Question:
The specific heat at constant volume for the monoatomic argon is 0.075 kcal/kg-K, whereas its gram molecular specific heat is \(C_V = 2.98\) cal/mol K. The mass of the argon atom is
The specific heat at constant volume for the monoatomic argon is 0.075 kcal/kg-K, whereas its gram molecular specific heat is \(C_V = 2.98\) cal/mol K. The mass of the argon atom is
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Always convert units consistently: 1 kcal/kg·K = 1000 cal/1000 g·K = 1 cal/g·K. Then \(M = C_V(\text{molar})/c_V(\text{specific})\).
Updated On: Apr 20, 2026
- \(6.60 \times 10^{-23}\) g
- \(3.30 \times 10^{-23}\) g
- \(2.20 \times 10^{-23}\) g
- \(13.20 \times 10^{-23}\) g
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Molar specific heat = Molecular weight \(\times\) specific heat per gram.
Step 2: Detailed Explanation:
\(C_V(\text{molar}) = M \times c_V\): \[ 2.98 \text{ cal/mol·K} = M \times 0.075 \times 10^3 \text{ cal/kg·K} = M \times 75 \text{ cal/kg·K} \] \[ M = \frac{2.98}{75} \times 10^3 \text{ g} = 39.7 \text{ g/mol} \] Mass per atom \(= \dfrac{39.7}{6.023\times10^{23}} = 6.60\times10^{-23}\) g.
Step 3: Final Answer:
Mass of argon atom \(= 6.60 \times 10^{-23}\) g.
Molar specific heat = Molecular weight \(\times\) specific heat per gram.
Step 2: Detailed Explanation:
\(C_V(\text{molar}) = M \times c_V\): \[ 2.98 \text{ cal/mol·K} = M \times 0.075 \times 10^3 \text{ cal/kg·K} = M \times 75 \text{ cal/kg·K} \] \[ M = \frac{2.98}{75} \times 10^3 \text{ g} = 39.7 \text{ g/mol} \] Mass per atom \(= \dfrac{39.7}{6.023\times10^{23}} = 6.60\times10^{-23}\) g.
Step 3: Final Answer:
Mass of argon atom \(= 6.60 \times 10^{-23}\) g.
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