Explain the Maxwell-Boltzmann distribution law with a graph.

(N/A) The Maxwell-Boltzmann distribution law describes the distribution of molecular speeds in a gas at a given temperature. The fraction of molecules having a particular speed remains constant at a constant temperature,which is represented by the Maxwell-Boltzmann distribution curve.
Maxwell and Boltzmann indicated that the distribution of molecular speeds in gases depends on the temperature and the molar mass of the gas.
Graph of Maxwell-Boltzmann speed distribution: The graph is plotted with the fraction of molecules $\left(\frac{\Delta N}{N}\right)$ on the y-axis against the molecular speed on the x-axis.
Key features of the graph:
$(i)$ The fraction of molecules with very low or very high speeds is very small.
$(ii)$ The fraction of molecules possessing higher speeds increases until it reaches a peak and then starts decreasing.
$(iii)$ The maximum fraction of molecules possesses a speed corresponding to the peak in the curve. This speed is called the most probable speed $\left(u_{mp}\right)$.