The molar specific heats of an ideal gas at constant volume and constant pressure are respectively 4.98 and 6.96 cal `mol^(-1) K^(-1)`. If the molecular weight of the gas be 32, then calculate the root means square speed of the molecule of the gas at `120^@ C`. (1 cal = 4.2 J)

Explanation

To solve the problem, we need to calculate the root mean square (RMS) speed of the molecules of an ideal gas using the provided specific heats and the molecular weight. Here are the steps to solve the problem:

### Step 1: Identify the given values
- Molar specific heat at constant volume (CV) = 4.98 cal mol⁻¹ K⁻¹
- Molar specific heat at constant pressure (CP) = 6.96 cal mol⁻¹ K⁻¹
- Molecular weight (m) = 32 g/mol
- Temperature (T) = 120°C
- Conversion factor: 1 cal = 4.2 J
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