Not so long ago, in a chemistry lab far far away…

May the FORCE/area be with you

Ideal GasesIdeal gases are imaginary gases that perfectly fit all of the assumptions of the

kinetic molecular theory:

1) Gases consist of tiny particles that are far apart relative to their size. Volume of particles assumed to be negligible.

2) Collisions between gas particles and between particles and the walls of the container are elastic collisions. Assume particles are in constant motion.3) There are no forces of attraction between gas

particles

4) The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.

The Nature of Gases

Gases expand to fill their containers

Gases are fluid – they flow Gases have low density

1/1000 the density of the equivalent liquid or solid

Gases are compressible Gases effuse and diffuse

PressureIs caused by the collisions of molecules with

the walls of a container is equal to force/unit area SI units = Newton/meter2 = 1 Pascal (Pa) 1 atmosphere = 101,325 Pa 1 atmosphere = 1 atm = 760 mm Hg = 760

torr1 atm = 29.92inHg = 14.7 psi = 0.987 bar =

10 m column of water.

Measuring Pressure

The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century.The device was called a “barometer”

  Baro = weight   Meter = measure

An Early Barometer

The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high.

Standard Temperature and Pressure

“STP”

P = 1 atmosphere, 760 torr T = 0°C, 273 Kelvins The molar volume of an ideal gas is 22.42 liters at STP

Converting Celsius to KelvinGas law problems involving temperature require that the temperature be in KELVINS!

Kelvins = C + 273

°C = Kelvins - 273

The Combined Gas Law

The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

1 1 2 2

1 2

PV PV

T T

Boyle’s law, Gay-Lussac’s law, and Charles’ law are all derived from this by holding a variable constant.

Boyle’s Law

Pressure is inversely proportional to volume when temperature is held constant.

1 1 2 2PV PV

Charles’s Law  The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.

(P = constant)

1 2

1 2

V V

T T

Gay Lussac’s Law

The pressure and temperature of a gas are directly related, provided that the volume remains constant.

1 2

1 2

P P

T T

Avogadro’s Law

For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures).

V = an a = proportionality constant V = volume of the gas n = number of moles of gas

Ideal Gas Law

PV = nRT P = pressure in atm V = volume in liters n = moles R = proportionality constant

= 0.08206 L atm/ mol·K T = temperature in Kelvins

Holds closely at P < 1 atm

Standard Molar Volume

Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.

- Amedeo Avogadro

Gas Densitymolar mass

molar volume

massDensity

volume

… so at STP…

molar mass

22.4 LDensity

Density and the Ideal Gas Law

Combining the formula for density with the Ideal Gas law, substituting and rearranging algebraically:

MPD

RT

M = Molar Mass

P = Pressure

R = Gas Constant

T = Temperature in Kelvins

Gas Stoichiometry #1If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios.

3 H2(g) + N2(g) 2NH3(g)

3 moles H2 + 1 mole N2 2 moles NH3 3 liters H2 + 1 liter N2 2 liters NH3

Gas Stoichiometry #2

How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen in a closed container at constant temperature?

3 H2(g) + N2(g) 2NH3(g)

12 L H2

L H2

= L NH3 L NH3

3

28.0

Gas Stoichiometry #3How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?

2 KClO3(s) 2 KCl(s) + 3 O2(g)

= L O2

50.0 g KClO3 1 mol KClO3

122.55 g KClO3

3 mol O2

2 mol KClO3

22.4 L O2

1 mol O2

13.7

Gas Stoichiometry #4

nRT

VP

How many liters of oxygen gas, at 37.0C and 0.930 atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?

2 KClO3(s) 2 KCl(s) + 3 O2(g)

= “n” mol O2

50.0 g KClO3 1 mol KClO3

122.55 g KClO3

3 mol O2

2 mol KClO3 = 0.612 mol O2

L atm(0.612mol)(0.0821 )(310K)

mol K0.930atm

= 16.7 L

Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

This is particularly useful in calculating the pressure of gases collected over water.

Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

Diffusion

EffusionEffusion: describes the passage of gas into an evacuated chamber.

I look like Abe Lincoln but I’m really Thomas Graham!

Rate of effusion for gas 1Rate of effusion for gas 2

2

1

MM

Distance traveled by gas 1Distance traveled by gas 2

2

1

MM

Effusion:

Diffusion:

Graham’s LawRates of Effusion and Diffusion

Real Gases

[ ]P a V nb nRTobs2( / ) n V

­ ­corrected pressure corrected volume

Pidea

l

Videa

l

Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).