The mass of a single molecule of an allotrope of sulphur is `3.20 xx 10^(-22)`g. How many sulphur atoms are present in a molecular of this allotrope?

Options

A. 4
B. 6
C. 8
D. 12

Answer

To determine how many sulfur atoms are present in a molecule of the given allotrope of sulfur, we can follow these steps:

### Step 1: Understand the given data
We are given the mass of a single molecule of an allotrope of sulfur, which is \(3.20 \times 10^{-22}\) g.

### Step 2: Convert the mass of the molecule to atomic mass units (amu)
To convert grams to atomic mass units (amu), we use the conversion factor:
1 amu = \(1.66 \times 10^{-24}\) g.

We can find the mass in amu by dividing the mass in grams by the conversion factor:
\[ \text{Mass in amu} = \frac{3.20 \times 10^{-22} \text{ g}}{1.66 \times 10^{-24} \text{ g/amu}}. \]

### Step 3: Calculate the mass in amu
Now, we perform the calculation:
\[ \text{Mass in amu} = \frac{3.20 \times 10^{-22}}{1.66 \times 10^{-24}} \approx 192.77 \text{ amu}. \]

### Step 4: Determine the molecular weight of sulfur
The molecular weight of sulfur (S) is approximately 32 g/mol. However, we need to find out how many sulfur atoms are in the molecule based on the mass we calculated.

### Step 5: Calculate the number of moles
To find the number of moles of sulfur atoms in the molecule, we can use the formula:
\[ \text{Number of moles} = \frac{\text{mass of the molecule (in amu)}}{\text{molecular weight (in amu)}}. \]
Using the molecular weight of sulfur:
\[ \text{Number of moles} = \frac{192.77 \text{ amu}}{32 \text{ amu}} \approx 6.02. \]

### Step 6: Conclusion
Since the number of moles corresponds to the number of sulfur atoms in the molecule, we conclude that there are approximately 6 sulfur atoms in a molecule of this allotrope.

### Final Answer:
The number of sulfur atoms present in a molecule of this allotrope is **6**.

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