​$$∆G^0$$of a reaction shows the following temperature dependence.​

​What is the expected dependence of  $$K_{eq}$$ of the reaction on the temperature, where C is a temperature-independent constant?​

Correct option is B

The correct option is (b)

Explanation:
1.  Basic Thermodynamics Relation:

The standard Gibbs free energy change $$\Delta G^{0}$$​  is related to the equilibrium constant $$K_{eq}$$​  by the equation:

$$\Delta G^{0} = -RT \ln K_{eq}$$

where,

R is the universal gas constant,
T is the absolute temperature in Kelvin,
ln is the natural logarithm.

2.  Given Condition:
From the graph ,$$\Delta G^0$$​ does not change with temperature T. This implies:​​

​$$\Delta G^{0} = \text{constant} = C$$

3. Finding $$K_{eq}$$

  Substitute  $$\Delta G^0 = C$$ into the thermodynamic relation​​

​$$C = -RT \ln K_{eq}$$​​
Rearranging $$\ln K_{eq}$$ :​​

​$$\ln K_{eq} =- \frac{C}{RT}$$

4. Exponentiating both sides:

$$K_{eq} = e^{-\frac{C}{RT}} = e^{-\frac{C}{R} \times \frac{1}{T}}$$​​​​
5.  Interpreting the result:

        This shows that $$K_{eq}$$ depends exponentially on $$\frac{1}{T}$$ when $$\Delta G^{0}$$ is constant

                                                      So  the correct relation is: ​$$K_{eq} = C \times e^{1/T}$$​