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2 Fall 1999 Chapter 7 Gases and Gas Laws

3 Some Gases in Our Lives Air: oxygen O 2 nitrogen N 2 ozone O 3 argon Ar carbon dioxide CO 2 water H 2 O Noble gases: helium He neon Ne krypton Kr xenon Xe Other gases: fluorine F 2 chlorine Cl 2 ammonia NH 3 methane CH 4 carbon monoxide CO

4 Properties of a Gas Volume V L, mL, cc Temperature T  C, K Moles n g/mole Pressure P mmHg, atm, torr

5 Units of Pressure One atmosphere (1 atm)  Is the average pressure of the atmosphere at sea level  Is a standard of pressure  P = Force Area 1.00 atm = 760 mm Hg = 760 torr

6 Types of Pressure Units All equal to 1 atm PressureUsed in 760 mm Hg or 760 torrChemistry 14.7 lb/in. 2 U.S. pressure gauges 29.9 in. HgU.S. weather reports kPa (kilopascals)Weather in all countries except U.S bars Weather

7 Measuring Pressure Barometers 760 mmHg atm pressure Hg

8 Learning Check A. What is 475 mm Hg expressed in atm? 1) 475 atm 2) atm 3) atm B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 1) 2.00 mm Hg 2) 1520 mm Hg 3) mm Hg

9 Solution A. What is 475 mm Hg expressed in atm? 475 mm Hg x 1 atm = atm (2) 760 mm Hg B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 29.4 psi x 1.00 atm x 760 mmHg = 1520 mmHg 14.7 psi 1.00 atm(2)

10 Pressure and Altitude As altitude increases, atmospheric pressure decreases

11 Pressure and Boiling Point As P atm decreases, water boils at lower temperatures and foods cook more slowly

12 Boyle’s Law Pressure and Volume

13 Pressure and Volume ExperimentPressureVolume P x V (atm) (L) (atm x L) _____ _____ _____ Boyle's Law P x V = k (constant) when T,n remain constant P1V1= 8.0 atm x 2.0 L = 16 atm L P2V2= 4.0 atm x 4.0 L = 16 atm L P1V1 = P2V2 = k Use this equation to calculate how a volume changes when pressure changes, or how pressure changes when volume changes. new vol. old vol. x Pfactor new P old P x Vfactor V2 = V1 x P1 P2 = P1 x V1 P2 V2

14 P and V Changes P1P1 P2P2 V1V1 V2V2

15 Boyle's Law The pressure of a gas is inversely related to the volume when T,n does not change The PV product remains constant P 1 V 1 = P 2 V 2 P 1 V 1 = 8.0 atm x 2.0 L = 16 atm L P 2 V 2 = 4.0 atm x 4.0 L = 16 atm L

16 PV Calculation What is the new volume (L) of a 1.6 L sample of Freon gas initially at 50. mm Hg after its pressure is changed to 200. mm Hg? ( T and n are constant)

17 HINT The pressure goes from 50. mmHg to 200. mmHg. Is that an increase or decrease in pressure ? What will happen to the volume? P V

18 Finding the New Volume Take the old volume and multiply by a factor of pressures to make the result bigger.

19 Solution 1.6 L x 200 mmHg = 6.4 L 50 mmHg Factor greater than 1; answer is larger

20 Learning Check A sample of nitrogen gas is 6.4 L at a pressure of 0.70 atm. What will the new volume be if the pressure is changed to 1.40 atm? (T and n constant) Explain. 1) 3.2 L 2) 6.4 L 3) 12.8 L

21 Solution A sample of nitrogen gas is 6.4 L at a pressure of 0.70 atm. What will the new volume be if the pressure is changed to 1.40 atm? (T and n constant) 6.4 L x 0.70 atm = 3.2 L (1) 1.40 atm Volume must decrease to cause an increase in the pressure

22 Learning Check A sample of helium gas has a volume of 12.0 L at 600. mm Hg. What new pressure is needed to change the volume to 36.0 L? (T and n constant) Explain.

23 Solution A sample of helium gas has a volume of 12.0 L at 600. mm Hg. What new pressure is needed to change the volume to 36.0 L? (T constant) Explain mm Hg x 12.0 L = 200. mmHg (1) 36.0 L Pressure decrease when volume increases.

24 Worksheet 7-1 Do the problems from Worksheet 7-1 You can work these problems alone or with others around you. You may use your notes and textbook. When you have finished, compare answers with someone else.

25 Charles’ Law T = 273 K T = 546 K Observe the V and T of the balloons. How does volume change with a temperature increase ?

26 Charles’ Law: V and T At constant pressure, the volume of a gas is directly related to its absolute (K) temperature V 1 = V 2 T 1 T 2 1. If final T is higher than initial T, final V is (greater, or less) than the initial V. 2. If final V is less than initial V, final T is (higher, or lower) than the initial T.

27 Charles’ Law: V and T At constant pressure, the volume of a gas is directly related to its absolute (K) temperature V 1 = V 2 T 1 T 2 1. If final T is higher than initial T, final V is (greater) than the initial V. 2. If final V is less than initial V, final T is (lower) than the initial T.

28 V and T Calculation A balloon has a volume of 785 mL when the temperature is 21°C. As the balloon rises, the gas cools to 0°C. What is the new volume of the balloon? Think about what happens to T;always use K !!!

29 Solution 785 mL x 273 K=729 mL 294 K Factor less than 1; answer is smaller

30 Learning Check A sample of oxygen gas has a volume of 420 mL at a temperature of 18°C. What temperature (in °C) is needed to change the volume to 640 mL? 1) 443°C2) 170°C 3) - 82°C

31 Solution A sample of oxygen gas has a volume of 420 mL at a temperature of 18°C. What temperature (in °C) is needed to change the volume to 640 mL? T 2 = 291 K x 640 mL = 443 K 420 mL = 443 K K = 170°C(2) 170°C 3) - 82°C

32 P and T P (mm Hg)T (°C) When temperature decreases, the pressure of a gas (decreases or increases). When temperature increases, the pressure of a gas (decreases or increases).

33 Gay-Lussac’s Law Pressure and Absolute temperature are directly proportional T P

34 P and T Calculation A gas has a pressure at 2.0 atm at 18°C. What will be the new pressure if the temperature rises to 62°C? (V,n constant) T = 18°C T = 62°C

35 Solution 2.0 atm x 335 K=2.3 atm 291 K Factor more than 1; answer is larger

36 Learning Check Answer with 1) Increases 2) Decreases 3) Does not change A. Pressure _________, when V decreases B. When T decreases, V __________ C. Pressure ____________ when V changes from 12.0 L to 24.0 L (constant n and T) D. Volume _______when T changes from 15.0 °C to 45.0°C (constant P and n )

37 Solution Answer with 1) Increases 2) Decreases 3) Does not change A. Pressure 1) Increases, when V decreases B. When T decreases, V 2) Decreases C. Pressure 2) Decreases when V changes from 12.0 L to 24.0 L (constant n and T) D. Volume 1) Increases when T changes from 15.0 °C to 45.0°C (constant P and n )

38 Worksheet 7-2 Do the problems from Worksheet 7-2. You can work these problems alone or with others around you. You may use your notes and textbook. When you have finished, compare answers with someone else.

39 C ombined G as L aw CGL gives the result of changing 2 properties P 1 V 1 P 2 V 2 = T 1 T 2

40 Problem Oxygen gas has a pressure of 0.15 atm when the volume is 15. L and the temperature is 27º C. What will the new volume be if T becomes 127 º C and the pressure becomes 900. mmHg?

41 Answer Change T to Kelvin: 27  C +273 = 300 K,127  C +273 = 400 K Change mmHg to atm: 900. mmHg x 1 atm = 1.18 atm 760 mmHg

42 Algebraic solution 15. L x 0.15 atm x 400 K = 1.2 L 300 K 1.18 atm

43 Alternate solution 15 L x 0.15 atm x 400 K = 1.2 L 1.18 atm 300 K P V T V

44 Worksheet 7-3 Do the problems from Worksheet 7-3. You can work these problems alone or with others around you. You may use your notes and textbook. When you have finished, compare answers with someone else.

45 Avogadro’s Law Volume is directly related to the number of moles of gas

46 Avogadro’s Law 0.60 moles of O 2 gas has a volume of 50.L. What is the volume when 1.0 moles of O 2 is added?

47 Does a balloon get bigger or smaller when air is added? Add air

48 Does a balloon get bigger or smaller when air is added? Add air

49 Solution 50 L x 1.6 moles= 133 L 0.6 moles Factor more than 1; answer is larger

50 STP Standard temperature 0  C or 273 K Standard pressure 760 mmHg or 1 atm

51 Molar Volume At STP, 1 mole of gas has a volume of 22.4 L. 1 mole = 22.4 L (at STP)

52 Problem What is the mass of 50. L of CO 2 gas at STP? Hint: find moles first

L x 1 mole x 22.4 L 44.0 g = 98. g 1 mole

54 What is the volume of 100. g of nitrogen gas N 2 at STP?

g x 1 mole x 22.4 L = 28.0 g 1 mole 80.0 L

56 Worksheet 7-4 Do the problems from Worksheet 7-4. You can work these problems alone or with others around you. You may use your notes and textbook. When you have finished, compare answers with someone else.

57 Dalton’s Law Total pressure is the sum of all the partial pressures P total =P 1 + P 2 + P 3 + ……..

58 What is the total pressure in a container with atm of oxygen and 450. mmHg of nitrogen? Give answer in mmHg.

59 ANSWER atm x 760 mmHg = 85 mmHg 1 atm P t = P 1 + P 2 = = 535 mmHg

60 Nature of Gases Gases fill a container completely and uniformly Gases exert a uniform pressure on all inner surfaces of their containers

61 Kinetic Theory of Gases The particles in gases Are very far apart Move very fast in straight lines until they collide Have no attraction (or repulsion) Move faster at higher temperatures

62 Question Use the KMT to explain why increasing the temperature of a gas increases the pressure. (n and V are constant)

63 T 1 < T 2 O O O O O O O O

64 The End