Calculations involving gases
In a nutshell
There are two calculations to find the volume of a gas. One equation involves the molar gas volume, the other is known as the ideal gas equation.
Equations
WORD EQUATION | SYMBOL EQUATION |
number of moles=molar gas volumevolume | n=VmV |
pressure × volume=number of moles × gas constant × temperature | |
Constants
constant | symbol | value |
molar gas volume | | 24dm3mol−1 (at r.t.p) 22.4dm3mol−1 (at s.t.p) |
gas constant | | 8.31JK−1mol−1 |
Note: r.t.p is room temperature and pressure (293K,101.3kPa), whereas s.t.p is standard temperature and pressure (273K,101.3kPa).
Variable units
quantity name | symbol | unit name | unit |
number of moles | | | |
| | cubic decimeter orcubicmetre | dm3 orm3 |
molar gas volume | | cubic decimeter per mole | dm3mol−1 |
pressure | | | |
gas constant | | joule per kelvin per per mole | JK−1mol−1 |
temperature | | | |
Molar gas volume equation
The molar gas volume is known as the volume that one mole of gas occupies at a certain temperature and pressure.
The equation to work out the number of moles given the volume and molar gas volume is:
number of moles=molar gas volumevolumen=VmV
This equation can be rearranged to calculate the volume of a gas:
volume=number of moles×molar gas volumeV=n×Vm
At room temperature and pressure the molar gas volume is 24dm3mol−1.
At standard temperature and pressure the molar gas volume is 22.4dm3mol−1.
Note: cm3 can be converted to dm3 by dividing by 1000.
Example
Work out the number of moles there are in 50000cm3 of nitrogen at room temperature and pressure.
First convert cm3 to dm3 to work out the volume in dm3:
V=100050000cm3=50dm3
Work out which value for the molar gas volume is needed based on the conditions stated in the question. At room temperature and pressure (r.tp):
Vm=24dm3mol−1
Next, write down the equation you will use:
n=VmV
Substitute the values into the equation to find your answer:
n=24dm3mol−150dm3=2.08mol
There are 2.08moles in 50000cm3 of nitrogen gas.
Measuring molar gas volume
The experiment below can be used to measure molar gas volume, using the measurement of the amount of gas produced in a reaction.
Note: 1. Reaction mixture 2. Delivery tube 3. Gas collection 4. Gas syringe
procedure
1. | Measure a known volume of acid into a conical flask connected to a gas syringe. |
2. | Add a known mass of salt into the conical flask filled with acid. Make sure to replace the bung and let the reaction progress until finished. |
3. | Record the volume of gas produced in the gas syringe. |
4. | Repeat steps 1-3 with a different mass of salt each time. |
5. | Plot a graph of mass of salt (x-axis) against volume of gas produced (y-axis). |
6. | Read the volume of gas produced at a certain mass of salt. |
7. | Calculate the amount of salt using the mass and M. number of moles=Molar massmass |
8. | Use the balanced equation to work out the molar ratios of the salt and gaseous product. The number of moles of the gas product can be calculated using this. |
9. | Use the number of moles of the gas product along with the volume to find the molar gas volume by rearranging the following equation. number of moles=molar gas volumevolume Rearranged: molar gas volume=number of molesvolume |
Mole calculations to calculate gas volumes
The mole equation can be used to calculate the volume of gas produced using the molar ratio of the reactants compared to the products.
procedure
1. | Calculate the number of moles of the reactant mass using the following equation. number of moles=molar gas volumevolume |
2. | Use the number of moles of the reactant, along with the molar ratios from the balanced symbol equation of the reaction to work out the number of moles of the gas that is produced. |
3. | Use the number of moles and the molar gas volume (depending on the reaction conditions) to calculate the volume of gas produced. volume=number of moles × molar gas volume |
Volume calculations to calculate gas volumes
The volume of reactant gases can be used alongside the molar ratios within the balanced equation to calculate the volume of gas that is produced.
procedure
1. | Use the balanced symbol equation to work out the molar ratio of the gaseous reactant (with the known volume) compared to the gaseous product. |
2. | Once the molar ratio is determined, work out the volume of gaseous product produced using the volume of gaseous reactant. |
Ideal gas equation
The ideal gas equation is used to calculate the number of moles of a gas. This can be used to work out either the mass or molar mass of a substance depending on the information provided in the question.
pressure × volume=number of moles × gas constant × temperaturepV=nRT
Note: The gas constant has a value of 8.31JK−1mol−1.
This equation can be rearranged to make each variable the subject, so can therefore be used to calculate a number of different things.
Unit conversions
There are lots of different units in this equation. Use the following unit conversions to help you:
- To convert from a kilo to a gram, multiply by 1000 (103).
- To convert from cm3 to m3, multiply by 10−6.
- To convert from dm3 to m3 multiply by 10−3 (divide by 1000).
- To convert from oC to K add 273.
Example
At a temperature of 25oC and pressure of 150kPa, methane occupies a volume of 1760cm3. What is the mass of methane?
First convert all of the variables that have been given in the question:
T(K)=25(oC)+273=298K
P(Pa)=150(kPa)×103=150000Pa
V(m3)=1760(cm3)×10−6=1760×10−6m3
You will need your gas constant with the correct unit:
8.31JK−1mol−1
Write the equation you will use:
pV=nRT
Rearrange the equation to make the number of moles the subject (this can be used to calculate the mass of methane):
n=RTpV
Substitute in your values into this equation:
n=8.31JK−1mol−1×298K150000Pa×(1760×10−6)m3=0.11mol
Write down the equation you will use to find the mass:
m=n×M
Work out the Mr of methane (CH4):
M(CH4)=(12(ArofC)×1)+(1(ArofH)×4)=16 g/mol
Substitute your values for the number of moles and relative molecular mass (Mr) to find the mass of methane:
m=0.11mol×16=1.76g
The mass of methane is 1.76g , given that there is 0.11mol of methane.