The number of atoms in 10.6 moles of Fe are?

Options

A. 4.4×`10^23`
B. 14.4×`10^23`
C. 63.8×`10^23`
D. 69.23×`10^23`

Explanation

To find the number of atoms in 10.6 moles of iron (Fe), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Moles**:
- One mole of any substance contains Avogadro's number of entities (atoms, molecules, etc.). Avogadro's number is approximately \(6.02 \times 10^{23}\).

2. **Identify the Given Information**:
- We are given that we have \(10.6\) moles of iron (Fe).

3. **Use the Formula to Calculate the Number of Atoms**:
- To find the total number of atoms in \(10.6\) moles of iron, we use the formula:
\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]
- Substituting the values:
\[ \text{Number of atoms} = 10.6 \, \text{moles} \times 6.02 \times 10^{23} \, \text{atoms/mole} \]

4. **Perform the Calculation**:
- Now, calculate the multiplication:
\[ \text{Number of atoms} = 10.6 \times 6.02 \times 10^{23} \]
- First, calculate \(10.6 \times 6.02\):
\[ 10.6 \times 6.02 \approx 63.812 \]
- Now, include the power of ten:
\[ \text{Number of atoms} \approx 63.812 \times 10^{23} \]

5. **Express in Scientific Notation**:
- To express \(63.812 \times 10^{23}\) in standard scientific notation, we can write it as:
\[ 6.3812 \times 10^{24} \, \text{atoms} \]
- However, since the question does not specify the need for scientific notation, we can state the answer as:
\[ 63.812 \times 10^{23} \, \text{atoms} \]

### Final Answer:
The number of atoms in \(10.6\) moles of iron is approximately \(63.812 \times 10^{23}\) atoms.

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