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Explainer Video

Tutor: Aimee LeBrun

Summary

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 = volumemolar gas volumenumber \space of \space moles \, = \, \frac{volume}{molar \space gas \space volume}number of moles=molar gas volumevolume​​​
​n=VVmn = \frac{V}{V_m}n=Vm​V​​​
​pressure × volume = number of moles × gas constant × temperaturepressure \space \times \space volume \, = \, number \space of \space moles \space \times \space gas \space constant \space \times \space temperaturepressure × volume=number of moles × gas constant × temperature​​
​pV=nRTpV=nRTpV=nRT​​

​​​

Constants 

​​constant 

symbol

value

​molar gas volumemolar \space gas \space volumemolar gas volume​​
​VmV_mVm​​​
24 dm3 mol−124 \, dm^3 \,mol^{-1} 24dm3mol−1 (at r.t.p) 

​22.4 dm3 mol−122.4 \, dm^3 \, mol^{-1}22.4dm3mol−1​ (at s.t.p)

​gas constantgas \space constantgas constant​​
​RRR​​
​8.31 J K−1 mol−18.31 \, J \, K^{-1} \, mol^{-1}8.31JK−1mol−1​​


Note: r.t.p is room temperature and pressure (293 K,101.3 kPa293 \, K, 101.3 \, kPa293K,101.3kPa), whereas s.t.p is standard temperature and pressure (273 K,101.3 kPa273 \, K, 101.3 \, kPa273K,101.3kPa). 


Variable units 

​​quantity name 

symbol

unit name

unit

​number of molesnumber \space of \space molesnumber of moles​​
​nnn​​
​molemolemole​​
​molmolmol​​
​volumevolumevolume​​
​VVV​​
​cubic decimeter orcubic metrecubic \space decimeter \space or \newline cubic \, metrecubic decimeter orcubicmetre​​
​dm3 orm3dm^3 \space or \newline m^3dm3 orm3​​
​molar gas volumemolar \space gas \space volumemolar gas volume​​
​VmV_mVm​​​
​cubic decimeter per molecubic \space decimeter \space per \space molecubic decimeter per mole​​
​dm3 mol−1dm^3 \, mol^{-1}dm3mol−1​​
​pressurepressurepressure​​
​ppp​​
​pascalpascalpascal​​
​PaPaPa​​
​gas constantgas \space constantgas constant​​
​RRR​​
​joule per kelvin per per molejoule \space per \space kelvin \space per \space per \space molejoule per kelvin per per mole​​
​J K−1 mol−1J \, K^{-1} \, mol^{-1}JK−1mol−1​​
​temperaturetemperaturetemperature​​
​TTT​​
​kelvinkelvinkelvin​​
​KKK​​


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 = volumemolar gas volumen=VVmnumber \space of \space moles \, = \, \frac{volume}{molar \space gas \space volume} \newline n = \frac{V}{V_m}number of moles=molar gas volumevolume​n=Vm​V​

​​​

​​

This equation can be rearranged to calculate the volume of a gas:


​volume = number of moles × molar gas volumeV = n × Vmvolume \, = \, number \space of \space moles \, \times \, molar \space gas \space volume \newline V \, = \, n \, \times \, V_mvolume=number of moles×molar gas volumeV=n×Vm​

​​​

At room temperature and pressure the molar gas volume is 24 dm3 mol−124 \, dm^3 \, mol^{-1}24dm3mol−1​.

At standard temperature and pressure the molar gas volume is 22.4 dm3 mol−122.4 \, dm^3 \, mol^{-1}22.4dm3mol−1​.


Note: cm3cm^3cm3 can be converted to dm3dm^3dm3 by dividing by 1000. 


Example 

Work out the number of moles there are in 50 000 cm3 50 \, 000 \,cm^350000cm3 of nitrogen at room temperature and pressure. 


First convert cm3cm^3 cm3 to dm3dm^3dm3 to work out the volume in dm3dm^3dm3:​


V = 50 000 cm31000 = 50 dm3V \, = \, \frac{50 \, 000 \, cm^3}{1000} \, = \, 50 \, dm^3V=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 = 24 dm3 mol−1V_m \, = \, 24 \, dm^3 \, mol^{-1}Vm​=24dm3mol−1​​


Next, write down the equation you will use:


n=VVmn = \frac{V}{V_m}n=Vm​V​​​


Substitute the values into the equation to find your answer:


n = 50 dm324 dm3 mol−1 = 2.08 moln \, = \, \frac{50 \, dm^3}{24 \, dm^3 \, mol^{-1}} \, = \, 2.08 \, moln=24dm3mol−150dm3​=2.08mol​​


There are 2.08 moles‾\underline{2.08 \, moles}2.08moles​ in 50 000 cm350 \, 000 \, cm^350000cm3​ 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. 


Chemistry; Formulae, equations and amounts of substances; KS5 Year 12; Calculations involving gases

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 (xxx-axis) against volume of gas produced (yyy​-axis). 

6.

Read the volume of gas produced at a certain mass of salt.

7.

Calculate the amount of salt using the mass and MMM​. 


​number of moles = massMolar massnumber \space of \space moles \, = \, \frac{mass}{Molar \ mass}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 =volumemolar gas volumenumber \space of \space moles \, = \frac{volume}{molar \space gas \space volume}number of moles=molar gas volumevolume​



Rearranged:

​

​molar gas volume = volumenumber of molesmolar \space gas \space volume \, = \, \frac{volume}{number \space of \space moles}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 = volumemolar gas volumenumber \space of \space moles \, = \, \frac{volume}{molar \space gas \space volume}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 volumevolume \, = \, number \space of \space moles \space \times \space molar \space gas \space volumevolume=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=nRTpressure \space \times \space volume \, = \, number \space of \space moles \space \times \space gas \space constant \space \times \space temperature \newline pV=nRTpressure × volume=number of moles × gas constant × temperaturepV=nRT​​

​​​

Note: The gas constant has a value of 8.31 J K−1 mol−18.31 \, J \, K^{-1} \, mol^{-1}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 (10310^3103). 
  • To convert from cm3cm^3cm3 to m3m^3m3, multiply by 10−610^{-6}10−6. 
  • To convert from dm3dm^3dm3 to m3m^3m3 multiply by 10−310^{-3}10−3 (divide by 1000).
  • To convert from oC^oCoC to KKK add 273.


Example  

At a temperature of 25oC25^oC25oC and pressure of 150 kPa150 \, kPa150kPa, methane occupies a volume of 1760 cm31760 \, cm^31760cm3. What is the mass of methane?


First convert all of the variables that have been given in the question:


T (K) = 25 (oC) + 273 = 298 KT \, (K) \, = \, 25 \, (^oC) \, + \, 273 \, = \, 298 \, KT(K)=25(oC)+273=298K

P (Pa) = 150 (kPa) × 103 = 150 000 PaP \, (Pa) \, = \, 150 \, (kPa) \, \times \, 10^3 \, = \, 150 \, 000 \, PaP(Pa)=150(kPa)×103=150000Pa

V (m3) = 1760 (cm3) ×10−6 = 1760 × 10−6 m3V \, (m^3) \, = \, 1760 \, (cm^3) \, \times 10^{-6} \, = \, 1760 \, \times \, 10^{-6} \, m^3V(m3)=1760(cm3)×10−6=1760×10−6m3


You will need your gas constant with the correct unit:


8.31 J K−1 mol−18.31 \, J \, K^{-1} \, mol^{-1}8.31JK−1mol−1


Write the equation you will use: 


pV=nRTpV=nRTpV=nRT


Rearrange the equation to make the number of moles the subject (this can be used to calculate the mass of methane):


n = pVRTn \, = \, \frac{pV}{RT}n=RTpV​​​


Substitute in your values into this equation:


n = 150 000 Pa × (1760 × 10−6) m38.31 J K−1 mol−1 × 298 K = 0.11 moln \, = \, \frac{150 \, 000 \, Pa \, \times \, (1760 \, \times \, 10^{-6}) \, m^3}{8.31 \, J \, K^{-1} \, mol^{-1} \, \times \, 298 \, K} \, = \, 0.11 \, moln=8.31JK−1mol−1×298K150000Pa×(1760×10−6)m3​=0.11mol


Write down the equation you will use to find the mass:


m = n × Mm \, = \, n \, \times \, Mm=n×M​​


Work out the MrM_rMr​ of methane (CH4CH_4CH4​):


M (CH4) = (12 (Ar of C) × 1) + (1 (Ar of H) × 4) = 16 g/molM \, (CH_4) \, = \, (12 \, (A_r \, of \, C) \, \times \, 1) \, + \, (1 \, (A_r \, of \, H) \, \times \, 4) \, = \, 16 \ g/molM(CH4​)=(12(Ar​ofC)×1)+(1(Ar​ofH)×4)=16 g/mol


Substitute your values for the number of moles and relative molecular mass (MrM_rMr​) to find the mass of methane:


m = 0.11 mol × 16 = 1.76 gm \, = \, 0.11 \, mol \, \times \, 16 \, = \, 1.76 \, gm=0.11mol×16=1.76g​​

​

The mass of methane is 1.76 g‾\underline{1.76 \, g} 1.76g​ , given that there is 0.11 mol0.11 \, mol0.11mol of methane.

​

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Mole calculations and Avogadro's constant - Higher

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Mole calculations and Avogadro's constant - Higher

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Calculating gas volumes using moles - Higher

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FAQs - Frequently Asked Questions

What is the value for the gas constant?

The value for the gas constant is 8.31 J K^-1 mol^-1.

What is the ideal gas equation?

The ideal gas equation is: Pressure X Volume = Number of moles X Gas constant X Temperature.

What is the equation to work out the volume of gas using the molar gas volume?

The equation to work out the volume of a gas from molar gas volume is: Volume = Number of moles X Molar gas volume.

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