{HC} \equiv \text{CH(g)} \rightleftharpoons \text{C}_6\text{H}_6(g) \]

at 298 K, we will use the given Gibbs free energy of formation (\( \Delta_f G^\circ \)) values and the relationship between Gibbs free energy change and the equilibrium constant.

### Step-by-Step Solution:

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