A complex of iron contains 45.6% iron by mass. Calculate the number of iron atoms present in 15.0 g of this complex.

Answer

To solve the problem of calculating the number of iron atoms present in 15.0 g of a complex that contains 45.6% iron by mass, we can follow these steps:

### Step 1: Determine the mass of iron in the complex
Given that the complex contains 45.6% iron by mass, we can calculate the mass of iron in 15.0 g of the complex.

\[ \text{Mass of iron} = \text{Percentage of iron} \times \text{Mass of complex} \]

\[ \text{Mass of iron} = 0.456 \times 15.0 \, \text{g} = 6.84 \, \text{g} \]

### Step 2: Calculate the number of moles of iron
To find the number of moles of iron, we use the formula:

\[ \text{Number of moles} = \frac{\text{Mass of iron}}{\text{Molar mass of iron}} \]

The molar mass of iron (Fe) is approximately 56 g/mol.

\[ \text{Number of moles of iron} = \frac{6.84 \, \text{g}}{56 \, \text{g/mol}} \approx 0.122857 \, \text{mol} \]

### Step 3: Calculate the number of iron atoms
Now, we can calculate the number of iron atoms using Avogadro's number, which is approximately \(6.022 \times 10^{23} \, \text{atoms/mol}\).

\[ \text{Number of iron atoms} = \text{Number of moles} \times \text{Avogadro's number} \]

\[ \text{Number of iron atoms} = 0.122857 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 7.39 \times 10^{22} \, \text{atoms} \]

### Final Answer
The number of iron atoms present in 15.0 g of the complex is approximately \(7.39 \times 10^{22}\) atoms.

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