OCR AS Chemistry

Revision Notes

2.2.4 The Ideal Gas Equation

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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

Exam 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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