Equal volumes of different gases at the same temperature and pressure contain the same number of molecules.
So, at constant temperature and pressure, the volume of a sample of gas is proportional to the number of molecules in the gas sample.
Since 1 mole = 6.02 x 1023 molecules, at constant temperature and pressure, the volume, V, of a sample of gas is proportional to the moles of gas, n, in the sample.
V/n = constant
V1/n1 = V2/n2
If the quantity of gas increases, then at the same temperature and pressure the volume the gas occupies must also increase.
If the quantity of gas decreases, then at the same temperature and pressure the volume the gas occupies must also decrease.
Examples
Changing Quantity of Gas
10 moles of carbon dioxide gas has a volume of 245L at 25o and 1atm pressure.
If 5 moles of the carbon dioxide is removed at the same temperature and pressure, what volume will the gas now occupy?
V1 = 245L
V2 = ?L
n1 = 10mol
n2 = 5mol
V1 n1
=
V2 n2
V2 =
V1n2 n1
=
245 x 5 10
= 122.5L
Changing Volume of Gas
At 0oC and 1atm pressure, 0.5mol of oxygen gas has a volume of 11.2L.
If the volume of gas is expanded to 22.4L by allowing more oxygen gas into the system while maintaining the same temperature and pressure, what is the final quantity of gas in moles?
V1 = 11.2L
V2 = 22.4L
n1 = 0.5mol
n2 = ?mol
V1 n1
=
V2 n2
n2 =
V2n1 V1
=
22.4 x 0.5 11.2
= 1mol
Comparing Different Gases at the Same Temperature and Pressure
At a certain temperature and pressure, a 500mL flask contains 25 mol of nitrogen gas.
A different flask at the same temperature and pressure contains 100 ml of helium gas.
How many moles of helium are in the second flask?
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