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Avogadro's law

This important law was proposed by Avogadro in 1811 and then independently by Ampere in 1814. It states that:

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

This can be verified using the ideal gas equation. Consider two gases 1 and 2. The gas equation for each gas is:
Gas 1: P1 V1 = n1RT1 Gas 2: P2V2 = n2RT2

Now if P1 = P2, V1 = V2 and T1 = T2 we have that n1 = n2 and so Avogadro's law is proved.

The volume of one mole of any gas at STP is 22.4 litres. A mole of any substance contains 6.02x1023 molecules Ė a number known as Avogadroís number or Avogadroís constant.

Avogadro's constant is the number of particles in a mole of the substance. This number is always the same.
So in:
1 mole of hydrogen (2 g) there are 6.02x1023 molecules (hydrogen exists as H2)
1 mole of oxygen (32 g) there are 6.02x1023 molecules (oxygen exists as O2)
1 mole of copper (63 g) there are 6.02x1023 atoms
1 mole of uranium 235 (235 g) there are 6.02x1023 atoms

For example if we have 2 kg of uranium in a fuel rod we have 2000/235 = 8.51 moles and this contains 8.51x6.02x1023 = 5.12x1023 atoms and so 5.12x1023 uranium nuclei.

Dalton's law of partial pressures

If two or more gases are mixed in a container then the final pressure can be found from Dalton's law, which states that:

The pressure in a container is the sum of the partial pressures of the gases that occupy the container.

The partial pressure of a gas is that pressure that the gas would exert if it alone occupied the container.
For example, consider a container with a volume V and a temperature T. Let the container be occupied by two different gases, there being n1 moles of gas 1 and n2 moles of gas 2. Let the partial pressures of the gases be P1 and P2.

Now P1V = n1RT and P2V = n2RT.
But the total pressure in the container is P, where PV = nRT for n = n1 + n2, the total number of moles of whatever type occupying the container.

P1 = n1RT/V P2 = n2RT/ V and P= nRT/V and since n = n1 + n2 we have P1V/RT + P2V/RT = PV/RT

P = P1 + P2
which is Dalton's law.

A useful application of this law is in cases where volumes of the same gas occupy separate but connected containers at differing temperatures.

Example problem
Example problem A volume of gas V at a temperature T1 and a pressure p is enclosed in a sphere. It is connected to another sphere of volume V/2 by a tube and stopcock. The second sphere is initially evacuated and the stopcock is closed.
If the stopcock is opened the temperature of the gas in the second sphere becomes T2. The first sphere is maintained at a temperature T1.
Show that the final pressure pí within the apparatus is: pí = 2pT2/[2T2+T,]

Let there be a molecules of gas, and let there be n1 molecules in the larger sphere and n2 molecules in the smaller sphere after the stopcock is opened.

Now n= n1 + n2, but pV= nRT. So PV/RT1 = píV/RT1 + píV/2RT2
Therefore: p/T1 = pí(1/T1 + 1/2T2) pí = 2pT2/2T2+T1
© Keith Gibbs 2010