The mass of a gas molecule can be computed form the specific heat at constant volume. `Cv` for argon is `0.15 Kcal//kg-k`. The molecular weight of an argon atom is (approximately) `(R = 2 cal//mol-K)`

Options

A. `5 xx 10^(-3) kg`
B. `2.5 xx 10^(-3) kg`
C. `40 xx 10^(-3) kg`
D. `20 xx 10^(-3) kg`

Explanation

To compute the molecular weight of an argon atom using the specific heat at constant volume (\(C_v\)), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Specific heat at constant volume for argon, \(C_v = 0.15 \, \text{kcal/kg-K}\)
- Universal gas constant, \(R = 2 \, \text{cal/mol-K}\)

2. **Convert \(C_v\) to Calories:**
- Since \(1 \, \text{kcal} = 1000 \, \text{cal}\), we convert \(C_v\):
\[ C_v = 0.15 \, \text{kcal/kg-K} = 0.15 \times 1000 \, \text{cal/kg-K} = 150 \, \text{cal/kg-K} \]

3. **Use the Formula for \(C_v\):**
- For a monatomic ideal gas, the relation between \(C_v\) and molecular weight (\(m\)) is given by:
\[ C_v = \frac{3}{2} R \]
- Rearranging this gives:
\[ m = \frac{C_v \cdot 2}{3R} \]

4. **Substitute the Values:**
- Substitute \(C_v\) and \(R\) into the equation:
\[ m = \frac{150 \, \text{cal/kg-K} \cdot 2}{3 \cdot 2 \, \text{cal/mol-K}} \]

5. **Simplify the Expression:**
- The \( \text{cal} \) units cancel out:
\[ m = \frac{150 \cdot 2}{3 \cdot 2} \, \text{kg/mol} = \frac{150}{3} \, \text{kg/mol} = 50 \, \text{kg/mol} \]

6. **Convert to kg:**
- Since we need the molecular weight in kg, we can express it as:
\[ m = 0.02 \, \text{kg} \]

### Final Answer:
The molecular weight of an argon atom is approximately \(0.02 \, \text{kg}\).