Argon has a molar mass of 40 g/mol. Find the most probable speed, the average speed and the rms…

Step 1. Most probable. $v_{mp} = \sqrt{\dfrac{2 \times 8.314\ \text{J/(mol K)} \times 400\ \text{K}}{0.040\ \text{kg/mol}}} = 407.8$ m/s.

Step 2. Average. $v_{avg} = \sqrt{\dfrac{8 \times 8.314\ \text{J/(mol K)} \times 400\ \text{K}}{\pi \times 0.040\ \text{kg/mol}}} = 460.1$ m/s.

Step 3. rms. $v_{rms} = \sqrt{\dfrac{3 \times 8.314\ \text{J/(mol K)} \times 400\ \text{K}}{0.040\ \text{kg/mol}}} = 499.4$ m/s.