A sample of phosphorus trichloride `(PCl_(3))` contains 1.4 moles of the substance. How many atoms are there in the sample ?

Options

A. 4
B. `8.4xx10^(23)`
C. `3.36xx10^(24)`
D. `5.6`

Explanation

To find the total number of atoms in a sample of phosphorus trichloride (PCl₃) containing 1.4 moles, we can follow these steps:

### Step 1: Calculate the number of molecules in the sample
We use Avogadro's number, which states that one mole of any substance contains approximately \(6.022 \times 10^{23}\) particles (molecules or atoms).

**Formula:**
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]

**Calculation:**
\[ \text{Number of molecules} = 1.4 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \]
\[ = 8.4 \times 10^{23} \, \text{molecules} \]

### Step 2: Determine the number of atoms in one molecule of PCl₃
Each molecule of phosphorus trichloride (PCl₃) consists of:
- 1 phosphorus atom
- 3 chlorine atoms

Thus, the total number of atoms in one molecule of PCl₃ is:
\[ 1 + 3 = 4 \, \text{atoms} \]

### Step 3: Calculate the total number of atoms in the sample
Now, we can calculate the total number of atoms in the sample by multiplying the number of molecules by the number of atoms per molecule.

**Formula:**
\[ \text{Total number of atoms} = \text{Number of molecules} \times \text{Number of atoms per molecule} \]

**Calculation:**
\[ \text{Total number of atoms} = 8.4 \times 10^{23} \, \text{molecules} \times 4 \, \text{atoms/molecule} \]
\[ = 3.36 \times 10^{24} \, \text{atoms} \]

### Final Answer
The total number of atoms in the sample of phosphorus trichloride (PCl₃) is:
\[ \boxed{3.36 \times 10^{24}} \, \text{atoms} \]

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