the standard heat of formation of Fe2O3 (s) is 824.2kJ mol-1 Calculate heat change for the reaction. 4Fe(s) + 302 (g)= 2Fe2O3(s)

Explanation

To calculate the heat change for the reaction:

\[ 4 \text{Fe}(s) + 3 \text{O}_2(g) \rightarrow 2 \text{Fe}_2\text{O}_3(s) \]

we will use the standard heat of formation values. The standard heat of formation (\( \Delta H_f^\circ \)) of a compound is the heat change that results when one mole of the compound is formed from its elements in their standard states.

### Step-by-Step Solution:

1. **Identify the Heat of Formation Values**:
- The heat of formation of \( \text{Fe}_2\text{O}_3(s) \) is given as \( 824.2 \, \text{kJ/mol} \).
- The heat of formation of elemental iron \( \text{Fe}(s) \) is \( 0 \, \text{kJ/mol} \) (since it is in its standard state).
- The heat of formation of elemental oxygen \( \text{O}_2(g) \) is also \( 0 \, \text{kJ/mol} \) (since it is in its standard state).

2. **Write the Formula for Heat Change**:
The heat change for the reaction (\( \Delta H^\circ \)) can be calculated using the formula:
\[ \Delta H^\circ = \sum (\Delta H_f^\circ \text{ of products}) - \sum (\Delta H_f^\circ \text{ of reactants}) \]

3. **Calculate the Heat of Formation for Products**:
- For the products, we have \( 2 \, \text{Fe}_2\text{O}_3(s) \):
\[ \Delta H_f^\circ \text{ of products} = 2 \times 824.2 \, \text{kJ/mol} = 1648.4 \, \text{kJ} \]

4. **Calculate the Heat of Formation for Reactants**:
- For the reactants, we have \( 4 \, \text{Fe}(s) \) and \( 3 \, \text{O}_2(g) \):
\[ \Delta H_f^\circ \text{ of reactants} = 4 \times 0 \, \text{kJ/mol} + 3 \times 0 \, \text{kJ/mol} = 0 \, \text{kJ} \]

5. **Substitute Values into the Formula**:
\[ \Delta H^\circ = 1648.4 \, \text{kJ} - 0 \, \text{kJ} = 1648.4 \, \text{kJ} \]

6. **Determine the Sign of Heat Change**:
Since the reaction is exothermic (formation of products from reactants), we need to consider the stoichiometry of the reaction. The heat change for the reaction as written is negative:
\[ \Delta H^\circ = -1648.4 \, \text{kJ} \]

### Final Answer:
The heat change for the reaction is:
\[ \Delta H^\circ = -1648.4 \, \text{kJ} \]