The value of `log_(10)K` for a reaction `A hArr B` is (Given: `Delta_(f)H_(298K)^(Theta) =- 54.07 kJ mol^(-1)`,
`Delta_(r)S_(298K)^(Theta) =10 JK^(=1) mol^(-1)`, and `R = 8.314 J K^(-1) mol^(-1)`

Options

A. `5`
B. `10`
C. `95`
D. `100`

Explanation

To find the value of \( \log_{10} K \) for the reaction \( A \rightleftharpoons B \), we will use the given thermodynamic data and the relationship between Gibbs free energy, enthalpy, and entropy.

### Step-by-Step Solution:

1. **Given Data:**
- \( \Delta_f H_{298K}^{\Theta} = -54.07 \, \text{kJ mol}^{-1} \)
- \( \Delta_r S_{298K}^{\Theta} = 10 \, \text{J K}^{-1} \, \text{mol}^{-1} \)
- \( R = 8.314 \, \text{J K}^{-1} \, \text{mol}^{-1} \)
...