The equilibrium constant shall not depend on temperature if (E-energy of activation)

Options

A. `E_(f)=E_(b)`
B. `E_(f)gtE_(b)`
C. `E_(b)gtE_(f)`
D. `(DeltaH)_("reaction")=0`

Answer

To determine when the equilibrium constant does not depend on temperature, we need to analyze the relationship between the equilibrium constant (K) and the thermodynamic parameters of the reaction, particularly the enthalpy change (ΔH) and the entropy change (ΔS).

### Step-by-Step Solution:

1. **Understanding the Equilibrium Constant**:
The equilibrium constant (K) for a reaction at a given temperature is related to the standard Gibbs free energy change (ΔG°) of the reaction by the equation:
\[ \Delta G° = -RT \ln K \]
where R is the universal gas constant and T is the temperature in Kelvin.

2. **Relating ΔG° to ΔH and ΔS**:
The Gibbs free energy change can also be expressed in terms of enthalpy and entropy changes:
\[ \Delta G° = \Delta H° - T\Delta S° \]
By combining these two equations, we can express K in terms of ΔH and ΔS:
\[ \ln K = \frac{\Delta S°}{R} - \frac{\Delta H°}{RT} \]

3. **Analyzing Temperature Dependence**:
From the equation \(\ln K = \frac{\Delta S°}{R} - \frac{\Delta H°}{RT}\), we can see that K depends on T due to the \(-\frac{\Delta H°}{RT}\) term. Therefore, for K to not depend on temperature, the term involving T must be eliminated.

4. **Condition for Independence from Temperature**:
The term \(-\frac{\Delta H°}{RT}\) will not depend on temperature if ΔH° is equal to zero. This means that the enthalpy change for the reaction is zero, indicating that the energy of the products is equal to the energy of the reactants:
\[ \Delta H° = 0 \implies \text{Energy of products} = \text{Energy of reactants} \]

5. **Conclusion**:
Therefore, the equilibrium constant (K) shall not depend on temperature if the energy of activation (E) is such that the enthalpy change (ΔH) for the reaction is zero.

### Final Answer:
The equilibrium constant shall not depend on temperature if the enthalpy change (ΔH) of the reaction is zero.