Gases don’t have a set volume, they can expand or compress to fit any container
If heated up the molecules expand and have more energy so they move faster
Gases feature spread out molecules. A sample of gas has no set volume or set shape. A gas will fill whatever container is available to it.
Definition of pressure from a scientific standpoint: force divided by area.
- like a bed of nails
Newtons third law applies to gasses and pressure because the gas will push on the container with the same force that the container will push with, push of contianer can be reduced by making it bigger
P = F/A
Pressure is defined as force per unit area. When the gas molecules collide with the sides of the container they are in the molecules will apply a force on the sides.
- Expansion: the force is still equal
Barometer is used for pressure
- uses mercury, temperature, a vacuum, and pressure to measure
1 atm = 760mmHg = 760torr = 1.0132bar = 101325 pa (n/m^2)= 14.7 psi (lbs/in^2)
Manometers: tool for measuring the pressure og a gas sample. Connects our gas sample to a column of mercury that is either exposed to atmospheric pressure or a vacuum
- P of gas = height + P of atm
Closed manometer: Pgas = height
Gas Laws
Boyle’s Law: As Volume goes up, Pressure goes down P1V1 = P2V2 When the volume increases, there is more space for the particles to move so they hit the walls of the container less often (mean free space).
Charles’ Law: As temperature increases, volume increases
Avogadro’s Law: Equal volumes of a gas contain the same number of molecules at the same temperature and pressure, volume expands to account for collision rate
Gay-Lussac’s Law: As the temperature of an enclosed gas increases, the pressure increases (constant volume), P and T have a direct linear relationship
Combined Gas Law: P1V1/T1 = P2V2/T2
- valid for the changing in values for any gas sample (moles remain constant)
Ideal Gas Law: PV = nRT where R is a constant
- n = num of moles
- T = temperature in K (absolute because it is a capital T)
- P = pressure
- V = volume
Temperature Scale
- Temperature measures the average kinetic energy of the gas molecules in a sample
- Since we are not compxaring the temperature at 2 different points but rather using a single temperature we need to use an absolute temperature scale
- T=0 means there is NO kinetic energy
- Kelvin scale
- K = C + 273.15
Plug in numbers, convert units, and use PV = nRT
Partial Pressures and Mole Fractions
- Since gas molecules do not interact with one another when we mix gases together the total pressure of the mixture is equal to the sum of each individual gas’ pressure
- This is according to Dalton’s Law, P(tot)=P(1)+P(2)+… If a box has 2 sides and each side has 1 atm of a separate gas, the total pressure of the box is 0.5 atm of each gas, so the total is 1 atm. The barrier is removed so the space icnreases but the volume doesnt
A related idea is mole fraction. The mole fraction is the moles of the mixture any one has in the mixture comprises compared to the total
PA=Ptot(XA) where X is the mole fraction x1 = (n1/ntot) = (P1/Ptot)
P can be replaced with NRT/V
Kinetic Molecular Theory
Physical theory behind why the ideal gas law works. We have been using it to explain the gas laws, but it is worth digging a little bit deeper.
- Gases are made up of many molecules that are in continuous, random motion
- The voluyme of the particles of gas does not matter
- The gas molecules do not apply forces on one another
- Every collision between molecules are elastic (overall kinetic energy of the gas stays constant)
- The average kinetic energy is proportional to the temperature of the gas
- KE = 1/2mv
- Kinetic energy depends on both mass and speed, less mass means more KE
Average Kinetic Energy Maxwell-Boltzman Distribution
![[Screenshot 2025-12-04 at [email protected]]]
Which curve has highest temperature → higher temperature
Because temperature is the average kinetic energy and kinetic energy is equal to 0.5mv^2 Less massive molecules will be moving faster when at the same temperature as more massive molecules
More mass peaks sooner, less mass is more of a level curve
more level curve means it is moving faster
Graham’s Law of Effusion/Diffusion
The effusion of a gas is the escape of a gas through a hole in a container. It will be directly related to the speed of a gas molecule. Solving the kinetic energy equation for speed gives us: v=sqrt(3RT/MM) where R is a constant and MM is in kg/mol. Effusion goes through an opening, diffusion is just the combination
- rate1/rate2 = sqrt(MM2/MM1) dont need ot know
Assumptions of Ideal Gasses
- Gasses have no interactions with one another. All collisions between molecules are elastic. (This means the total kinetic energy remains constant even as some molecules speed up and others slow down due to collisions)
- The volume of the molecules does not affect the volume of the sample.
Attractions are small, doesn’t take a ton of energy to turn the element into a gas/move them further apart (small but not zero)
As pressure goes up, volume goes down is not physciall possible because the particles have to occupy at least some space
Deviations from the Ideal Gas Law
We made assumptions about the behavior of gases to create the ideal gas law. Mainly that the molecules do not have volume and that the forces of attraction between the molecules does not matter. This is generally fair at most temperatures and pressures, but at extreme values it starts to fall apart.
Ideal gas law assumes highest temperature lwoest pressure to get the ideal behavioor out of a gas
At high pressure the gas molecules tend to get squeezed together.