Math Snap

STEP 1

1. The balanced chemical equation is $2 \text{Al}(s) + \text{Fe}_2\text{O}_3(s) \rightarrow 2 \text{Fe}(s) + \text{Al}_2\text{O}_3(s)$.
2. The heat of reaction is $-851.5 \, \text{kJ}$.
3. We are given 74 grams of aluminum ($\text{Al}$).
4. We need to calculate the heat produced when 74 grams of $\text{Al}$ react.

STEP 2

1. Calculate the molar mass of aluminum.
2. Determine the number of moles of aluminum in 74 grams.
3. Use stoichiometry to find the heat produced.

STEP 3

Calculate the molar mass of aluminum ($\text{Al}$).
The atomic mass of aluminum is approximately $26.98 \, \text{g/mol}$.

STEP 4

Determine the number of moles of aluminum in 74 grams.
Use the formula:
$$\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}}$$ Substitute the known values:
$$\text{Number of moles of Al} = \frac{74 \, \text{g}}{26.98 \, \text{g/mol}} \approx 2.74 \, \text{mol}$$

Use stoichiometry to find the heat produced.
According to the balanced equation, 2 moles of $\text{Al}$ produce $-851.5 \, \text{kJ}$ of heat.
Calculate the heat produced for 2.74 moles of $\text{Al}$:
$$\text{Heat produced} = \left(\frac{-851.5 \, \text{kJ}}{2 \, \text{mol}}\right) \times 2.74 \, \text{mol}$$ $$\text{Heat produced} \approx -1166.5 \, \text{kJ}$$ The heat produced when 74 grams of aluminum react is approximately $-1166.5 \, \text{kJ}$.