The resting of iron occurs as:
`4Fe(s) +3O_(2)(g) rarr 2Fe_(2)O_(3)(s)`
The entalpy of formation of `Fe_(2)O_(3)(s) is -824.0 kJ mol^(-1)` and entropy change for the reaction is `+550 J K^(-1) mol^(-1)`. Calculate `Delta_(surr)S` and predict whether resuting of iron is spontaneous or not at `298 K`.
Given `Delta_(sys) H =- 553.0 J K^(-1) mol^(-1)`

Explanation

To determine whether the rusting of iron is spontaneous, we will calculate the change in entropy of the surroundings (ΔS_surr) and the total entropy change (ΔS_total) for the reaction at 298 K.

### Step-by-Step Solution:

1. **Identify the Reaction and Given Data:**
The rusting of iron can be represented by the reaction:
\[
4Fe(s) + 3O_2(g) \rightarrow 2Fe_2O_3(s)
...