Gasses

1. A gas is composed of a very large number of molecules
2. These molecules are separated by a large distance relative to their own size
3. A gas is composed of a large number of molecules in ceaseless motion

The speeds of ideal gas molecules obey the Maxwell-Boltzmann speed distribution:

also written as:

where:

• is the Boltzmann constant given by:
• is the molarity of the gas
• is Euler's Number
• is the universal gas constant
• is the temperature in kelvin

Find the maximum value of the distribution function by setting the derivative to 0:

Find the expected value of the distribution function by evaluating the integral:

Evaluate the integral and take the square root:

• Tempetrature
  • Higher temperature results in a broader range of speeds
  • Distribution shifts towards higher speeds as temperature increases
• Mass
  • Lower molecular weight results in a broader range of speeds
  • Distribution shifts towards higher speeds for molecules with a lower molecular weight

Postulates:

• A gas is composed of a very large number of molecules in ceaseless random straight-line motion
• These molecules are separated by a large distance relative to their own size
• The molecules behave like hard spheres that undergo perfectly elastic collisions with one another and the walls of the container
• There are no forces of attraction or repulsion between the molecules

Two containers of argon gas are illustrated below. Both containers contain the same number of moles of argon and are at the same temperature.

1. Is the root-mean-square speed of the argon the same in both containers?
   Yes
2. Is the frequency with which the argon atoms collide with the walls the same in both containers?
   No
3. Is the average force of each collision between an argon atom and the wall the same in both containers?
   Yes

where:

• is the pressure in kilopascals
• is the molar mass
• is the universal gas constant
• is the temperature in kelvin