Maxwell Distribution of Molecular Speeds
Maxwell and Boltzmann derived an equation to find the distribution of various types of molecular speeds in a gas. The number of molecules per unit speed is indicated on the y-axis of the Maxwell-Boltzmann distribution graph. The quantity of molecules in the gas is represented by the total area under the whole curve. The peak of the graph will move to the right if we heat the gas to a greater temperature (since the average molecular speed will increase). The graph grows higher and more narrow as the gas gets colder, similar to how the graph shortens and widens as the gas heats up.
Inferences from the Graph
- The most probable speed is represented by the peak of the curve. The average molecular speed is the speed that is just a little higher than the most probable speed. The root mean square speed coincides with the average kinetic energy of the gas molecules.
- The curve will spread and flatten out when we observe the gas at increasing temperatures.
- The shape of the curve is dependent upon the molar mass and temperature of the gas.
- The curve gets taller and flatter when we consider gases of increasing molar mass.
- With the increase in temperature, the most probable speed increases, and the peak of the curve shifts to the right. The particles of gas also tend to move faster.
Molecular Speed Formula
Molecular speed is defined as the speed of the group of molecules in an ideal gas. Molecular speed is an important concept in the kinetic theory of gases. According to the kinetic theory of gases, the molecules of a gas are in constant motion and move in a straight line until they collide with another molecule. All the molecules of an ideal gas undergo elastic collision. It explains why small molecules diffuse more rapidly than large molecules. The molecular speed of a gas is directly proportional to its speed and inversely proportional to its molar mass. The molecular speed of a gas increases with an increase in the temperature of the gas. For example, Helium has the lowest molecular mass and thus has the highest molecular speed.