Variables

P = pressure

V = volume

T = temperature

Background

• The identity of gas doesn't really matter - nitrogen and oxygen aren't that different

  • Polar/non-polar doesn't matter - and chemical properties don't really matter

Boyle's Law (1662)

At constant temperature, the volume occupied by a fixed amount of gas is inversely proportional to applied pressure.

When the temperature is the same, additional pressure applied to one object will be counteracted with decreased volume.

Assumed:

• Temperature is the same

• Amount of gas is the same

P1 x V1 = P2 x V2

Charles' Law (1787)

At constant pressure, the volume occupied by a fixed amount of gas is directly proportional to temperature in Kelvin.

When the pressure is the same, the higher the temperature, the more the gas expands.

Assumed:

• Pressure of gas is the same

• Amount of gas is the same

V1 / T1 = V2 / T2

Gay-Lussac's Law (1802)

At constant volume (in a container), the pressure exerted by a fixed amount of gas is directly proportional to temperature.

When the volume is the same, pressure increases with temperature.

Assumed:

• Volume is the same

  • Putting the gas in a jar and heating it would work

• Amount of gas is the same

P1 / T1 = P2 / T2

Combined Gas Law

Combining Boyle and Charles:

(P1 x V1) / T1 = (P2 x V2) / T2

Avogadro's Law

At fixed temperature and pressure, equal volumes of any gas contain equal moles.

Volume is proportional to moles.

Ideal Gas Law

We're stealing from Boyle, Charles, and Avogadro today.

Pressure x Volume = amount of gas x Ideal Gas Constant x Temperature

Ideal Gas Constant

Experimentally, R = .0821 (L x atm / mol x K)

THIS MUST BE IN ATMOSPHERES FOR THIS TO WORK

Density

Density = (moles x weight x temperature) / ideal gas constant x temperature

Dalton's Law of Partial Pressures

Pressure (total) = sums of all pressures inside that volume

Each gas contributes its own pressure - each gas is completely independent of the pressure of other gasses

Measurements of a Gas

• Volume (of gas in a trapped container) - mL, L, cm^3, m^3

• Temperature (affects molecular motion - how fast they're moving) - Celsius, Kelvin (Celsius, but absolute zero is 0)

• Amount of gas: grams ➝ moles (unit: n)

• Pressure: atm (atmosphere), mmHg or Torr, 101.3 kPa (kilopascal)

Metric Stuff

Metric stuff: mL = cm^3 in volume

Kelvin = Celsius + 273.15

1atm = 760 mmHg (millimetres of mercury - barometer) or 760 Torr

Standard Conditions

• 1atm

• 0 degrees celsius / 273.15 kelvin

Barometer

A barometer is a tube with liquid inside of it. There's a vacuum at the top - this helps represent pressure.

Contributing to how low the liquid is, the force of gravity pushes down on the liquid, but the force of air pushing down on the liquid below pushes the liquid up.

Properties of an Ideal Gas

• Gases consist of a large number of particles in continuous random motion

• The volume (size) of the particles is negligible (doesn't matter) compared to the size of the container

• Attractive and repulsive forces between particles are negligible

• The average kinetic energy of a gas is constant at a given temperature

  • During collisions, energy can be transferred, but never lost

• Kinetic energy is proportional to temperature

• All gases at the same temperature have the same average kinetic energy

Kinetic Energy Formula

KE = 1/2 x mass x velocity squared

Example

Non-Ideal Behaviour

• If molecules stick together (polar molecules, like water)

• Large molecules (sulfur hexafluoride versus helium - gravity)

• Low temperature - liquifies gases

• High pressure (push-back effect) - liquifies gases