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 : P_iV_i = P_fV_f

  where P_i is the initial (original) pressure, V_i is its initial (original) volume, P_f is its final pressure, V_f is its final volume
  P_i and P_f must be in the same units of measurement (eg, both in atmospheres), V_i and V_f 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 25^oC

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 : P_iV_i = P_fV_f

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 10.0L container at the same temperature?
   P_i = 90 kPa         V_i = 2.5L
   P_f = ?                 V_f = 10.0L
   P_iV_i = P_fV_f
   90 x 2.5 = P_f x 10.0
   225 = P_f x 10.0
   225 ÷ 10.0 = P_f
   P_f = 22.5 kPa

2. 4.5L of gas at 125 kPa is expanded at constant temperature until the pressure is 75kPa. What is the final volume of the gas?
   P_i = 125 kPa         V_i = 4.5L
   P_f = 75 kPa         V_f = ?
   P_iV_i = P_fV_f
   125 x 4.5 = 75 x V_f
   562.5 = 75 x V_f
   V_f 562.5 ÷ 75 = 7.5L

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