Find the no. of mole of phosphorus in `92.9 g` of phosphorus assuming that molecular formula of phosphorus in `P_(4^(.)`. Also determine the no. of atoms and molecules of phosphorus in the sample.

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the number of moles of phosphorus (P4)
1. **Identify the molar mass of phosphorus (P)**:
- The atomic mass of phosphorus (P) is given as 31 g/mol.
- Since phosphorus exists as P4 in the molecular form, the molar mass of P4 is:
\[ \text{Molar mass of } P_4 = 4 \times 31 \text{ g/mol} = 124 \text{ g/mol} \]

2. **Use the formula to find the number of moles**:
- The formula to find the number of moles (n) is:
\[ n = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
- Substituting the values:
\[ n = \frac{92.9 \text{ g}}{124 \text{ g/mol}} \approx 0.749 \text{ moles of } P_4 \]

### Step 2: Calculate the number of molecules of phosphorus (P4)
1. **Use Avogadro's number**:
- Avogadro's number is \(6.022 \times 10^{23} \text{ molecules/mol}\).
- The number of molecules (N) can be calculated using:
\[ N = n \times \text{Avogadro's number} \]
- Substituting the values:
\[ N = 0.749 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 4.50 \times 10^{23} \text{ molecules of } P_4 \]

### Step 3: Calculate the number of atoms of phosphorus
1. **Determine the number of atoms in P4**:
- Each molecule of P4 contains 4 phosphorus atoms.
- Therefore, the total number of atoms (A) is:
\[ A = N \times 4 \]
- Substituting the values:
\[ A = 4.50 \times 10^{23} \text{ molecules} \times 4 \approx 1.80 \times 10^{24} \text{ atoms of phosphorus} \]

### Final Results:
- Number of moles of phosphorus (P4): **0.749 moles**
- Number of molecules of phosphorus (P4): **\(4.50 \times 10^{23}\) molecules**
- Number of atoms of phosphorus: **\(1.80 \times 10^{24}\) atoms**