Boyle's law - SCIENCE

Postulates of Kinetic Molecular Theory (KMT) of Gases

• Gases are composed of particles (molecules or atoms) in constant random motion.

• Gas particles collide with each other and the walls of their container; all collisions are elastic (no net loss of energy).

• The size of gas particles is small compared to the total volume of the gas.

• There are no attractive or repulsive forces between gas particles.

• The average kinetic energy of gas particles is proportional to the absolute temperature; gases at the same temperature have the same average kinetic energy

• Consider the properties of the gas and the volume of each flask.

Experiments with Gas Volume and Pressure

• Syringe Experiment:

  • When you push down the plunger, the volume in the syringe decreases.

  • As the volume decreases, the pressure exerted by the gas increases.

Boyle's Law

• Definition: The pressure and volume of a gas are inversely proportional.

  • When volume decreases, pressure increases (and vice versa), given constant mass and temperature.

  • Mathematically:
    $PV = k$
    or
    $p V = ext{constant}$

Units of Pressure

Mathematical Expression of Boyle’s Law

• The mathematical relationship:

  • P1V1 = P2V2

  • Where:

  • $P_1$ = initial pressure

  • $V_1$ = initial volume

  • $P_2$ = final pressure

  • $V_2$ = final volume

• Standard units include:

  • Pressure: atm, mmHg, Pa, torr

  • Volume: Liters (L), milliliters (mL)

Sample Problems

Problem 1: Ground-Level Pressure Calculation

• Given:

  • $P_1 = 0.8 ext{ atm}$

  • $V_2 = 1.3 ext{ L}$

  • $V_1 = 0.735 ext{ L}$

• To find: $P_2$

• Solution:

  • Using Boyle's Law:

  • $P<em>1 imes V</em>1 = P<em>2 imes V</em>2$

  • Rearranging gives:

  • $P<em>2 = rac{P</em>1 imes V<em>1}{V</em>2}$

  • Substituting values:

  • $P_2 = rac{(0.8 ext{ atm}) imes (0.735 ext{ L})}{1.3 ext{ L}} = 0.452 ext{ atm}$

Problem 2: New Volume Calculation

• Given:

  • $V_1 = 4.01 ext{ L}$

  • $P_2 = 1.93 ext{ atm}$

  • $P_1 = 2.44 ext{ atm}$

• To find: $V_2$

• Solution:

  • Using Boyle's Law:

  • $P<em>1 imes V</em>1 = P<em>2 imes V</em>2$

  • Rearranging gives:

  • $V<em>2 = rac{P</em>1 imes V<em>1}{P</em>2}$

  • Substituting values:

  • $V_2 = rac{(2.44 ext{ atm}) imes (4.01 ext{ L})}{1.93 ext{ atm}} = 5.07 ext{ L}$

Classroom Problems for Practice

1. An oxygen gas sample of volume 225 mL at 1.12 atm pressure. Volume at 0.98 atm?

2. A balloon of 0.666 L at 1.03 atm placed in a chamber with 5.68 atm pressure. Calculate new volume.

3. Gas in a 5 L piston at 1 atm pressure changed to 3.5 atm. What is the new volume?

Summary of Boyle's Law

• Expression: $PV = k$

• Pressure is inversely related to volume.

• Boyle's Law is essential for relating different conditions of a gas at constant temperature.