Gas Laws

6.3.1 Ideal Gases

Assumptions we make for a gas to be ideal:

• Gas particles are identical, spherical, and hard;
• Volume of a particles is negligible compared to volume of the container;
• Collisions between the particles, and particles and walls of the container is elastic with no friction;
• Time of collisions is negligible compared to time spent between collisions;
• There are no intermolecular bonds between particles, the only force is due to collisions;
• The particles are in constant random motion (Brownian motion), with variety of velocities, with a certain mean (average) velocity.

We change 3 parameters in ideal gases:

1. Pressure: originates from force from collision of particles with walls of the container. As particles’ motion is random and we assume an average velocity for them, the collision force is distributed uniformly on walls of the container.

2. Volume: because of Brownian motion, the molecules fill up the container and volume of a gas is the volume of the container. 

3. Temperature: increasing the temperature increases the KE of the particles (only KE! as we assume no bond between particles) and average velocity. In a fixed volume this increases the pressure. Or if we allow volume to change we can keep pressure constant.

6.3.2-1 The Gas Laws

Boyle’s Law: if we keep temperature constant, volume and pressure are inversely proportional (for a fixed mass of ideal gas of course!):

Charles’ Law: if we keep pressure constant, the volume is directly proportional to absolute temperature (for a fixed mass of ideal gas of course!).

Pressure- Temperature Law (Amonton’s Law): if we keep volume constant, the pressure is directly proportional to absolute temperature (guess what!)

Gas Laws Combined:

Remember:

Unit of temperature for all gas laws is Kelvin: 0^oC = 273^oK

Unit of pressure is usually pascals (Pa) which is the same as N/m²

Another unit of pressure: atm (atmospheres) 1 atm = 101’325 Pa = 1.01 x 10⁵ Pa

STP means: Standard Temperature and Pressure: 273^oK and 1.01 x 10⁵ Pa

RTP: Room Temperature and Pressure: 25^oC = 278K and 1.01 x 10⁵ Pa

6.3.1-2 Moles and Avogadro constant 

1 mole of a substance contains 6.02 x 10²³ particles = N_A (Avogadro’s constant). 

The definition of mole is the number of atoms carbon-12 that add up to have a mass of 12 grams. 

Also for other elements, 1 mole has a mass equal to their mass number (nucleon number) in grams!

e.g.

Avogadro’s Law: Under same pressure and temperature, equal volume of gases contain the same number of particles (atoms or molecules). 

Combining all four gas laws above, we get the following formulae:

or:

This shows that pressure of an ideal gas does not depend on mass of its particles. 

Molar and Molecular Mass:

Molar mass (M_m): mass of 1 mole of a substance

Molecular mass (m): mass of a molecule of a substance

M_m = N_A m

6.3.1-3 Work Done on Gas

6.3.2 Molecular kinetic theory model

All four gas laws explained before are empirical (based on experiments) but the Kinetic Theory Model is theoretical. 

Brownian motion is instrumental to explain the relationship between p, V, and T; and as a reason for existence of atoms.