If `K_(c ) = 1`, what will be the value of `Delta G`?

Answer

To determine the value of ΔG when Kc = 1, we can follow these steps:

### Step 1: Understand the relationship between Kc and ΔG
The equilibrium constant (Kc) is related to the change in Gibbs free energy (ΔG) by the following equation:
\[ \Delta G = \Delta G^\circ + RT \ln K_c \]
where:
- ΔG is the change in Gibbs free energy at non-standard conditions,
- ΔG° is the standard Gibbs free energy change,
- R is the universal gas constant (8.314 J/(mol·K)),
- T is the temperature in Kelvin,
- Kc is the equilibrium constant.

### Step 2: Substitute Kc = 1 into the equation
Since we are given that Kc = 1, we can substitute this value into the equation:
\[ \Delta G = \Delta G^\circ + RT \ln(1) \]

### Step 3: Evaluate the natural logarithm
The natural logarithm of 1 is 0:
\[ \ln(1) = 0 \]
Thus, the equation simplifies to:
\[ \Delta G = \Delta G^\circ + RT \cdot 0 \]

### Step 4: Simplify the equation
This further simplifies to:
\[ \Delta G = \Delta G^\circ \]

### Step 5: Understand the significance of Kc = 1
When Kc = 1, it indicates that the system is at equilibrium. At equilibrium, the change in Gibbs free energy (ΔG) is always 0:
\[ \Delta G = 0 \]

### Conclusion
Therefore, when Kc = 1, the value of ΔG is:
\[ \Delta G = 0 \]