Gases. Chapter 5. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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1 Gases Chapter 5 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1

2 Elements that exist as gases at 25 0 C and 1 atmosphere 2

3 3

4 Physical Characteristics of Gases Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower densities than liquids and solids. NO 2 gas 4

5 Pressure = Force Area (force = mass x acceleration) Units of Pressure 1 pascal (Pa) = 1 N/m 2 1 atm = 760 mmhg = 760 torr 1 atm = 101,325 Pa 5

6 10 miles 0.2 atm 4 miles 0.5 atm Sea level 1 atm 6

7 Manometers Used to Measure Gas Pressures closed-tube open-tube 7

8 Apparatus for Studying the Relationship Between Pressure and Volume of a Gas As P (h) increases V decreases 8

9 Boyle s Law P 1/V P x V = constant P 1 x V 1 = P 2 x V 2 Constant temperature Constant amount of gas 9

10 A sample of chlorine gas occupies a volume of 946 ml at a pressure of 726 mmhg. What is the pressure of the gas (in mmhg) if the volume is reduced at constant temperature to 154 ml? P x V = constant P 1 x V 1 = P 2 x V 2 P 1 = 726 mmhg P 2 =? V 1 = 946 ml V 2 = 154 ml P 2 = P 1 x V 1 V mmhg x 946 ml = = 4460 mmhg 154 ml 10

11 Variation in Gas Volume with Temperature at Constant Pressure As T increases V increases 11

12 Variation of Gas Volume with Temperature at Constant Pressure Charles & Gay-Lussac s Law V T V = constant x T Temperature must be in Kelvin V 1 /T 1 = V 2 /T 2 T (K) = t ( 0 C)

13 A sample of carbon monoxide gas occupies 3.20 L at C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V 1 /T 1 = V 2 /T 2 V 1 = 3.20 L T 1 = K V 2 = 1.54 L T 2 =? T 1 = 125 ( 0 C) (K) = K T 2 = V 2 x T 1 V L x K = = 192 K 3.20 L 13

14 V number of moles (n) V = constant x n Avogadro s Law Constant temperature Constant pressure V 1 / n 1 = V 2 / n 2 14

15 Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure? 4NH 3 + 5O 2 4NO + 6H 2 O 1 mole NH 3 1 mole NO At constant T and P 1 volume NH 3 1 volume NO 15

16 Summary of Gas Laws Boyle s Law 16

17 Charles Law 17

18 Avogadro s Law 18

19 Ideal Gas Equation Boyle s law: P 1 (at constant n and T) V Charles law: V T (at constant n and P) Avogadro s law: V n (at constant P and T) nt V P V = constant x nt P = R nt P R is the gas constant PV = nrt 19

20 The conditions 0 0 C and 1 atm are called standard temperature and pressure (STP). Experiments show that at STP, 1 mole of an ideal gas occupies L. PV = nrt R = PV nt = (1 atm)(22.414l) (1 mol)( K) R = L atm / (mol K) 20

21 What is the volume (in liters) occupied by 49.8 g of HCl at STP? T = 0 0 C = K PV = nrt V = nrt P P = 1 atm n = 49.8 g x 1 mol HCl g HCl = 1.37 mol V = L atm 1.37 mol x x K mol K 1 atm V = 30.7 L 21

22 Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0 C is heated to 85 0 C at constant volume. What is the final pressure of argon in the lightbulb (in atm)? PV = nrt nr V P 1 = P T = constant P 2 = T 1 T 2 P 2 = P 1 x T 2 T 1 n, V and R are constant P 1 = 1.20 atm T 1 = 291 K = 1.20 atm x 358 K 291 K P 2 =? T 2 = 358 K = 1.48 atm 22

23 Density (d) Calculations d = m V = PM RT m is the mass of the gas in g M is the molar mass of the gas Molar Mass (M ) of a Gaseous Substance M = drt P d is the density of the gas in g/l 23

24 A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and C. What is the molar mass of the gas? M = drt P d = m V 4.65 g = = 2.21 g 2.10 L L M = 2.21 g L x atm L atm mol K x K M = 54.5 g/mol 24

25 Gas Stoichiometry What is the volume of CO 2 produced at 37 0 C and 1.00 atm when 5.60 g of glucose are used up in the reaction: C 6 H 12 O 6 (s) + 6O 2 (g) 6CO 2 (g) + 6H 2 O (l) g C 6 H 12 O 6 mol C 6 H 12 O 6 mol CO 2 V CO 2 1 mol C 5.60 g C 6 H 12 O 6 H 12 O 6 6 x 180 g C 6 H 12 O 6 6 mol CO x 2 = mol CO 1 mol C 6 H 12 O 2 6 V = nrt P L atm mol x x K mol K = = 4.76 L 1.00 atm 25

26 Dalton s Law of Partial Pressures V and T are constant P 1 P 2 P total = P 1 + P 2 26

27 Consider a case in which two gases, A and B, are in a container of volume V. P A = n ART V P B = n BRT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B X A = n A n A + n B X B = n B n A + n B P A = X A P T P B = X B P T P i = X i P T mole fraction (X i ) = n i n T 27

28 A sample of natural gas contains 8.24 moles of CH 4, moles of C 2 H 6, and moles of C 3 H 8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C 3 H 8 )? P i = X i P T X propane = P T = 1.37 atm = P propane = x 1.37 atm = atm 28

29 Collecting a Gas over Water 2KClO 3 (s) 2KCl (s) + 3O 2 (g) P T = P O + P H O

30 Vapor of Water and Temperature 30

31 Depth (ft) Chemistry in Action: Scuba Diving and the Gas Laws Pressure (atm) P V 31

32 Kinetic Molecular Theory of Gases 1. A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume. 2. Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic. 3. Gas molecules exert neither attractive nor repulsive forces on one another. 4. The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy KE = ½ mu 2 32

33 Kinetic theory of gases and Compressibility of Gases Boyle s Law P collision rate with wall Collision rate number density Number density 1/V P 1/V Charles Law P collision rate with wall Collision rate Average kinetic energy P T average kinetic energy of gas molecules T 33

34 Kinetic theory of gases and Avogadro s Law P collision rate with wall Collision rate number density Number density n P n Dalton s Law of Partial Pressures Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas P total = P i 34

35 Apparatus for Studying Molecular Speed Distributiona 35

36 The distribution of speeds of three different gases at the same temperature The distribution of speeds for nitrogen gas molecules at three different temperatures u rms = 3RT M 36

37 Chemistry in Action: Super Cold Atoms Maxwell velocity distribution of Rb atoms at about 1.7 x 10 7 K Bose-Einstein condensate (BEC) 37

38 Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. r 1 M 2 = r 2 M 1 molecular path NH 4 Cl NH 3 17 g/mol HCl 36 g/mol 38

39 Gas effusion is the is the process by which gas under pressure escapes from one compartment of a container to another by passing through a small opening. r 1 t 2 M 2 = = r 2 t 1 M 1 Nickel forms a gaseous compound of the formula Ni(CO) x What is the value of x given that under the same conditions methane (CH 4 ) effuses 3.3 times faster than the compound? r 1 = 3.3 x r 2 M 1 = 16 g/mol M 2 = r 1 ( ) 2 x M 1 = (3.3) 2 x 16 = r x 28 = x = 4.1 ~ 4 39

40 Deviations from Ideal Behavior 1 mole of ideal gas PV = nrt n = PV RT = 1.0 Repulsive Forces Attractive Forces 40

41 Effect of intermolecular forces on the pressure exerted by a gas. 41

42 Van der Waals equation nonideal gas ( P + an 2 )(V nb) = nrt V 2 } corrected pressure } corrected volume 42