Calculate `DeltaG^(@)` (kJ/mol) at `127^(@)C` for a reaction with `K_("equilibrium")=10^(5)` :

Options

A. `-38.294`
B. `-16.628`
C. `-9.16`
D. None of these

Explanation

To calculate the standard Gibbs free energy change (ΔG°) at 127°C for a reaction with an equilibrium constant (K_eq) of 10^5, we can use the following relationship:

\[ \Delta G° = -RT \ln K_{eq} \]

### Step-by-Step Solution:

**Step 1: Convert the temperature from Celsius to Kelvin.**
- The temperature in Celsius is given as 127°C.
- To convert to Kelvin, use the formula:
\[ T(K) = T(°C) + 273.15 \]
- Thus,
\[ T = 127 + 273.15 = 400.15 \, K \approx 400 \, K \]

**Step 2: Identify the values for R and K_eq.**
- The universal gas constant \( R \) is typically given as:
\[ R = 8.314 \, \text{J/(mol·K)} \]
- The equilibrium constant \( K_{eq} \) is given as:
\[ K_{eq} = 10^5 \]

**Step 3: Calculate the natural logarithm of K_eq.**
- We need to find \( \ln K_{eq} \):
\[ \ln(10^5) = 5 \ln(10) \]
- Using the approximation \( \ln(10) \approx 2.303 \):
\[ \ln(10^5) = 5 \times 2.303 = 11.515 \]

**Step 4: Substitute the values into the ΔG° equation.**
- Now, substitute \( R \), \( T \), and \( \ln K_{eq} \) into the equation:
\[ \Delta G° = - (8.314 \, \text{J/(mol·K)})(400 \, K)(11.515) \]

**Step 5: Perform the multiplication.**
- Calculate:
\[ \Delta G° = - (8.314 \times 400 \times 11.515) \]
- First calculate \( 8.314 \times 400 \):
\[ 8.314 \times 400 = 3325.6 \, \text{J/mol} \]
- Then multiply by \( 11.515 \):
\[ 3325.6 \times 11.515 \approx 38327.5 \, \text{J/mol} \]

**Step 6: Convert J/mol to kJ/mol.**
- Since we want the answer in kJ/mol, divide by 1000:
\[ \Delta G° \approx -38.3275 \, \text{kJ/mol} \]

**Final Result:**
\[ \Delta G° \approx -38.33 \, \text{kJ/mol} \]