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Boyle's Law (Mariotte's Law)

Key Concepts

  • At constant temperature, the volume of a given quantity of gas is inversely proportional to its pressure : V ∝ 1/P

    So at constant temperature, if the volume of a gas is doubled, its pressure is halved.
    OR
    At constant temperature for a given quantity of gas, the product of its volume and its pressure is a constant : PV = constant, PV = k

  • At constant temperature for a given quantity of gas : PiVi = PfVf

    where Pi is the initial (original) pressure, Vi is its initial (original) volume, Pf is its final pressure, Vf is its final volume
    Pi and Pf must be in the same units of measurement (eg, both in atmospheres), Vi and Vf must be in the same units of measurement (eg, both in litres).

  • All gases approximate Boyle's Law at high temperatures and low pressures.

    A hypothetical gas which obeys Boyle's Law at all temperatures and pressures is called an Ideal Gas.
    A Real Gas is one which approaches Boyle's Law behaviour as the temperature is raised or the pressure lowered.

Graphical Representations

Compression of Hydrogen gas at 25oC

Pressure
(mm Hg)*
Volume
(mL)
P x V Graph
760 23 1.75 x 104
912 19.2 1.75 x 104
1064 16.4 1.75 x 104
1216 14.4 1.75 x 104
1368 12.8 1.75 x 104
1520 11.5 1.75 x 104

Volume
(mL)
1/Pressure
(1/mm Hg)*
Graph
11.5 6.6 x 10-4
12.8 7.3 x 10-4
14.4 8.2 x 10-4
16.4 9.4 x 10-4
19.2 1.1 x 10-3
23 1.3 x 10-3

* A pressure of 760 mm Hg is equal to 1 atmosphere (atm) or 101.3 kilopascals (kPa)

Calculations : PiVi = PfVf

  1. A certain mass of gas occupies a volume of 2.5L at 90 kPa pressure. What pressure would the gas exert if it were placed in a 10.0 L container at the same temperature?
    Pi = 90 kPa         Vi = 2.5 L
    Pf = ?                 Vf = 10.0 L
    PiVi = PfVf
    90 x 2.5 = Pf x 10.0
    225 = Pf x 10.0
    225 ÷ 10.0 = Pf
    Pf = 22.5 kPa

  2. 4.5L of gas at 125 kPa is expanded at constant temperature until the pressure is 75 kPa. What is the final volume of the gas?
    Pi = 125 kPa         Vi = 4.5 L
    Pf = 75 kPa         Vf = ?
    PiVi = PfVf
    125 x 4.5 = 75 x Vf
    562.5 = 75 x Vf
    Vf 562.5 ÷ 75 = 7.5 L


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