Gas Laws: Boyle's, Charles's, and Gay-Lussac's Law Explanation

1. Gas Laws Section 11.2

2. Boyle’s Law • Boyle’s law shows the relationship between pressure and volume • The relationship is inverse • volume  pressure  • Mathematically: PV = k • k is a constant

3. Boyle’s Law

4. Using Boyle’s Law • When temperature is held constant: • P1V1 = P2V2 • P1V1 is the initial pressure and volume • P2V2 is the ending pressure and volume

5. Problem 1 • A sample of oxygen gas has a volume of 150.0 mL when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature remains constant? • Identify every quantity in the problem with the units

6. Problem Solution • P1 = 0.947 atm • V1 = 150.0 mL • P2 = 0.987 atm • V2 = ? • Use Boyle’s law to solve • 144 mL O2

7. Charles’s Law • Charles’s law show the relationship between volume and temperature • The relationship is direct • Temperature  volume  • V = kT or V/T = k

9. Using Charles’s Law • When pressure is held constant: • V1 and T1 are initial conditions • V2 and T2 are ending conditions • Temperatures must be in Kelvin to use gas laws (add 273 to degrees Celsius)

10. Problem 2 • A sample of neon gas occupies a volume of 752 mL at 25°C. What volume will the gas occupy at 50°C if the pressure remains constant? • Identify every quantity in the problem with the units

11. Solution • V1 = 752 mL • T1 = 25°C + 273 = 298 K • T2 = 50°C + 273 = 323 K • Use Charles’s law to solve • 815 mL Ne

12. Gay-Lussac’s Law • Gay-Lussac’s law shows the relationship between pressure and temperature • The relationship is direct • Temperature  pressure  • P = kT or P/T = k

14. Using Gay-Lussac’s Law • When volume is held constant: • P1 and T1 are initial conditions • P2 and T2 are ending conditions • Temperatures must be in Kelvin to use gas laws (add 273 to degrees Celsius)

15. Problem 3 • The gas in a container is at a pressure of 3.00 atm at 25°C. Directions on the container warn the user not to keep it in a place where the temperature exceeds 52°C. What would the gas pressure in the container be at 52°C? • Identify every quantity in the problem with the units

16. Solution • P1 = 3.00 atm • T1 = 25°C + 273 = 298 K • T2 = 52°C + 273 = 325 K • P2 = ? • Use Gay-Lussac’s law to solve • 3.27 atm

17. Graphical Representations of the Gas Laws • Boyle’s law Charles’s law Gay-Lussac’s law

18. Combined Gas Law • A gas sample frequently undergoes changes in temperature, pressure, and volume all at the same time. • The amount of gas remains constant • Combined gas law: expresses the relationship between pressure, volume, and temperature of a fixed amount of gas

19. When the amount of the gas is held constant

20. Problem 4 • A helium-filled balloon has a volume of 50.0 L at 25°C and 1.08 atm. What volume will it have at 0.855 atm and 10.0°C? • Identify every quantity in the problem with the units

21. Solution • P1 = 1.08 atm • T1 = 25°C + 273 = 298 K • V1 = 50.0 L • P2 = 0.855 atm • T2 = 10.0°C + 273 = 283.0 K • V2 = ? • Use the combined gas law to solve

22. Solution • 60.0 L He