Chapter 12

1. Chapter 12 The Behavior of Gases

2. Kinetic Theory Revisited… • Remember that an increase in heat energy increases the kinetic energy and, therefore, the temperature of gases and a decrease in heat energy causes the temperature to go down, decreasing the kinetic energy of gases. • Ex.: Balloons!!! A balloon on a cold day feels hard and doesn’t blow up! Put the same balloon in the car on a very hot day and it feels soft and eventually EXPLODES! Why?!

3. Compressibility of Gases • Compressibility: a measure of how much the volume of matter decreases under pressure

4. Variables That Describe a Gas

5. Factors Affecting Gas Pressure • Number of gas particles • Volume of container • Temperature

6. Number of Particles vs. Pressure • An increase in the number of gas particles causes an increase in gas pressure. • The more gas = the higher the pressure • The less gas = the lower the pressure • Direct relationship!

7. Volume vs. Pressure

8. Volume vs. Pressure • If you reduce the volume of gas (compress) then the pressure will increase. • If you increase the volume of gas then the pressure will decrease. • Inverse relationship!

9. Temperature vs. Pressure • Temperature can change pressure as well. (Think: balloons)! • An increase in temperature will increase the pressure of the gas due to increase of kinetic energy. • A decrease in temperature will cause the pressure to decrease due to decrease of kinetic energy. • Direct relationship! • http://www.youtube.com/watch?v=t-Iz414g-ro

10. The Gas Laws • Boyle’s Law: for a given mass of gas at constant temperature, the volume of gas varies inversely with pressure. • So…. As volume decreases pressure increases. As volume increases pressure decreases!

11. Boyle’s Law • http://www.youtube.com/watch?v=J_I8Y-i4Axc

12. Math for Boyle’s Law • Boyle’s Formula: P1 V1 = P2 V2 • Example: A balloon contains 30.0L of helium gas at 103 kPa. What is the volume when the balloon rises to an altitude where the pressure is only 25.0 kPa? (Assume that the temperature remains constant)? 1.24 x 102 L

13. Charles’s Law • The volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant. • So…. As temperature decreases volume decreases. As temperature increases volume increases!

14. Charles’s Law • http://www.youtube.com/watch?v=IkRIKGN3i0k&feature=related

15. Math for Charles’s Law • Charles’s Formula: V1/T1 = V2/T2 • Example: A balloon inflated in a room at 24 °C has a volume of 4.00 L. The balloon is then heated to 58 °C. What is the new volume if the pressure remains constant? 4.46 L

16. Gay-Lussac’s Law • States that the pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant. • So…. As temperature decreases pressure decreases. As temperature increases pressure increases! • P1/T1 = P2/T2

17. The Combined Gas Law

18. Combined Gas Law • The other laws can be obtained from this law by holding one quantity (pressure, volume, or temp) constant. • It also enables you to do calculations for situations in which none of the variables are constant!!

19. The volume of a gas-filled balloon is 30.0L at 40 °C and 153 kPa. What volume will the balloon have at standard temperature and pressure? • Celsius must be in Kelvin! • 40 + 273 = 313 K • Rearrange combined gas law: • V2 = V1 x P1 x T2/P2 x T1 • Plug in numbers: • V2= 30.0L x 153kPa x 273K / 101.3kPa x 313K V2 = 39.5L

20. Ideal Gas Law • Ideal Gas Law: used to describe the behavior of an ideal gas PV = nRT • R: is the ideal gas constant: has a value of 8.31 (L * kPa) / (K * mol) • Advantage of ideal gas law over combined gas law is it permits you to solve for the number of moles of a contained gas.

21. Ideal Gas Law Equation • PV = nRT PERVNERT!! • P = Pressure (kPa) • V = Volume (L) • n = Number of moles • R = Gas constant (8.31 L kPa/K mol) • T = Temperature (K)

22. You fill a steel cylinder that has a volume of 20.0 L with nitrogen gas to a final pressure of 2.0 x 104 kPa at 28 °C. How many moles of nitrogen does the cylinder contain? PV = nRT • P = 2.0x104kPa • V = 20.0L • n = ??? • R = 8.31 • T = 28C + 273 = 301K 1.60x102 mol N2

23. Avogadro’s Hypothesis • Equal volumes of gases at the same temperature and pressure contain equal numbers of particles.

24. Dalton’s Law • Law of Partial Pressure: At constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases. • Ptotal = P1 + P2 + P3 +………..

25. Graham’s Law • Graham’s Law of Effusion: The rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass. This is also true for the diffusion of a gas. • Effusion: the process in which a gas escapes through a tiny hole in its container • Gases of lower molar mass effuse faster than gases of higher molar mass.

26. Scuba Diving and Gas Laws • How can divers dive safely into the underwater world with out feeling the effects of high pressure? • What kind of pressure is exerted by water? How does it affect our physiology? • What kind of gas do they breathe??

27. Divers can breathe under water because the gases they take with them are under pressure. A regulator automatically adjusts the pressure of the air coming out of the tanks and into the lungs. It equalizes pressure inside the lungs to match outside the lungs. Just like popping your ears. • Diving at even moderate depths creates enough pressure that more gas dissolves in the blood than normal. Any gas in the tank dissolves in higher concentrations. • What kind of problems do we have here in terms of gas laws???

28. The main component of air is molecular nitrogen. When nitrogen dissolves in the blood and reaches certain concentrations two different things can happen. • 1. Nirtogen Narcosis: basically having alcohol poisoning, but underwater!!!  • 2. The bends! Dissolved nitrogen comes out of solution (blood) and forms tiny bubbles of N2.