Gas Laws: Introduction At the conclusion of our time together, you should be able to:

1. Gas Laws: IntroductionAt the conclusion of our time together, you should be able to: List 5 properties of gases Identify the various parts of the kinetic molecular theory Define pressure Convert pressure into 3 different units Define temperature Convert a temperature to Kelvin

2. Importance of Gases • Airbags fill with N2 gas in an accident. • Gas is generated by the decomposition of sodium azide, NaN3. • 2 NaN3 ---> 2 Na + 3 N2

3. THREE STATES OF MATTER

4. General Properties of Gases • There is a lot of “free” space in a gas. • Gases can be expanded infinitely. • Gases fill containers uniformly and completely. • Gases diffuse and mix rapidly.

5. To Review • Gases expand to fill their containers • Gases are fluid – they flow • Gases have low density • 1/1000 the density of the equivalent liquid or solid • Gases are compressible • Gases effuse and diffuse

6. Properties of Gases Gas properties can be modeled using math. This model depends on — • V = volume of the gas (L) • T = temperature (K) • ALL temperatures in the entire unit MUST be in Kelvin!!! No Exceptions! • n = amount (moles) • P = pressure (atmospheres)

7. Ideal Gases Ideal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory. • Gases consist of tiny particles that are far apart relative to their size. • Collisions between gas particles and between particles and the walls of the container are elastic collisions • No kinetic energy is lost in elastic collisions

8. Ideal Gases (continued) • Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion • There are no forces of attraction between gas particles • The average kinetic energy of gas particles • depends on temperature, not on the identity of the particle.

9. Pressure • Is caused by the collisions of molecules with the walls of a container • Is equal to force/unit area • SI units = Newton/meter2 = 1 Pascal (Pa) • 1 atmosphere = 101,325 Pa • 1 atmosphere = 1 atm = 760 mm Hg = 760 torr • 1 atm = 29.92 in Hg = 14.7 psi = 0.987 bar = 10 m column of water.

10. Measuring Pressure The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century. The device was called a “barometer” • Baro = weight • Meter = measure

11. An Early Barometer The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high.

12. Pressure Column height measures Pressure of atmosphere • 1 standard atmosphere (atm) * = 760 mm Hg (or torr) * = 29.92 inches Hg * = 14.7 pounds/in2 (psi) = 101.325 kPa (SI unit is PASCAL) = about 34 feet of water!

13. And now, we pause for this commercial message from STP OK, so it’s really not THIS kind of STP… STP in chemistry stands for Standard Temperature and Pressure Standard Pressure = 1 atm (or an equivalent) Standard Temperature = 0 deg C (273 K) STP allows us to compare amounts of gases between different pressures and temperatures

14. Let’s Review: Standard Temperature and Pressure“STP” • P = 1 atmosphere, 760 torr • T = 0°C, 273 Kelvins • The molar volume of an ideal gas is 22.42 liters at STP

15. Pressure Conversions A. What is 475 mm Hg expressed in atm? B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 1 atm 760 mm Hg 475 mm Hg x = 0.625 atm 760 mm Hg 14.7 psi 29.4 psi x = 1.52 x 103 mm Hg

16. Pressure Conversions – Your Turn A. What is 2.00 atm expressed in torr? B. The pressure of a tire is measured as 32.0 psi. What is this pressure in kPa? 760 torr 1 atm 2.00 atm x = 1520 torr 101.325 kPa 14.7 psi 32.0 psi x = 221 kPa

17. Converting Celsius to Kelvin Gas law problems involving temperature require that the temperature be in KELVINS! Kelvins = C + 273 °C = Kelvins - 273

18. Gas Laws: Boyle’s and Charles’ LawAt the conclusion of our time together, you should be able to: Describe Boyle’s Law with a formula. Use Boyle’s Law to determine either a pressure or volume Describe Charles’ Law with a formula. Use Charles’ Law to determine either a temperature or volume

19. Boyle’s Law P α 1/V This means Pressure and Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). For example, P goes up as V goes down. Robert Boyle (1627-1691). Son of Earl of Cork, Ireland.

20. Boyle’s Law Summary Pressure is inversely proportional to volume when temperature is held constant.

21. Boyle’s Law Example A bicycle pump is a good example of Boyle’s law. As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire.

22. Example P1 V1 P2 V2 (0.947 atm) (0.15 L) (0.987 atm) V2 0.14 L or 140 mL

23. Boyle’s Law Practice #1 P1 V1 P2 V2 (1 atm) (0.5 L) (0.5 atm) V2 1 L

24. Charles’ Law If n and P are constant, then V α T V and T are directly proportional. • If one temperature goes up, the volume goes up! Jacques Charles (1746-1823). Isolated boron and studied gases. Balloonist.

25. Charles’s Original Balloon Modern Long-Distance Balloon

26. Charles’ Law Summary • The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. • (P = constant)

27. Charles’ Law

28. Example V1 V2 T1 T2 0.075 L V2 298 K 323 K 0.081 L

29. Charles’ Law Practice #1 V1 V2 T1 T2 2.75 L 2.46 L 293.0 K T2 262 K or -10.9 oC

30. Gas Laws: Gay-Lussac’s and CombinedAt the conclusion of our time together, you should be able to: Describe Gay-Lussac’s Law with a formula Use Gay-Lussac’s Law to determine either a temperature or volume Combine all three laws into the Combined Gas Law Use the Combined Gas Law to determine either temperature, volume or pressure

31. Gay-Lussac’s Law If n and V are constant, then P α T P and T are directly proportional. • If one temperature goes up, the pressure goes up! Joseph Louis Gay-Lussac (1778-1850)

32. Gay Lussac’sLaw Summary The pressure and temperature of a gas are directly related, provided that the volume remains constant.

33. Example P1 P2 T1 T2 3.00 atm P2 298 K 325 K 3.3 atm

34. Gay-Lussac’s Law Practice #1 P1 P2 T1 T2 1.8 atm 1.9 atm 293 K T2 310 K or 36 oC

35. Now let’s put all 3 laws together into one big law…….

36. Combined Gas Law • The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! No, it’s not related to R2D2

37. The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas. Boyle’s law, Gay-Lussac’s law, and Charles’ law are all derived from this by holding a variable constant.

38. Combined Gas Law If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! = P1 V1 P2 Boyle’s Law Charles’ Law Gay-Lussac’s Law V2 T1 T2

39. Combined Gas Law Problem A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm? Set up Data Table P1 = 0.800 atm V1 = 180 mLT1 = 302 K P2 = 3.20 atmV2 = 90 mLT2 = ??

40. Calculation • P1 = 0.800 atm V1 = 180 mL T1 = 302 K • P2 = 3.20 atm V2 = 90 mL T2 = ?? P1 V1 P2 V2 = P1 V1 T2 = P2 V2 T1 T1 T2 T2 = 3.20 atm x 90.0 mL x 302 K 0.800 atm x 180.0 mL T2 = 604 K - 273 = 331 °C = 604 K

41. Gas Laws: Avogadro’s and IdealAt the conclusion of our time together, you should be able to: Describe Avogadro’s Law with a formula. Use Avogadro’s Law to determine either moles or volume Describe the Ideal Gas Law with a formula. Use the Ideal Gas Law to determine either moles, pressure, temperature or volume Explain the Kinetic Molecular Theory

42. twice as many molecules Avogadro’s Law Equal volumes of gases at the same T and P have the same number of molecules. V = an V and n are directly related.

43. Avogadro’s Law Summary • For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). • V = an • a = proportionality constant • V = volume of the gas • n = number of moles of gas

44. Standard Molar Volume Equal volumes of all gases at the same temperature and pressure contain the same number of molecules. - Amedeo Avogadro

45. Avogadro’s Law Practice #1 V1 V2 n1 n2 4.00 L 7.12 L 0.21 mol n2 0.37 mol total 0.16 mol added

46. IDEAL GAS LAW P V = n R T Brings together gas properties. Can be derived from experiment and theory. BE SURE YOU KNOW THIS EQUATION!

47. Ideal Gas Law • PV = nRT • P = pressure in atm • V = volume in liters • n = moles • R = proportionality constant • = 0.08206 L atm/ mol·K • T = temperature in Kelvins Holds closely at P < 1 atm

48. Review of Kinetic Molecular Theory • Particles of matter are ALWAYS in motion • Volume of individual particles is  zero. • Collisions of particles with container walls cause pressure exerted by gas. • Particles exert no forces on each other. • Average kinetic energy µ Kelvin temperature of a gas.

49. Deviations from Ideal Gas Law • Real molecules have volume. The ideal gas consumes the entire amount of available volume. It does not account for the volume of the molecules themselves. • There areintermolecular forces. An ideal gas assumes there are no attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions. • Otherwise a gas could not condense to become a liquid.

50. R is a constant, called the Ideal Gas Constant Instead of learning a different value for R for all the possible unit combinations, we can just memorize one value and convert the units to match R. R = 0.08206 L • atm mol • K