Calculate the number of molecules in `1" cm"^(3)` of an ideal gas at `27^(@)C` and a pressure of 10 mm of mercury. Mean kinetic energy of a molecule at `27^(@)C` is `4xx10^(-14)` erg, the density of mercury is 13.6 gm/c.c.

Explanation

To calculate the number of molecules in \(1 \, \text{cm}^3\) of an ideal gas at \(27^\circ C\) and a pressure of \(10 \, \text{mm}\) of mercury, we can follow these steps:

### Step 1: Convert the pressure from mm of mercury to dynes per cm²
The pressure given is \(10 \, \text{mm Hg}\). We know that:
- The density of mercury is \(13.6 \, \text{g/cm}^3\).
- The acceleration due to gravity \(g\) is approximately \(980 \, \text{cm/s}^2\).

Using the formula for pressure in cgs units:
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