19.8 : Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).

This distribution function f(v) is defined by saying that the expected number N(v₁,v₂)of particles with speeds between v₁and v₂is given by

Since N is dimensionless and the unit of f(v)is seconds per meter, the equation can be conveniently modified into a differential form:

Consider a sample of nitrogen gas in a cylinder with a molar mass of 28.0 g/mol at a room temperature of 27 °C. Determine the ratio of the number of molecules with a speed very close to 300 m/s to the number of molecules with a speed very close to 100 m/s.

To solve the problem, examine the situation, and identify known and unknown quantities.

Second, convert all the known values into proper SI units. For example, convert the molecular weight to kilograms (kg) and the temperature to kelvin (K). Recall the distribution function for the velocity equation. Lastly, substitute the known values into the equation to determine the unknown quantity.