• The ideal gas law describes how pressure, volume, temperature, and moles of gas change.

• Kinetic molecular theory describes the behavior of all gasses and why they behave the way they do

The Gas Laws

• Gasses have four properties

  • Temperature (T)

  • Pressure (P)

  • Volume (V)

  • Moles of gas (n)

• Each gas law holds two properties constant while one of the properties is changed

Boyle’s Law

• Boyle’s law is the inverse pressure-volume relationship

• If a sample of gas starts with initial conditions of pressure and volume and an experiment is done ONLY affecting pressure and volume, you get the equation

  • PiVi=PfVf

    • i = initial

    • f = final

Charles’s Law

• Charles’s law is the direct relationship of temperature and volume

• (Vi)/(Ti) = (Vf)/(Tf)

• Absolute zero is the lowest possible temperature.

  • -273 celsius or 0 Kelvin

Gay-Lussac’s Law

• Gay-Lussac’s law is the direct relationship of pressure and temperature

• (Pi)/(Ti)=(Pf)/(Tf)

Avogadro’s Principle

• Also known as Avogadro’s Law, it describes that equal numbers of molecules/atoms contain equal volumes of gases under identical conditions of temperature and pressure

• (ni)/(Vi)=(nf)/(Vf)

Ideal Gas Law

• Combining the previous gas laws, the ideal gas law is obtained

  • PV = nRT

  • R is the universal gas constant. In this equation, R is .08206 L·atm/mol·K

• Example

  • A gas occupies 250 mL, and its pressure is 550 mmHg at 25°C.

    • If the gas is expanded to 450 mL, what is the pressure of the gas now?

    • What temperature is needed to increase the pressure of the gas to exactly 1 atmosphere and 250 mL?

    • How many moles of gas are in this sample?

    • The sample is an element and has a mass of 0.525g. What is it?

    

Standard Temperature and Pressure (STP)

• If a gas is stated to be at STP, it will be at 1 atm and 273 kelvin

Molar Mass, Density, and Molar Volume

• Molar mass can be determined if P, V, g, and T are known

  • PV = (g/molar mass)RT

• Density can be determined if P, T, and molar mass are known

  • P(molar mass) = (g/V)RT

• Molar volume can be determined by rearranging the ideal gas law equation

  • (V/n) = (RT/P) or

  • (V/n) = 22.4 L/mol if at STP

Kinetic Molecular Theory

• Kinetic molecular theory describes gasses at the particle level.

  • Gasses consist of molecules or atoms in continuous random motion

  • Collision between molecules/atoms are elastic

  • Volume taken up by gaseous molecules is negligibly small

  • The attractive and repulsive forces between gaseous molecules is negligible

  • Average kinetic energy of gaseous molecules is directly proportional to the Kelvin temperature of the gas

• Pressure is determined by the velocity of gas particles colliding with container walls. Changing temperature changes the force of collision in addition to the frequency.

• If the volume of a container is decrease, the particles will collide with the wall more frequently, and pressure will increase

• By increasing temperature, the average kinetic energy is increase so the particle velocity is increased, and the pressure will increase since the collisions are stronger

• Graham’s law of effusion compares the rate of effusion of two gasses and says the rates are inversely related to the square root of the mass of the gas particles

  

• Effusion through a pinhole in a vacuum requires a gas to hit the pinhole just right in order to escape. More collisions mean a higher rate of effusion, or a higher likelihood that it will escape.

Average Kinetic Energies and Velocities

• Average kinetic energy is sometimes higher or lower than estimated.

  • KE = (.5)mv^2

Real Gasses

• The ideal gas law does not work well at very high pressures or very low temperatures

  • Gases close to the condensation point will deviate slightly because it breaks two gas assumptions: gasses have no volume and have no repulsive/attractive forces

• An ideal gas must follow the assumptions stated earlier.

Dalton’s Law of Partial Pressures

• Dalton’s law of partial pressures says that if two gasses are mixed together, they will act independently of each other.

  • Total pressure is the sum of all partial pressure of gasses in a container

• Example

  • A mixture of gasses contain 2 mol of O2, 3 mol of N2, and 5 mol of He. Total pressure is 850 torr. What is the partial pressure of each gas?

    

Experiments Involving Gases

• Pneumatic troughs are used to collect gases produced in a reaction vessel.

• To find the gas collected in pressure,

  • Pgas = Patm - Pwater