A LevelPhysicsOCRRevision Notes5. Newtonian World & AstrophysicsIdeal GasesIdeal Gas Equation

Ideal Gas Equation (OCR A Level Physics)

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Ideal Gas Equation

  • An ideal gas is a specific type of gas which:

    • Has molecules with negligible volume

    • Collisions which are elastic

    • Cannot be liquified

    • Has no interactions between the molecules (except during collisions)

    • Obeys the (ideal) gas laws (Boyles law, Charles’ law and Pressure law)

  • All of these can occur at any temperature or pressure

  • The ideal gas equation for number of moles can be expressed as:

Ideal gas equation

  • The ideal gas equation for number of molecules can also be written in the form:

Ideal gas equation 2

  • An ideal gas is therefore defined as:

    A gas which obeys the equation of state pV = nRT at all pressures, volumes and temperatures

Worked Example

A storage cylinder of an ideal gas has a volume of 8.3 × 103 cm3. The gas is at a temperature of 15 °C and a pressure of 4.5 × 107 Pa.

Calculate the amount of gas in the cylinder, in moles.

Answer:

Step 1: State the known quantities

  • Pressure, P = 4.5 × 107 Pa 

  • Volume, V = 8.3 × 103 cm3 = 8.3 × 103 × 10−6 = 8.3 × 10−3 m3

  • Temperature, T = 15 °C = 15 + 273 = 288 K

Step 2: Write down the ideal gas equation

pV = nRT

Step 3: Rearrange for the number of moles n

Ideal Gas Equation equation 1

Step 4: Substitute in values and calculate number of moles of gas

n space equals space fraction numerator 4.5 cross times 10 to the power of 7 cross times 8.3 cross times 10 to the power of negative 3 end exponent over denominator 8.31 cross times 288 end fraction equals 160 space mol

Examiner Tips and Tricks

Don’t worry about remembering the values of R and k, they will both be given in the equation sheet in your exam.

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.