Given below are observations on molar specific heats at room temperature of some common gases.
| Gas | (J mol K) | (J mol K) |
|---|---|---|
| He | 20.8 | 12.5 |
| H | 28.8 | 20.4 |
| N | 29.1 | 20.8 |
| O | 29.4 | 21.1 |
| CO | 37.0 | 28.5 |
The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically, molar specific heat of a monatomic gas is 2.92 cal/mol K. Explain this difference. What can you infer from the somewhat larger (than the rest) value for chlorine?
The measured molar specific heats of gases like H₂, N₂, O₂, and CO₂ are markedly different from monatomic gases due to their molecular structure and available degrees of freedom.
From the table, He (monatomic) has Cv = 12.5 J mol⁻¹ K⁻¹, which closely matches the typical monatomic gas value of 2.92 cal/mol K. Monatomic gases have only translational kinetic energy (three degrees of freedom), contributing to their lower specific heat.
Diatomic gases (H₂, N₂, O₂) have Cv values around 20-21 J mol⁻¹ K⁻¹, higher than monatomic gases. This is because diatomic molecules possess additional rotational degrees of freedom, requiring more heat energy for the same temperature rise.
CO₂ (polyatomic) has the highest Cv = 28.5 J mol⁻¹ K⁻¹ due to even more degrees of freedom including rotational and vibrational modes.
The larger value for chlorine compared to other diatomic gases suggests that chlorine molecules have significant vibrational energy contributions at room temperature. Being a heavier molecule, chlorine's vibrational modes are more easily excited, leading to higher specific heat than gases like N₂ and O₂.
Explanation
The question asks students to explain why polyatomic and diatomic gases have higher molar specific heats than monatomic gases. The key concept is degrees of freedom - monatomic gases have only 3 translational degrees, diatomic gases have 5 (3 translational + 2 rotational), and polyatomic gases have even more including vibrational modes. The chlorine inference relates to its heavier molecular mass making vibrational modes more accessible at room temperature. The context provides the data table showing the progression: He (monatomic) < H₂, N₂, O₂ (diatomic) < CO₂ (polyatomic).