The rusting of iron occurs as `4Fe(s)+3O_(2)(g)to 2Fe_(2)O_(3)(s)`. Enthalpy of formation of `Fe_(2)O_(3)(s)` is `-824.2 kJ mol^(-1)` and entropy change for the reaction, i.e., `Delta S_("system")`, is `-549 J K^(-1) mol^(-1)`. Calculate `Delta S_("surrounding")` and predict whether rusting of iron is spontaneous or not at 298 K.

Explanation

To solve the problem, we need to calculate the change in entropy of the surroundings (ΔS_surroundings) and then determine whether the rusting of iron is spontaneous at 298 K.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Reaction: \( 4Fe(s) + 3O_2(g) \rightarrow 2Fe_2O_3(s) \)
- Enthalpy of formation of \( Fe_2O_3(s) \): \( \Delta H_f = -824.2 \, \text{kJ/mol} \)
- Entropy change of the system: \( \Delta S_{\text{system}} = -549 \, \text{J/K/mol} \)
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