Comparison of Solids, Liquids, and Gases

Transcription

1 CHAPTER 8 GASES

2 Comparison of Solids, Liquids, and Gases The density of gases is much less than that of solids or liquids. Densities (g/ml) Solid Liquid Gas H O CCl Gas molecules must be very far apart compared to liquids and solids.

3 The Kinetic-Molecular Theory The basic assumptions of kineticmolecular theory are: Postulate Gases consist of molecules that are relatively far apart. Gases have few intermolecular attractions. The volume of individual molecules is very small compared to the gas s volume. Proof - Gases are easily compressible. 3

4 The Kinetic-Molecular Theory Postulate Gas molecules are in constant, random, straight line motion with varying velocities. Postulate 3 Gas molecules have elastic collisions with themselves and the container. Total energy is conserved during a collision. 4

5 The Kinetic-Molecular Theory Postulate 4 The kinetic energy of the molecules is proportional to the Kelvin temperature. The average kinetic energies of molecules of different gases are equal at a given temperature. Proof - Motion increases as temperature increases. 5

6 The Kinetic-Molecular Theory The kinetic energy of the molecules is proportional to the absolute temperature. 6

7 Pressure Pressure is force per unit area. lb/in N/m Atmospheric pressure is measured using a barometer. Hg density 3.6 g/ml 7

8 Pressure 8

9 Boyle s Law: The Volume-Pressure Relationship Volume of a gas decreases, pressure increases. Volume of a gas increases, pressure decreases. NO CHANGE IN TEMPERATURE NO CHANGE IN # MOLES OF GAS Thus we write Boyle s Law mathematically as P V P V We can use any pressure or volume units as long as we use the same units for both P and P or V and V. 9

10 Boyle s Law: The Volume-Pressure Relationship 0

11 Boyle s Law: The Volume-Pressure Relationship Example -: At 5 o C a sample of He has a volume of 4.00 x 0 ml under a pressure of 7.60 x 0 torr. What volume would it occupy under a pressure of.00 atm at the same T? P V V P V P V P ( 760 torr)( 400 ml) 50 torr.00 0 ml

12 Boyle s Law: The Volume-Pressure Relationship Inhale decrease pressure in lungs Breathe in until pressure in lungs equals atmospheric pressure Exhale decrease volume in lungs Air released to decrease the pressure

13 Charles Law: The Volume-Temperature Relationship; The Absolute Temperature Scale Charles s law states that the volume of a gas is directly proportional to the absolute temperature at constant pressure. Gas laws must use the Kelvin scale to be correct. Relationship between Kelvin and centigrade. o K C

14 Charles Law: The Volume-Temperature Relationship; The Absolute Temperature Scale V T V T 4

15 Charles Law: The Volume-Temperature Relationship; The Absolute Temperature Scale Example -: A sample of hydrogen, H, occupies.00 x 0 ml at 5.0 o C and.00 atm. What volume would it occupy at 50.0 o C under the same pressure? T T V T V V T V VT T.00 0 ml 33 K 98 K 08 ml 5

16 Gay-Lussac s Law Pressure-Temperature Relationship Pressure of a gas is directly related to its temperature As long as the volume and the number of moles or gas do not change P P T T 6

17 Gay-Lussac s Law Pressure-Temperature Relationship In an open container, molecules with enough kinetic energy leave the surface and evaporate In a closed container, vapor accumulates and creates a pressure called vapor pressure A liquid s boiling point is the point where the vapor pressure is equal to the outside pressure 7

18 Gay-Lussac s Law Pressure-Temperature Relationship 8

19 Gay-Lussac s Law Pressure-Temperature Relationship 9

20 Gay-Lussac s Law Pressure-Temperature Relationship 0

21 Summary of Gas Laws

22 Standard Temperature and Pressure Standard temperature and pressure is given the symbol STP. It is a reference point for some gas calculations. Standard P atm or 0.3 kpa Standard T 73.5 K or 0.00 o

23 The Combined Gas Law Equation The gas laws presented so far can be combined into one statement is called the combined gas law equation. Useful when the V, T, and P of a gas are changing. P T V P T V 3

24 The Combined Gas Law Equation Example -3: A sample of nitrogen gas, N, occupies 7.50 x 0 ml at C under a pressure of 8.0 x 0 torr. What volume would it occupy at STP? P T V 750 ml V 348 K T 80 torr Solve for V ( 80 torr )( 750 ml )( 73 K ) ( 760 torr )( 348 K ) P 67 ml? 73 K 760 torr P V T P T 4

25 The Combined Gas Law Equation Example -4 : A sample of methane, CH 4, occupies.60 x 0 ml at 3 o C under a pressure of atm. At what temperature would it occupy 5.00 x 0 ml under a pressure of.0 x 0 3 torr? You do it! 5

26 The Combined Gas Law Equation V P T T 60 ml atm 380 torr 305 K T P V P V 85 K 580 ( 305 K)( 00 torr)( 500 ml) ( 380 torr)( 60 ml) o C V P T 500 ml 00 torr? 6

27 Avogadro s Law and the Standard Molar Volume Example -5: One mole of a gas occupies 36.5 L and its density is.36 g/l at a given temperature and pressure. (a) What is its molar mass? (b) What is its density at STP?? g 365. L 36. g mol mol L? L g STP 49.6 mol g mol.4 L g/mol. g/l 7

28 Avogadro s Law and the Standard Molar Volume Avogadro s Law states that at the same temperature and pressure, equal volumes of two gases contain the same number of molecules (or moles) of gas. If we set the temperature and pressure for any gas to be STP, then one mole of that gas has a volume called the standard molar volume. The standard molar volume is.4 L at STP. This is another way to measure moles. For gases, the volume is proportional to the number of moles.. L of a gas at STP mole 44.8 L? moles 8

29 Avogadro s Law and the Standard Molar Volume 9

30 Summary of Gas Laws: The Ideal Gas Law All of the gas laws can be combined to give a single Law called the Ideal Gas Law. PV nrt R is a proportionality constant called the universal gas constant. 30

31 Summary of Gas Laws: The Ideal Gas Law We must determine the value of R. Recognize that for one mole of a gas at.00 atm, and 73 K (STP), the volume is.4 L. Use these values in the ideal gas law. R PV nt atm. 4 L ( )( ) (.00 mol )( 73 K) L atm mol K 3

32 Summary of Gas Laws: The Ideal Gas Law Example -6: What volume would 50.0 g of ethane, C H 6, occupy at.40 x 0 o C under a pressure of.8 x 0 3 torr? To use the ideal gas law correctly, it is very important that all of your values be in the correct units!. T K. P 80 torr ( atm/760 torr).39 atm g ( mol/30 g).67 mol 3

33 Summary of Gas Laws: The Ideal Gas Law V n R T P (.67 mol ) 0.08 ( 43 K ) 3.6 L L atm mol K.39 atm 33

34 Summary of Gas Laws: The Ideal Gas Law Example -7: Calculate the number of moles in, and the mass of, an 8.96 L sample of methane, CH 4, measured at standard conditions. You do it! 34

35 Summary of Gas Laws: The Ideal Gas Law (.00 atm )( 896. L) n PV RT 0.08 L atm mol K 6.0 g? g CH mol mol ( 73 K) 6.40 g mol CH 4 35

36 Summary of Gas Laws: The Ideal Gas Law Example -8: Calculate the pressure exerted by 50.0 g of ethane, C H 6, in a 5.0 L container at 5.0 o C. P n.67 mol You do it! and 98 n R T P V L atm mol K 5.0 L P.63 atm (.67 mol ) 0.08 ( 98 K ) T K 36

37 Dalton s Law of Partial Pressures Dalton s law states that the pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases. P total P A + P B + P C

38 Composition of the Atmosphere and Some Common Properties of Gases Composition of Dry Air Gas % by Volume N O 0.94 Ar 0.93 CO 0.03 He, Ne, Kr, Xe 0.00 CH H

39 Dalton s Law of Partial Pressures 39

40 Dalton s Law of Partial Pressures Example -: If.00 x 0 ml of hydrogen, measured at 5.0 o Cand 3.00 atm pressure, and.00 x 0 ml of oxygen, measured at 5.0 o Cand.00 atm pressure, were forced into one of the containers at 5.0 o C, what would be the pressure of the mixture of gases? P P + P Total H O 3.00 atm +.00 atm 5.00 atm 40

41 Dalton s Law of Partial Pressures Blood Gasses 4

42 Dalton s Law of Partial Pressures Blood Gasses 4