Avogadro’s law

Equal volumes of different gases at the same temperature and pressure have the same number of moles.

Example: Cl2 (g) + H2 (g) 2HCl (g)

10 cm3 reacts with 10 cm3 to form 20cm3

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

10 cm3 30 cm3 20cm3

Avogadro’s law• In other words, if there are x molecules/moles of O2

in 10 cm3 of oxygen gas, then there are x molecules/moles of N2 in 10 cm3 of nitrogen gas and there are 2x molecules/moles of CO2 in 20 cm3 of carbon dioxide gas.

• Another way of putting this is that the volume of a gas depends on the amount of moles of the gas, n (provided the conditions are the same). Or, if the volume of H2 gas is double the volume of O2 than there are twice as many moles of O2 as H2.

Molar volume

At s.t.p. (which is 273K and 1.01 x 105 Pa)

volume of 1 mole of any gas

= 2.27 x 10-2 m3 mol-1

or 22.7 dm3 mol-1

Gas laws: why do all gases have the same molar volume?

The gas laws describe the behaviour of gases i.e. the relationships between temperature, volume and pressure of a gas.

•pV = constant (Boyle’s Law)•V/T = constant (Charles’s Law)•p/T = constant•V/n = constant (Avogadro’s Law)

Ideal gas equation

pV = nRT

•R = 8.31 J K-1 mol-1 ( J = Nm) •Pressure must be in Pa (Pa = N m-2)•Volume should be in m3 (1m3 = 1000 dm3 and 1 dm3 = 1000 cm3 or ml)

•Temperature should be in K.•Can you cancel all units?

Using of ideal gas equation

Calculate the p, V or T values of a gas provided the 3 other properties are known.

Example:

What volume will be occupied by 0.216 g of CO2

at 21 C and at a pressure of 1.34 x 105 Pa?

answer

• Calculate the number of moles of the gas: 0.216 g/44.0 g = 4.91 x 10-3 mol

• Express temperature in Kelvin: 21 C = 294 K

• Apply pV = nRT 1.34 x 105 x V = 4.91 x 10-3 x 8.31 x 294 V = 8.95 x 10-5 m3 (= 89.5 cm3)(Cancel units)

Using of ideal gas equation

Calculate the new value of either p, V or T, when only one of the properties of a sample of a gas has been changed. As the number of moles and gas constant remain the same, the ideal equation can be simplified to:

V1 P1 = V2 P2

T1 T2

Example

A gas occupies 127 cm3 at a pressure of 8.4 x 104 Pa and at 28C.

•What volume will the same amount of gas occupy at 1.01 x 105 Pa and 0 C?•How many moles of gas are present?

answer• Express all temperatures in Kelvin: 28 C = 301 K and

0 C = 273 K • Apply: V1 P1/T1 = V2 P2/T2

• V2 = V1 x P1 x T2/ P2 T1

• V2 = 127 x 8.4 x 104 x 273 / 1.01 x 105 x 301 = 95.8 cm3

When using the above expression there is no need to change volume in dm3 (or even pressure in atm) provided they are in the same units.

What needs changing though is temperature as this needs to be in Kelvin.

Answer part 2

The number of moles can only be calculated by using the ideal gas equation. Remember when using the ideal gas equation, SI units need to be used

n = PV/RTn = 8.4 x 104 Pa x 1.27 x 10-4 m3/8.31 J K-1 mol-1 x 301 K = 4.3 x 10 -3 mol

Uses of ideal gas equation

Calculate the molar mass of a gas:

• we need to know the conditions it is in and the mass of the sample of the gas• we can then calculate n and then using n =

mass/Mr calculate the Mr

• we can also use this calculation to identify an unknown gas experimentally !!!

Sample calculation

A sample of a gas has a volume of 432 cm3 and a mass of 1.500g at a pressure of 0.974 atm and a temperature of 28 C.

Calculate the molar mass.

answer

• Mr = mass RT/pV

• = 88.28 g mol-1