1. Chap 12.2
Gas laws

2. 12.2 Gas Laws
Objectives
State Boyle’s law, and use it to solve problems involving pressure and volume.
State Charles’s law, and use it to solve problems involving volume and temperature.
State Gay-Lussac’s law, and use it to solve problems involving pressure and temperature.
State Avogadro’s law, and explain its importance in determining the formulas of chemical compounds.

3. 12.2 Gas Laws Measurable Properties of Gases
Gases are described by their measurable properties.
P = pressure exerted by the gas
V = total volume occupied by the gas
T = temperature in kelvins of the gas
n = number of moles of the gas

4. 12.2 Gas Laws T=constant, relationship between V and P
Volume _____________, Pressure _____________.
Boyle’s Law

5. 12.2 Gas Laws
The inverse relationship between pressure and volume is known as Boyle’s law.
Boyle’s law states that for a fixed amount of gas at a constant temperature, the volume of the gas increases as the pressure of the gas decreases and the volume of the gas decreases as the pressure of the gas increases.
Boyle’s Law

6. Chapter 12.2 Boyle’s Law, continued
T= constant, the product of the pressure and volume of a gas is constant.
PV = k
If the temperature and number of particles are not changed, the PV product remains the same, as shown in the equation below.
P1V1 = P2V2

7. Chapter 12.2
Volume Versus Pressure for a Gas at Constant Temperature

8. Solving Pressure-Volume Problems
Chapter 12.2
Solving Pressure-Volume Problems
Sample Problem
A given sample of gas occupies 523 mL at 1.00 atm. The pressure is increased to 1.97 atm, while the temperature remains the same. What is the new volume of the gas?

9. Chapter 12 Temperature-Volume Relationships
Section 2 The Gas Laws
Temperature-Volume Relationships
Heating a gas makes it expand.
Cooling a gas makes it contract.
In 1787, the French physicist Jacques Charles discovered that a gas’s volume is directly proportional to the temperature on the Kelvin scale if the pressure remains the same.

10. Chapter 12
Section 2 The Gas Laws
Charles’s Law
P = Constant, Relationship between temperature and volume - Charles’s law.
Charles’s law states that for a fixed amount of gas at a constant pressure, the volume of the gas increases as the temperature of the gas increases and the volume of the gas decreases as the temperature of the gas decreases.

11. Chapter 12 Charles’s Law, continued
Section 2 The Gas Laws
Charles’s Law, continued
If the absolute temperature is reduced by half, then the average kinetic energy is reduced by half, and the particles will strike the walls with half of the energy they had at the higher temperature.
In that case, the volume of the gas will be reduced to half of the original volume if the pressure remains the same.

12. Volume Versus Temperature for a Gas at Constant Pressure
Chapter 12
Section 2 The Gas Laws
Volume Versus Temperature for a Gas at Constant Pressure
V-T graph using the Kelvin scale.
at 0 K, the gas’s volume becomes zero.
Before this temperature is reached, the gas becomes a liquid and solid.

13. Chapter 12 Charles’s Law, continued
Section 2 The Gas Laws
Charles’s Law, continued
At constant pressure, the volume of a sample of gas divided by its absolute temperature is a constant, k.
Charles’s law can be stated as the following equation.
If all other conditions are kept constant, V/T will remain the same.

14. Solving Volume-Temperature Problems
Chapter 12
Section 2 The Gas Laws
Solving Volume-Temperature Problems
Sample Problem
A balloon is inflated to 665 mL volume at 27°C. It is immersed in a dry-ice bath at -78.5°C. What is its volume, assuming the pressure remains constant?

15. Solving Volume-Temperature Problems, continued
Chapter 12
Section 2 The Gas Laws
Solving Volume-Temperature Problems, continued
Sample Problem C Solution
V1 = 665 mL T1 = 27°C
V2 = ? T2 = −78.5°C
T1 = 27°C = 300 K T2 = −78.5°C = K

16. Chapter 12 Temperature-Pressure Relationships
Section 2 The Gas Laws
Temperature-Pressure Relationships
Temperature and pressure have a directly proportional relationship.
The direct relationship between temperature and pressure is known as Gay-Lussac’s law.
Gay-Lussac’s Law states that the pressure of a gas at a constant volume is directly proportional to the absolute temperature.

17. Measurable Properties of Gases, continued
Chapter 12
Section 2 The Gas Laws
Measurable Properties of Gases, continued
Temperature-Pressure Relationships, continued
Gas pressure is directly proportional to kelvin temperature, at constant volume.

18. Measurable Properties of Gases, continued
Chapter 12
Section 2 The Gas Laws
Measurable Properties of Gases, continued
Temperature-Pressure Relationships, continued
This equation can be rearranged to the following form.
At constant volume, the following equation applies.

19. Solving Pressure-Temperature Problems
Chapter 12
Section 2 The Gas Laws
Solving Pressure-Temperature Problems
Sample Problem D
An aerosol can containing gas at 101 kPa and 22°C is heated to 55°C. Calculate the pressure in the heated can.

20. Measurable Properties of Gases, continued
Chapter 12
Section 2 The Gas Laws
Measurable Properties of Gases, continued
Temperature-Pressure Relationships, continued
Sample Problem D Solution
P1 = 101 kPa T1 = 22°C
P2 = ? T2 = 55°C
T1 = 22°C = 295 K T2 = 55°C = 328 K