Sulphur exists in more than one solid form. The stable form at room temperature is rhombic sulphur. But above room temperature the following reaction occurs :
S (rhombic) `rarr` S (monoclinic)
If `Delta H = 276.144` J at 298 K and 1 atm and `Delta G = 75.312 J`
Assume that `Delta H` and `Delta S` do not vary significantly with temperature, calculate `T_(eq)`, the temperature at which rhombic and monoclinic sulphur exist in equilibrium with each other.

Explanation

To find the equilibrium temperature \( T_{eq} \) at which rhombic and monoclinic sulfur exist in equilibrium, we can use the Gibbs free energy equation under equilibrium conditions.

### Step-by-step Solution:

1. **Understanding the Gibbs Free Energy Equation**:
At equilibrium, the change in Gibbs free energy (\( \Delta G \)) is zero. The relationship between \( \Delta G \), \( \Delta H \) (enthalpy change), and \( \Delta S \) (entropy change) is given by:
\[
\Delta G = \Delta H - T \Delta S
...