Ch. 11: Molecular Composition of Gases

1. Ch. 11: Molecular Composition of Gases Volume-Mass Relationships of Gases

2. Pressure • P : force per unit area on a surface • Newton – SI unit for force (1 kg*m/s2) • why would shoes with smaller diameter heel not be allowed on gym floor? • As surface area decreases, pressure increases • Pressure exerted by a gas depends on • volume • temperature • number of molecules

3. Measuring Pressure • barometer • instrument used to measure atmospheric pressure • first one created by Torricelli in early 1600s • glass tube filled with mercury is inverted in a dish • mercury flows out of the tube until pressure of the Hg inside the tube is equal to the atmospheric pressure on the Hg in the dish

4. Measuring Pressure • manometer: • measures pressure of gas in a container • gas has less pressure than atmosphere if the Hg is closer to chamber • gas has more pressure than atmosphere if the Hg is further from chamber

5. Units of Pressure • millimeters of mercury (mmHg) • from mercury barometer • torr (torr) • from Toricelli inventing barometer • atmosphere of pressure (atm) • Pascal (Pa) = 1N/m2 (SI unit) • named after French scientist 1 atm = 760 mmHg = 760 torr = 101.325 kPa

6. Practice Conversions • Convert 0.927 atm to • mmHg • torr • kPa

7. Practice Conversions • Convert 148.6 kPa to • atm • mmHg • torr

8. The pressure of a gas is measured as 49 torr. Convert this pressure to atmospheres, kiloPascals, and mmHg.

9. Boyle’s Law: P and V • as one increases, the other decreases • inversely proportional • pressure is caused by moving molecules hitting container walls • If V is decreased and the # of molecules stays constant, there will be more molecules hitting the walls per unit

10. Boyle’s Law: P and V • Boyle’s Law: the V of fixed mass of gas varies inversely with P at a constant T. • PV = k • k is a constant for a certain sample of gas that depends on the mass of gas and T • What kind of graph is V vs. P? • If we have a set of new conditions for the same sample of gas, they will have same k so:

11. Boyle’s Law

12. Boyle’s Law: P and V • Discovered by Irish chemist, Robert Boyle • Used a J-shaped tube to experiment with varying pressures in multistory home and effects on volume of enclosed gas

13. Example: Boyle’s Law Consider a 1.53-L sample of gaseous SO2 at a pressure of 5.6 x 103 Pa. If the pressure is changed to 1.5 x 104 Pa at constant temperature, what will be the new volume of the gas?

14. Charles’ Law: V and T • if P is constant, gases expand when heated • when T increases, gas molecules move faster and collide with the walls more often and with greater force • to keep the P constant, the V must increase

15. Charles’ Law: V and T • Problem: if we use Celsius, we could end up with negative values from calculations in gas laws for volumes • we need a T system with no negative values: Kelvin Temperature Scale • starts at -273.15 ° C = absolute zero = 0 K • lowest possible temperature balloon going into liquid nitrogen

16. Charles’ Law: V and T • Charles’ Law: the V of fixed mass of gas at constant P varies directly with Kelvin T. • V = kT • k is a constant for a certain sample of gas that depends on the mass of gas and P • What kind of graph is V vs. T? • If we have a set of new conditions for the same sample of gas, they will have same k so:

17. Charles’ Law • discovered by French physicist, Jacques Charles in 1787 • first person to fill balloon with hydrogen gas and make solo balloon flight

18. Example: Charles’ Law & Temp. A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What volume will this gas occupy at 38°C and 1 atm?

19. A weather balloon is released at a pressure of 744 mmHg with a volume of 12 L. What will the volume be at a pressure of 704 torr?

20. Gay-Lussac’s Law of Combining Volumes of Gases • at constant T and P, coefficients in balanced equation represent ratio of volumes of gaseous reactants too 2H2(g) + O2(g)  2H2O(g) 2 L 1 L 2 L

21. Gay-Lussac’s Law: P and T • Gay-Lussac’s Law: the P of fixed mass of gas at constant V varies directly with Kelvin T. • P = kT • k is a constant for a certain sample of gas that depends on the mass of gas and V • What kind of graph is P vs. T? • If we have a set of new conditions for the same sample of gas, they will have same k so:

22. Example: Gay-Lussac’s Law The gas in an aerosol can is at a pressure of 3.00 atm at 25°C. Directions on the can warn the user not to keep the can in a place where temperature exceeds 52°C. What would the gas pressure be in the can at 52°C?

23. Example 3O2(g)  2O3(g) • How many liters of O3 can be made from 12 L of O2? • How many moles of O2 are needed to make 24 moles of O3? • How many molecules of O3 can be made from 18 molecules of O2?

24. Avogadro’s Law • equal volumes of gases at the same T and P contain equal numbers of molecules • at same T and P, volumes varies directly with number of moles (n) • V = kn

25. Molar Volume of Gases • like molar mass • mass of one mole of substance • but with volume • volume of one mole of substance • because of Avogadro’s law, one mole of any gas has the same volume as any other gas at the same T and P

26. Molar Volume of Gases • Standard Molar Volume of Gas • volume of one mole of gas at 1 atm and 0°C is 22.4 • 22.4 L of any gas has one mole of particles but has different masses • Standard Temperature and Pressure • STP • 1 atm and 0°C

27. Molar Volume of Gases

28. Example • A chemical reaction produces 0.0680 mol of oxygen gas. What volume in liters is occupied by this gas sample at STP? • 1 mol : 22.4 L

29. Example 2 • A chemical reaction produced 98.0 mL of sulfur dioxide gas at STP. What was the mass of gas made? • convert mL to L • convert L to moles using molar volume • convert moles to grams using molar mass

30. Example 3 • A chemical reaction produced 3.1 g of CO2 gas. What volume will it have in mL at STP? • convert grams to moles • convert moles to liters • convert liters to milliliters

31. Example 4 • How many moles of gas are in a container with a volume of 2.46 L at STP?

32. Combined Gas Law • a gas often changes in T, P, and V all at once • the other gas laws can be combined into one law • Combined Gas Law- relationship between P, V, and T of a fixed amount of gas

33. Example: Combined Gas Law • A Helium-filled balloon has volume of 50.0 L at 25°C and 1.08 atm. What volume will it have at 0.855 atm and 10.°C?

34. Example • A balloon containing 5.5 L of air at 25C and 755 torr is put at the bottom of the ocean. The new temperature is 4 C and the new volume is 230 mL. What is the new pressure?

35. Dalton’s Law of Partial Pressure • John Dalton • responsible for atomic theory • also studied gas mixtures • the P of gas mixture is the sum of the individual pressures of each gas alone • the P that each gas exerts in the mixture is independent of the P that are exerted by other gases

36. Dalton’s Law of Partial Pressure • the total P of a mixture of gases is equal to the sum of partial P of component gases, no matter how many different gases • PT = P1 + P2 + P3 + … • Partial Pressure- P of each gas in mixture

37. Why? • the particles of each gas in a mixture have an equal chance to hit the walls • so each gas exerts P independent of that exerted by other gases • total P is result of the total # of collisions per unit of wall area

38. set for a certain T equal to atmospheric pressure Water Displacement • gas produced is less dense than water so it replaces the water in the bottle • gas collected is not pure because it contains vapor from the water PT = Pgas + Pwater

39. Example • Oxygen gas from decomposition of KClO3 was collected by water displacement. The barometric pressure and the temperature during the experiment were 731.0 torr and 20.0°C respectively. If the partial pressure of water vapor is 17.5 torr at 20.0°C. What was the partial pressure of oxygen collected? • PT = PO2 + PH2O • 731.0 torr = PO2 + 17.5 • PO2 = 713.5 torr

40. Example • Find the partial pressure by 2 gases (A and B) mixed if the overall pressure is 790 mmHg. The percent by volume is A: 20% and B: 80%. • PT = PA + PB = 790 mmHg • A: 0.20 x 790 = 158 mmHg • B: 0.80 x 790 = 632 mmHg

41. Ch. 11: Molecular Composition of Gases Ideal Gas Law

42. Ideal Gas Law • relationship among P, V, T, and number of moles of gas (n) • combination of all the laws we learned • helps us approximate “real” gas behavior • where • R: ideal gas constant • 0.08206 L atm/mol K (use most often) • 8.314 J/mol K (only for when P is in Pascals) • check units before using equation

43. Example • What is the P in atm exerted by a 0.500 mol sample of nitrogen gas in a 10.0 L container at 298 K?

44. Example • What is the volume in liters of 0.250 mol of oxygen gas at 20.0°C and 0.974 atm?

45. Example • What mass of chlorine gas is in a 10.0 L tank at 27°C and 3.50 atm?

46. Finding Molar Mass • mass of one mole of substance • units : g/mol • represented by M

47. Finding Molar Mass • At 28°C and 0.974 atm, 1.00 L of gas has a mass of 5.16g. What is the molar mass?

48. Finding Density

49. Finding Molar Mass • The density of dry air at sea level (with pressure of exactly 1 atm) is 1.225 g/L at 15°C. What is the molar mass of air?

50. Finding Density • What is the density of carbon monoxide gas at STP?