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# THE PROPERTIES OF GASES

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1. THE PROPERTIES OF GASES • A gas uniformly fills any container, is easily compressed and mixes completely with any other gas. • Only four quantities define the state of a gas: a. the quantity of the gas, n (in moles) b. the temperature of the gas, T (in KELVINS) c. the volume of the gas, V (in liters) d. the pressure of the gas, P (in atmospheres)

2. PRESSURE • A measure of the force that a gas exerts on its container. • Force is the physical quantity that interferes with inertia. • Gravity is the force responsible for weight. • Newton’s 2nd Law: Force = m × a • The units of force follow: N = kg × m/s2 • Pressure - Force ÷ unit area; N/m2

3. PRESSURE • Standard Pressure • 760.00 mm Hg • 760.00 torr • 1.00 atm • 101.325 kPa ≈ 105 Pa • The SI unit of pressure is the Pascal; 1 Pa = 1 N/m2

4. PRESSURE • Pressure is measured in a variety of units. *We will use all of these but psi.

5. PRESSURE • Barometer - measures gas pressure (especially atmospheric). 1 mm of Hg = 1 torr • Manometer—a device for measuring the pressure of a gas in a container. The pressure of the gas is given by h [the difference in mercury levels] in units of torr (equivalent to mm Hg).

6. PRESSURE

7. PRACTICE ONE The pressure of a gas is measured as 49 torr. Represent this pressure in both atmospheres and pascals.

8. PRACTICE TWO Rank the following pressures in decreasing order of magnitude (largest first, smallest last): 75 kPa, 300. torr, 0.60 atm, and 350. mm Hg.

9. THE GAS LAWS • Boyle’s Law: V and P; inversely proportional. • Charles’ Law: T and V; directly proportional. • Gay-Lussac’s Law: P and T; directly proportional. • Avogadro’ Principle: moles and P or V; directly proportional.

10. BOYLE’S LAW

11. BOYLE’S LAW THE LAW: the volume of a confined gas is inversely proportional to the pressure exerted on the gas: P1V1= P2V2 • P ∝ 1/V plot = straight line

12. GOOD HABITS EVERY TIME you do a gas laws problem: • Write what you know and what you are trying to find • Write the formula • Plug in the numbers with units and solve with the correct number of sig figs.

13. PRACTICE THREE Consider a 1.53L sample of gaseous SO2 at a pressure of 5.6 × 1O3 Pa. If the pressure is changed to 1.5 × 104 Pa at a constant temperature, what will be the new volume of the gas ?

14. PRACTICE FOUR • Using the results listed below, calculate the Boyle’s law constant for NH3 at the various pressures. Experiment Pressure (atm) Volume (L) 1 0.1300 172.1 2 0.2500 89.28 3 0.3000 74.35 4 0.5000 44.49 5 0.7500 29.55 6 1.000 22.08

15. PV vs. P • What is the y-intercept? How about the 3rd graph on page two? • Molar Volume of a gas: 22.42L

16. CHARLES’ LAW

17. CHARLES LAW • THE LAW: If a given quantity of gas is held at a constant pressure, then its volume isdirectly proportional to the absolute temperature. V1T2 = V2T1 You must use the Kelvin! K = °C + 273

18. CHARLES’ LAW • Where do all the gases cross the x-intercept? • If the volume is zero, what is the temperature? • -273.15ºC or 0K

19. PRACTICE FIVE A sample of gas at 15ºC and 1 atm has a volume of 2.58 L. What volume will this gas occupy at 38ºC and 1 atm ?

20. GAY-LUSSAC’S LAW

21. GAY-LUSSAC’S LAW THE LAW: An increase in temperature increases the frequency of collisions between gas particles. In a given volume, raising the KELVIN temperature also raises the pressure. P1 T2= P2T1 You must use Kelvin!

22. AVOGADRO’S LAW Volume: 22.42L 22.42L22.42L Mass: 39.95g 32.00g 28.02g Quantity: 1 mol 1 mol 1 mol Pressure: 1 atm 1 atm 1 atm Temperature: 273K 273K 273K

23. AVOGADROS’S LAW • The volume of a gas, at a given temperature and pressure, is directly proportional to the quantity of gas. • Equal volumes of gases under the same conditions of temperature and pressure contain equal numbers of molecules. • In gas law problems, moles is designated by an “n”. • One mole of a gas has a volume of 22.42 L (dm3) at STP. It also has 6.02 x 1023 particles of that gas.

24. PRACTIVE SIX Suppose we have a 12.2-L sample containing 0.50 mol oxygen gas (O2) at a pressure of 1 atm and a temperature of 25ºC. If all this O2 were converted to ozone (O3) at the same temperature and pressure, what would be the volume of the ozone ?

25. HINT PTV

26. HINT PVT • Put the scientists' names in alphabetical order. Boyle’s uses the first 2 variables, Charles’ the second 2 variables and Gay-Lussac’s the remaining combination of variables.

27. COMBINED GAS LAW From the Boyle’s, Charles’, and Gay-Lussac’s laws, we can derive the CombinedGas Law: P1V1 T2 = P2V2 T1 Mnemonic:Potato and Vegetable on top of the Table for P1V1 = P2V2 T1 T2

28. STANDARDS T = 0°C = 273 K V = 22.4 L (at STP) P = 1.00 atm= 101.3 kPa = 760.0 mm Hg = 760.0 torr Remember only kPa has limited sigfigs.

29. PUTTING IT ALL TOGETHER Simulation on gas laws: Structure and Properties of Matter

30. IDEAL GAS LAW Ideal Gas Equation: PV = nRT “R” is the universal gas constant. V ∝ (nT)/P replace ∝ with constant, R

31. UNIVERSAL GAS CONSTANTS R = 0.08206 L• atm mol • K R = 62.36 L•mmHg mol • K R = 62.36 L • torr mol • K R = 8.314 L • kPa mol • K Why are there four constants?

32. IDEAL GAS LAW Remember: • Always change the temperature to KELVINS and convert volume to LITERS • Check the units of pressure to make sure they are consistent with the “R” constant given or convert the pressure to the gas constant (“R”) you want to use.

33. PRACTICE SEVEN A sample of hydrogen gas (H2) has a volume of 8.56 L at a temperature of 0ºC and a pressure of 1.5 atm. Calculate the moles of H2 molecules present in this gas sample.

34. PRACTICE EIGHT Suppose we have a sample of ammonia gas with a volume of 3.5 L at a pressure of 1.68 atm. The gas is compressed to a volume of 1.35 L at a constant temp. Use the ideal gas law to calculate the final pressure.

35. PRACTICE NINE A sample of methane gas that has a volume of 3.8 L at 5ºC is heated to 86ºC at constant pressure. Calculate its new volume.

36. PRACTICE TEN A sample of diborane gas (B2H6) has a pressure of 345 torr at a temp. of -15ºC and a volume of 3.48 L. If conditions are changed so that the temp. is 36ºC and the pressure is 468 torr, what will be the volume of the sample?

37. PRACTICE ELEVEN A sample containing 0.35 mol argon gas at a temp. of 13ºC and a pressure of 568 torr is heated to 56ºC and a pressure of 897 torr. Calculate the change in volume that occurs.

38. GAS STOICHIOMETRY VOLUME 1 mol 22.42 L @ STP 1 mole 1 mole PARTICLES MOLE MASS 6.02 x 1023 molar mass Use the ideal gas law to convert quantities that are NOT at STP.

39. HINT • You must have a balanced equation to do a stoichiometry problem.

40. PRACTICE TWELVE Use PV = nRTto solve for the volume of one mole of gas at STP.

41. PRACTICE THIRTEEN A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N2 are present?

42. PRACTICE FOURTEEN Calculate the volume of CO2 at STP made from the decomposition of 152 g CaCO3 by the reaction CaCO3(s) → CaO(s) + CO2(g).

43. PRACTICE FIFTEEN A sample of methane gas having a volume of 2.80 L at 25ºC and 1.65 atm was mixed with a sample of oxygen gas having a volume of 35.0 L at 31ºC and 1.25 atm. The mixture was then ignited to form carbon dioxide and water. Calculate the volume of CO2 formed at a pressure of 2.50 atm and a temperature of 125ºC.

44. DETERMINING DENSITY This modified version of the ideal gas equation can also be used to solve for the density of a gas. PV = nRTbcomes D = PM RT

45. DETERMINING DENSITY • D = m = PMMor D = PMM V RTRT • The density of gases is g/L NOT g/mL. • Mnemonic given in notes.

46. PRACTICE SIXTEEN • What is the approximate molar mass of air? • What is the approximate density of air? • List 3 gases that float in air. • List 3 gases that sink in air.

47. PRACTICE SEVENTEEN The density of a gas was measured at 1.50 atm and 27ºC and found to be 1.95 g/L. Calculate the molar mass of the gas.

48. DALTON’S LAW OF PARTIAL PRESSURES THE LAW: The pressure of a mixture of gases is the sum of the pressures of the different components of the mixture: Ptotal= P1 + P2 + P3 +.....Pn

49. DALTON’S LAW OF PARTIAL PRESSURES Also uses the concept of mole fraction, χ χ A = moles of A moles A + moles B + moles C + . . . so now, PA = χ A / Ptotal The partial pressure of each gas in a mixture of gases in a container depends on the number of moles of that gas. The total pressure is the SUM of the partial pressures and depends on the total moles of gas particles present, no matter what they are.

50. DALTON’S LAW OF PARTIAL PRESSURES