The Ideal Gas Equation (OCR A Level Chemistry)

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Ideal Gas Equation & Calculations

Kinetic theory of gases

  • The kinetic theory of gases states that molecules in gases are constantly moving
  • The theory makes the following assumptions:
    • That gas molecules are moving very fast and randomly
    • That molecules hardly have any volume
    • That gas molecules do not attract or repel each other (no intermolecular forces)
    • No kinetic energy is lost when the gas molecules collide with each other (elastic collisions)
    • The temperature of the gas is related to the average kinetic energy of the molecules

  • Gases that follow the kinetic theory of gases are called ideal gases
  • However, in reality gases do not fit this description exactly but may come very close and are called real gases

Ideal gases

  • The volume that an ideal gas occupies depends on:
    • Its pressure
    • Its temperature

  • When a gas is heated (at constant pressure) the particles gain more kinetic energy and undergo more frequent collisions with the container wall
  • To keep the pressure constant, the molecules must get further apart and therefore the volume increases
  • The volume is therefore directly proportional to the temperature (at constant pressure)

States of Matter Volume and Temperature, downloadable AS & A Level Chemistry revision notes

The volume of a gas increases upon heating to keep a constant pressure (a); volume is directly proportional to the temperature (b)

Limitations of the ideal gas law

  • At very low temperatures and high pressures real gases do not obey the kinetic theory as under these conditions:
    • Molecules are close to each other
    • There are instantaneous dipole- induced dipole or permanent dipole- permanent dipole forces between the molecules
    • These attractive forces pull the molecules away from the container wall
    • The volume of the molecules is not negligible

  • Real gases therefore do not obey the following kinetic theory assumptions at low temperatures and high pressures:
    • There is zero attraction between molecules (due to attractive forces, the pressure is lower than expected for an ideal gas)
    • The volume of the gas molecules can be ignored (volume of the gas is smaller than expected for an ideal gas)

Ideal gas equation

  • The ideal gas equation shows the relationship between pressure, volume, temperature and number of moles of gas of an ideal gas:

PV = nRT

P = pressure (pascals, Pa)

V = volume (m3)

n = number of moles of gas (mol)

R = gas constant (8.314 J mol-1 K-1)

T = temperature (kelvin, K)

Worked example

Calculating the volume of a gas

Calculate the volume occupied by 0.781 mol of oxygen at a pressure of 220 kPa and a temperature of 21 °C.

Answer

Step 1: Rearrange the ideal gas equation to find volume of gas

Vfraction numerator n R T over denominator P end fraction

Step 2: Calculate the volume the oxygen gas occupies

p = 220 kPa = 220 000 Pa

n = 0.781 mol

R = 8.314 J mol-1 K-1 

T = 21 oC = 294 K

V equals fraction numerator 0.781 space mol cross times 8.314 space straight J space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent cross times 294 space straight K over denominator 220000 space Pa end fraction equals 0.00867 space straight m cubed space equals space 8.67 space dm cubed 

Worked example

Calculating the molar mass of a gas

A flask of volume 1000 cm3 contains 6.39 g of a gas. The pressure in the flask was 300 kPa and the temperature was 23 °C.

Calculate the relative molecular mass of the gas.

Answer

Step 1: Rearrange the ideal gas equation to find the number of moles of gas

n = fraction numerator P V over denominator R T end fraction

Step 2: Calculate the number of moles of gas

p = 300 kPa = 300 000 Pa

V = 1000 cm3 = 1 dm3 = 0.001 m3

R = 8.314 J mol-1 K-1

T = 23 oC = 296 K

n = equals fraction numerator 300000 space Pa space cross times 0.001 space straight m cubed over denominator 8.314 space straight J space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent cross times 296 space straight K end fraction equals 0.1219 space mol

Step 3: Calculate the molar mass using the number of moles of gas

nfraction numerator mass over denominator molar space mass end fraction

Molar massequals fraction numerator 6.39 space straight g over denominator 0.1219 space mol end fraction equals 52.42 space straight g space mol to the power of negative 1 end exponent

Examiner Tip

To calculate the temperature in Kelvin, add 273 to the Celsius temperature - e.g. 100 oC is 373 Kelvin

You must be able to rearrange the ideal gas equation to work out all parts of it

The units are incredibly important in this equation - make sure you know what units you should use, and do the necessary conversions when doing your calculations!

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Richard

Author: Richard

Expertise: Chemistry

Richard has taught Chemistry for over 15 years as well as working as a science tutor, examiner, content creator and author. He wasn’t the greatest at exams and only discovered how to revise in his final year at university. That knowledge made him want to help students learn how to revise, challenge them to think about what they actually know and hopefully succeed; so here he is, happily, at SME.