Oxygen, M = 32.00 g/mol, is at 400 K. Find its most probable, average and rms speeds…

Step 1. The most probable speed. $u_{\text{mp}} = \sqrt{\dfrac{2 \times 8.314 \times 400}{0.03200}} = 456\ \text{m/s}$.

Step 2. The average speed. $\bar{u} = \sqrt{\dfrac{8 \times 8.314 \times 400}{\pi \times 0.03200}} = 514\ \text{m/s}$.

Step 3. The rms speed. $u_{\text{rms}} = \sqrt{\dfrac{3 \times 8.314 \times 400}{0.03200}} = 558\ \text{m/s}$.

Step 4. The share. $57.2\%$ of the molecules are faster than $u_{\text{mp}}$, and $39.2\%$ are faster than $u_{\text{rms}}$. The difference is $57.2 - 39.2 = 18.1\%$ before rounding.