Ideal Gas Law

Mathematical relationship between pressure, volume, temperature & number of moles of a gas

Assumptions of Kinetic Molecular Theory

Diffusion

• The random mixing of different gas

particles

Osmosis= diffusion of water

Rate of Diffusion

• Smaller molecules

diffuse faster than

larger molecules at

the same temperature

– Ex: Which of the

following molecules

will move faster at 298

K?

• Helium or oxygen?

• Chlorine or nitrogen?

Ideal Gases Vs. Real Gas

Ideal Gas- Accurately describes properties of most gases:

Fit all the assumptions of the kinetic molecular theory:

• Molecules far apart

• Collisions are elastic

• Continuous, rapid, random motion

• No forces of attraction between molecules.

Real Gas- a gas that does not behave ideally

Situations when they wouldn’t behave ideally:

• Gases that are at high pressures & low temperatures do not behave ideally

Why not:

• They get too close and move too slow and start to be attracted to each other.

Standard Temperature & Pressure (STP)

• Most experiments with gases are done at STP

• Known by everyone in science to be:– Standard temperature = 0 ºC (273 K)

– Standard pressure = 1 atm

(kind of like normal body temp. is known by everyone without having to say 98.6°F)

Avogadro’s Law

1 mol O2 gas

Volume = 22.4 L

Mass = 32.00 g

1 mol H2 gas

Volume = 22.4 L

Mass = 2.02 g

Avogadro’s Law

• 1 mole of any gas at STP occupies a

volume of 22.4 L

• 1 mole = 22.4 L (conversion factor)

• Same amount of gas = same volume

• The masses will be different!! 1 mole of

O2 has a higher molar mass than 1 mole

of H2, but contains the same number of

particles

Molar Volume Examples

• What volume will 0.068 mol of O2(g) occupy

at STP?

• How many moles of H2 (g) are in 40.6 L of

gas?

0.068 mol

O2

22.4 L

O2 = 1.5 L O2

1 mol O2

40.6 L H2 1 mol H2= 1.81 mol H2

22.4 L H2

Molar Volume Examples

• How much does 0.098 L of SO2 (g) weigh

at STP?

0.098 L SO2 1 mol SO2 64.07 g SO2 = .28

g SO222.4 L SO2 1 mol SO2

(molar mass)

Ideal Gas Law

PV = nRTPressure

(atm)Volume

(liters)# moles

Ideal gas constant

(.0821)

temperature

(Kelvin)

Ideal Gas Constant, “R”

• How did we find the value of R?

1. Solve ideal gas law for R

2. Substitute variables with values from

conditions of STP

R = 0.0821L·atm

mol·K

R =PV

nT

R =

(1 atm)(22.4 L)

= 0.0821

L·atm

(1 mol)(273 K) mol·K

Ideal Gas Law Example 1

• What is the pressure in atm exerted by a

0.5 mol sample of nitrogen gas in a 10 L

container at 298 K?

– Given: V = 10 L Find: P

n = 0.5 mol

R = 0.0821 (L·atm)/(mol·K)

T = 298 K

Ideal Gas Law Example 1– Given: V = 10 L Find: P

n = 0.5 mol

R = 0.0821 (L·atm)/(mol·K)

T = 298 K

– Plan: PV = nRT

P = nRT

V

– Solve: P = (0.5 mol)(0.0821 (L·atm)/(mol·K))(298 K)

10 L

P = 1 atm

Ideal Gas Law Example 2

• What is the volume, in liters, of

0.250 mol of oxygen gas at 20 C

and 0.947 atm?

– Given: P = 0.947 atm Find:V

n = 0.250 mol

R = 0.0821 (L·atm)/(mol·K)

T = 20 C + 273 = 293 K

Ideal Gas Law Example 2• Given: P = 0.947 atm Find: V

n = 0.250 mol

R = 0.0821 (L·atm)/(mol·K)

T = 20 C + 273 = 293 K

• Plan: PV = nRT

V = nRT

P

• Solve:

V = (0.250 mol)(0.0821 (L·atm)/(mol·K))(293 K)

0.947 atm

V = 6.35 L

Ideal Gas Law example 3

• What volume will 2.0 moles of nitrogen

occupy at 720 Torr and 20 C ?

Answer

• PV = nRT (formula to use)

P= 720 Torr x 1 Atm =.947 Atm760 Torr

V = ? n = 2.0 moles

T= 20 + 273 = 293 KR= .0821

Plug in values into PV = nRT

V= 51 L