# Maxwell's distribution curve for different gases

I have studied Maxwell's velocity distribution curve for same gas in different temperatures. I tried to plot the graph for gases of different molar mass. I understood that the most probable speed will be less for gases of higher molar mass will have lesser value of Most Probable Speed but I am not able to understand what will be the change in the Y coordinates of the graph (Fraction of molecules).

I will be grateful if you explain me this.

Thanks $$:)$$

• What do you mean by "what will be the change in the Y coordinate"? Jul 27, 2022 at 1:49
• @RC_23 In Maxwell's graph, X axis represents velocity and Y axis represents fraction of molecules which possess that speed. If there are two elements of masses M1 and M2 (M1> M2). Then for any point in the graph, whose Y coordinate will be greater? Jul 27, 2022 at 4:23

$$f(v)= \left( \frac{m}{2 \pi kT} \right)^{3/2} e^{-\left(\frac{m}{kT} \frac{v^2}{2}\right)} 4 \pi v^2$$
This curve is parameterized by the factor $$\sqrt{\frac{m}{T}}$$.
As you can see, decreasing the mass $$m$$ has exactly the same effect on the shape of the curve as increasing the temperature $$T$$. For example, you would expect helium at room temperature to have the same distribution of speeds as air at a higher temperature.