Consider the following reaction:

\[ \text{H}_2\text{O} (g) + \text{Cl}_2\text{O} (g) \rightleftharpoons 2\text{HOCl} (g) \]

Given:

\[ K_{298} = 0.090 \]

For \(\text{Cl}_2\text{O} (g)\):

\[ \Delta G_f = 97.9 \text{ kJ/mol} \]

\[ \Delta H = 80.3 \text{ kJ/mol} \]

\[ S = 266.1 \text{ J/K mol} \]

Calculate \(\Delta G\) for the reaction using the equation \(\Delta G = -RT \ln(K)\).

Using the given values and the formula ∆G = -RT ln(K), the Gibbs free energy change for the reaction is calculated to be 5.74 kJ/mol. This positive ∆G value indicates the reaction is nonspontaneous in the forward direction under the given conditions.

Explanation:

To calculate the Gibbs free energy change (∆G) for the reaction, we would use the given equation ∆G = -RT ln(K). Given that K = 0.090, R = 8.3145 J/mol*K, and T is 298K (which is usually the case for these kinds of problems). Inserting these values into the equation gives:

∆G = - (8.3145 J/mol K) * (298 K) ln(0.090)

Thus, ∆G = 5.74 kJ/mol.

This value indicates the spontaneity of the reaction under these given conditions. A positive ∆G means the reaction is nonspontaneous while a negative ∆G means the reaction is spontaneous. In this case, the reaction is nonspontaneous in the forward direction at 298K.

Learn more about Gibbs Free Energy here:

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