Gas laws
Boyle's law

Boyle's law states that the volume of a fixed mass of gas is inversely proportional to its pressure at constant temperature. This relationship means that as volume increases, pressure exerted by gaseous molecules decreases and vice versa

$$ p \propto \frac{1}{v} $$ $$ p = \frac{k}{v} $$ $$ k = PV $$ $$ \text{The mathematical expression is}; $$ $$P_1V_1 = P_2V_2 $$
Graphical representation

Calculations

Example 1: A gas at a volume \( V_o \) in a container at a pressure \( P_o \) is compressed to one-fifth of its volume. What will be its pressure if it maintains its original temperature, T. (JAMB)

Solution

$$ V_1 = V_o $$ $$ P_1 = P_o $$ $$ V_2 = \frac{1}{5}V_o $$ $$ P_2 = ? $$ $$ P_1V_1 = P_2V_2 $$ $$ P_2 = \frac{P_1V_1}{V_2} $$ $$ P_2 = \frac{P_oV_o}{\frac{1}{5}V_o} $$ $$ P_2 = \frac{5P_oV_o}{V_o} $$ $$ P_2 = 5P_o $$

Example 2: The volume occupied by a gas at 37°C and 740mmHg is 100cm³. What would be the volume of the gas (in cm³) if the pressure is increased to 2000mmHg at the same temperature. (NECO)

Solution

$$ \text{since temperature is constant} $$ $$ P_1 = 740mmHg $$ $$ V_1 = 100cm³ $$ $$ P_2 = 2000mmHg $$ $$ V_2 = ? $$ $$ P_1V_1 = P_2V_2 $$ $$ V_2 = \frac{P_1V_1}{P_2} $$ $$ V_2 = \frac{740 × 100}{2000} $$ $$ V_2 = 37cm³ $$

Example 3: A gas occupies a volume of 300cm³ at 410mmHg. What will be its pressure when the volume is decreased to 130cm³ at constant temperature? (NECO)

Solution

$$ P_1 = 410mmHg $$ $$ V_1 = 300cm³ $$ $$ P_2 = ? $$ $$ V_2 = 130cm³ $$ $$ P_1V_1 = P_2V_2 $$ $$ P_2 = \frac{P_1V_1}{V_2} $$ $$ P_2 = \frac{410 × 300}{130} $$ $$ P_2 = 946.15mmHg $$

Boyle's law Calculator







Formulas:
  1. For 1: \( P_2 = \frac{P_1V_1}{V_2} \)

  2. For 2: \( V_2 = \frac{P_1V_1}{P_2} \)

Summary