12 Gas Laws

Units

Pressure is measured in a variety of units. Atmospheres, bars, torrs etc.

The standard international unit of pressure is the Pascal (Pa)

P179 gives the conversion factors for other units.

S.T.P or standard temperature and pressure T = 273 (0oC)

P = 1 atmosphere

R.T.P or room temperature and pressure

T = 298 (25oC)

P = 1 atmosphere

Avogadros law

Equal volumes of gases at the same temperature and pressure have equal numbers of molecules

At STP 1 mol of any ideal gas occupies 22.4LAt RTP 1 mol of any ideal gas occupies 24.0L

What volume is occupied by 8g of hydrogen at STP?

1 mol H2 has a mass of 2g

8g = 8 = 4 mol 2

Volume occupied = 4 x 22.4 L = 89.6 L

250ml of carbon dioxide weighs 0.44g while the same volume of a gaseous oxide of nitrogen weighs 0.46g at the same temperature and pressure. Find the mass of 1mol of this oxide of nitrogen.

Moles of carbon dioxide present in 250ml = 0.44 44

= 0.01 mol 250ml of nitrogen also contain 0.01mol 0.46g = 0.01 mol

1 mol of the oxide nitrogen weighs 1 x 0.46 0.01 = 46g mol-1

Ideal Gases

The following assumptions are made for an ideal gas

1) The gaseous molecules or atoms occupy a volume which is completely negligible compared to the space occupied by the gas.

2) There are no attractive forces between the gaseous molecules or atoms

In practice we can treat most gases ideally except at extremes of temperature and pressure.

At low temperature and high pressures the molecules or atoms will be close enough together for Van der Waals forces to be effective.

Also the space occupied by the molecules or atoms will no longer be negligible.

At high pressures and low temperatures all gases deviate from ideal behaviour

The deviation will be greater for larger molecules.

Boyles Law

The volume occupied by a gas is inversely related to its pressure (assuming temperature constant)

PV = constant or v 1 P

Charles Law

At constant pressure the volume of a gas is directly proportional to its absolute temperature

V T or V = constant

T

Combined Gas Laws

Combining these 2 laws we get the relationship

PV = constant

T

Which can also be expressed as

P1V1 = P2V2

T1 T2

Ideal Gas Law

Combining Boyle’s law, Charles’s Law and Avogadros’ law we get the ideal gas equation

PV = nRT

Where n = no of molecules and R = molar gas constant

R will have different values depending on its units

R = 0.0821 atm L mol-1 K-1

How many moles of gaseous arsine (AsH3) will occupy 0.0400 L at STP?

PV = nRT

R = 0.0821 atm L mol-1 K-1

P = 1 atm

T = 273K

V = 0.0400 n = PV = 1 x 0.0400 = 1.78 x 10 -3 moles

RT 0.0821 x 273

The density of a noble gas is 2.71 g/L at 3.00 atm and 0oC.

Identify the gas.

PV = nRT

P = 3.00

V = 1 L

T = 273

n = 3 x 1 = 0.133 mols

0.0821 x 273

0.133 mol = 2.71 g 1 mol = 2.71 = 20 gas is neon

0.133

Krypton has a density of 3.44 g/L at 25oC and 1 atm. Find its RAM.

PV = nRT n = 1 x 1 = 0.0408 mols

0.0821 x (273 + 25)

0.0408 mols = 3.44 g

1mol = 3.44 = 84.3 g

0.0408

For the following reaction what volume of hydrogen at 1.01 atm and 225OC is needed to form 35.5g Cu.

CuO(s) + H2(g) Cu(s) + H2O(g)

35.5 g = 35.5 = 0.559 mols

63.5

V = nRT = 0.559 x 0.0821 x 498 = 22.6L

P 1.01

A volume of gas collected at 70OC and 1.04 atms occupies 265ml. What volume would it occupy at STP?

P1 = 1.04 atmsT1 = 273 + 70 = 343KV1 = 265ml

P2 = 1 atmsT2 = 273K

V2 =

P1V1 = P2V2 1.04 x 265 = 1 x V2

T1 T2 343 273

V2 = 219ml

What volume of oxygen is needed for the complete combustion of 100ml of propane? What volume of carbon dioxide is produced? (All gases are measured at the same temp and pressure)

C3H8(g) + 5O2(g) 3CO2(g) + 4H2O

1 molecule of propane reacts with 5 molecules of oxygen to give 3 molecules of carbon dioxide

By Avogadros’s Law 100 ml of propane will react with 500ml of oxygen to give 300 ml of carbon dioxide.

1. Correct the following gas volumes to STP

a) 205ml at 27OC and 1 atms

b) 355 ml at 310K and 1.23atms

2. A certain mass of ideal gas has a volume of 3.25L at 25oC and 1 atms. What pressure is required to compress the gas to 1.88L at the same temperature?

3. An ideal gas occupies a volume of 2.00L at 25OC and 1 atms. What will the volume of the gas be at 40OC and 2.22 atms?

1 a) 187ml b) 387ml2 1.73 atms3 0.943 L

On strong heating 40ml of ammonia give 20ml of nitrogen and60ml of hydrogen. Derive the equation for the reaction.

40 ml of ammonia gives 30ml of nitrogen and 60ml of hydrogen

2ml ammonia gives 1ml of nitrogen and 3ml of hydrogen

2 molecules of ammonia gives 1 molecule nitrogen and 3 molecules of hydrogen

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