Of course! Let's break down the process step-by-step to determine how many kilojoules are released when 2.70 g of iron (Fe) reacts, while ensuring we use two significant figures and include appropriate units in the final answer.
### Step 1: Determine the molar mass of iron
The molar mass of iron (Fe) is 55.845 g/mol.
### Step 2: Calculate the number of moles of Fe
We are given that the mass of iron is 2.70 g. To find the number of moles, we use the formula:
[tex]\[ \text{moles of Fe} = \frac{\text{mass of Fe}}{\text{molar mass of Fe}} \][/tex]
[tex]\[ \text{moles of Fe} = \frac{2.70 \text{ g}}{55.845 \text{ g/mol}} \][/tex]
[tex]\[ \text{moles of Fe} = 0.04834810636583401 \][/tex]
### Step 3: Calculate the energy released per mole of Fe
From the reaction equation, we know that:
[tex]\[ 4 \text{ moles of Fe} \rightarrow \Delta H = -1.7 \times 10^3 \text{ kJ} \][/tex]
This means [tex]\( \Delta H \)[/tex] for 4 moles of Fe is -1.7 x 10^3 kJ. We need to find the energy released per mole of Fe:
[tex]\[ \text{energy per mole of Fe} = \frac{\Delta H}{4} \][/tex]
[tex]\[ \text{energy per mole of Fe} = \frac{-1.7 \times 10^3 \text{ kJ}}{4} \][/tex]
[tex]\[ \text{energy per mole of Fe} = -425 \text{ kJ} \][/tex]
### Step 4: Calculate the total energy released for 2.70 g of Fe
Using the moles of Fe calculated from Step 2, we can determine the total energy released:
[tex]\[ \text{total energy released} = \text{moles of Fe} \times \text{energy per mole of Fe} \][/tex]
[tex]\[ \text{total energy released} = 0.04834810636583401 \times (-425 \text{ kJ/mol}) \][/tex]
[tex]\[ \text{total energy released} = -20.547945205479454 \text{ kJ} \][/tex]
### Step 5: Express the answer using two significant figures
Finally, we round the total energy released to two significant figures:
[tex]\[ \text{total energy released} \approx -21 \text{ kJ} \][/tex]
### Final Answer
- The number of kilojoules released when 2.70 g of Fe reacts is [tex]\(-21 \text{ kJ}\)[/tex].
