OCR A Level Physics

Revision Notes

5.2.2 Ideal Gas Equation

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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.

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 × 103 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 bold 160 bold space bold mol

Exam Tip

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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