A gas bulb of `1 L` capacity contains `2.0xx10^(11)` molecules of nitrogen exerting a pressure of `7.57xx10^(3)Nm^(-2)`. Calculate the root mean square (rms) speed and the temperature of the gas molecules. If the ratio of the most probable speed to the root mean square is `0.82`, calculate the most probable speed for these molecules at this temperature.

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the number of moles of nitrogen gas (N2)
To find the number of moles (n), we use the formula:
\[ n = \frac{N}{N_A} \]
where:
- \( N = 2.0 \times 10^{11} \) (number of molecules)
- \( N_A = 6.022 \times 10^{23} \) (Avogadro's number)
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