Standard free energy change for an equilibrium is zero, the value of `K_(p)` is

Options

A. zero
B. 1
C. 2
D. 100

Answer

To solve the problem, we need to find the value of \( K_p \) when the standard free energy change (\( \Delta G^0 \)) for an equilibrium is zero. Here’s the step-by-step solution:

### Step 1: Understand the relationship between Gibbs free energy and the equilibrium constant
The relationship between the standard Gibbs free energy change (\( \Delta G^0 \)) and the equilibrium constant (\( K_p \)) is given by the equation:
\[ \Delta G^0 = -2.303RT \log K_p \]
where:
- \( R \) is the universal gas constant (8.314 J/mol·K)
- \( T \) is the temperature in Kelvin

### Step 2: Substitute the given value of \( \Delta G^0 \)
According to the question, \( \Delta G^0 = 0 \). We can substitute this value into the equation:
\[ 0 = -2.303RT \log K_p \]

### Step 3: Simplify the equation
Since \( -2.303RT \) is a constant and cannot be zero, the only way for the equation to hold true is if:
\[ \log K_p = 0 \]

### Step 4: Solve for \( K_p \)
To find \( K_p \), we need to eliminate the logarithm. Recall that if \( \log K_p = 0 \), then:
\[ K_p = 10^0 \]
This simplifies to:
\[ K_p = 1 \]

### Conclusion
Thus, when the standard free energy change for an equilibrium is zero, the value of \( K_p \) is:
\[ \boxed{1} \]