1. CHARLES’S LAW The Second Gas Law

2. Objectives Upon completion of this presentation, you will be able to describe the relationship between the volume and the temperature of an ideal gas use Charles’s law to calculate the final volume of a gas when given the initial temperature and volume and the final temperature use Charles’s law to calculate the final temperature of a gas when given the initial temperature and volume and the final volume

3. Introduction In the 1780’s, Jacques Charles was investigating the properties of gases. He found a relationship between volume, V, and temperature, T, when the pressure, P, is held constant. Volume is directly related to temperature. As the temperature increases, the volume increases. As the temperature decreases, the volume decreases.

4. Introduction This behavior would be expected from the assumptions of the kinetic theory. As the temperature increases, the average speed of the gas particles also increases. This causes the collisions with the walls of the container to be more forceful. More force over the same area gives more pressure. To keep the pressure constant, we would need to increase the volume of the container.

5. Introduction We can write Charles’s law two different ways: V/T = k or V = kT where "k" is a constant. V 1 /T 1 = V 2 /T 2 where V 1 and T 1 are initial volume and temperature where V 2 and T 2 are final volume and temperature

6. Introduction Charles stated his law using the first notation, V = kT. The change in volume of a gas is directly proportional to the temperature when the pressure is held constant. V ∝ T ⇒ V = kT We most often use the second notation, V 1 /T 1 = V 2 /T 2, to solve problems.

7. Application When we are trying to solve a Charles's law problem, we will need to know three of the four variables. For V 1 /T 1 = V 2 /T 2 we can solve for: V 1 = V2T1V2T1 T2T2 T 1 = T2V1T2V1 V2V2 V 2 = V1T2V1T2 T1T1 T 2 = T1V2T1V2 V1V1

8. Example 1 – Finding V 2 What is the final volume, V 2, of 2.00 L of helium gas at an initial temperature of 300K, and a final temperature of 500 K? V 1 = 2.00 L T 1 = 300 K V 2 = ? L T 2 = 500 K V 2 = V1T2V1T2 T1T1 = (2.00 L)(500 K) 300 K = 3.33 L

9. Sample Problems – Finding V 2 1. What is the final volume of hydrogen gas with an initial volume of 3.00 L, an initial temperature of 300 K, and a final temperature of 400 K? 2. What is the final volume of oxygen gas with an initial volume of 0.120 L, an initial temperature of 500 K, and a final temperature of 200 K? 3. What is the final volume of chlorine gas with an initial volume of 2.40 L, an initial temperature of 200 K, and a final temperature of 250 K? 4. What is the final volume of carbon monoxide gas with an initial volume of 0.0480 L, an initial temperature of 273 K, and a final temperature of 625 K? V 2 = 4.00 L V 2 = 0.0480 L V 2 = 3.00 L V 2 = 0.110 L

10. Example 2 – Finding T 2 What is the final temperature, T 2, of argon gas at an initial volume of 4.20 L, an initial temperature of 250 K, and a final volume of 4.80 L? V 1 = 4.20 L T 1 = 250 K V 2 = 4.80 L T 2 = ? L T 2 = T1V2T1V2 V1V1 = (250 K)(4.80 L) 4.20 L = 285 K

11. Sample Problems – Finding T 2 1. What is the final temperature of neon gas with an initial volume of 4.00 L, an initial temperature of 350 K, and a final volume of 0.100 L? 2. What is the final temperature of helium gas with an initial volume of 1.20 L, an initial temperature of 250 K, and a final volume of 0.600 L? 3. What is the final temperature of argon gas with an initial volume of 480 L, an initial temperature of 300 K, and a final volume of 1,200 L? 4. What is the final temperature of fluorine gas with an initial volume of 40.4 L, an initial temperature of 280 K, and a final volume of 542 L? T 2 = 8.75 K T 2 = 125 K T 2 = 750 K T 2 = 3,760 K

12. Example 3 – Finding V 1 What was the initial volume, V 1, of neon gas that had an initial temperature of 200 K, a final volume of 0.500 L, and a final temperature of 500 K? V 1 = ? L T 1 = 200 K V 2 = 0.500 L T 2 = 500 K V 1 = V2T1V2T1 T2T2 = (0.500 L)(200 K) 500 K = 0.200 L

13. Sample Problems – Finding V 1 1. What is the initial volume of nitrogen gas with an initial temperature of 600 K, a final temperature of 300 K, and a final volume of 0.100 L? 2. What is the initial volume of oxygen gas with an initial temperature of 250 K, a final temperature of 300 K, and a final volume of 6.00 L? 3. What is the initial volume of chlorine gas with an initial temperature of 1,200 K, a final temperature of 400 K, and a final volume of 3,500 L? 4. What is the initial volume of fluorine gas with an initial temperature of 294 K, a final temperature of 742 K, and a final volume of 85.9 L? V 1 = 0.200 L V 1 = 5.00 L V 1 = 10,500 L V 1 = 34.0 L

14. Example 4 – Finding T 1 What was the initial temperature, T 1, of argon gas at an initial volume of 0.100 L, a final volume of 0.125 L, and a final temperature of 298 K? V 1 = 0.100 L T 1 = ? L V 2 = 0.125 L T 2 = 298 K T 1 = T2V1T2V1 V2V2 = (298 K)(0.100 L) 0.125 L = 238 K

15. Sample Problems – Finding T 1 1. What is the initial temperature of radon gas with an initial volume of 4.00 L, a final volume of 2.00 L, and a final temperature of 250 K? 2. What is the initial temperature of neon gas with an initial volume of 12.0 L, a final volume of 15.0 L, and a final temperature of 400 K? 3. What is the initial temperature of helium gas with an initial volume of 0.720 L, a final volume of 0.600 L, and a final temperature of 350 K? 4. What is the initial temperature of ammonia gas with an initial volume of 0.235 L, a final volume of 0.123 L, and a final temperature of 275 K? T 1 = 500 K T 1 = 320 K T 1 = 420 K T 1 = 525 K

16. Summary Charles’s Law: At a constant pressure, the volume of a gas is directly proportional to its volume. Equations: V/T = k or V = kT, where k is a constant V 1 /T 1 = V 2 /T 2