Lecture outline: Chapter 10. S. Ensign, gases

Transcription

1 Lecture outline: Chapter 10 States t of matter: gases 1

2 Which elements exist as gases at room temperature and pressure at sea level (1 atm. and 25 C)? What is their elemental form (X or X 2 )? 2

3 Composition: Gases Nonmetallic elements Simple formulas Low molar masses Features: Expand/compress Form homogeneous mixtures with each other Molecules l far apart 3

4 Properties of gases 1. Quantity of gas n mols 2. Temperature of gas T K 3. Volume of gas V liters 4. Pressure of gas P atmospheres 4

5 Pressure S. Ensign, S. Ensign, Chem. gases

6 Pressure 6

7 Pressure F P = A 7

8 A 1 m 2 column of air has a mass at sea level of 10,000 kg A 1 in 2 column of air has a mass at sea level of 15 pounds Pressure of Earth s Atmosphere Inflate to 15 psi 8

9 Units of pressure psi Atmospheres (atm) Kilopascals Torr (mm Hg) 9

10 Mercury Glass tube Under vacuum Barometer Air pressure 760 mm (29.92 in) Mercury 10

11 Gas laws Mathematical expressions of the relationships between P, V, n, and T 11

12 Boyle s Law: relation of P and V The volume of a fixed amount of gas at a constant temperature is inversely proportional to the pressure exerted on the gas V 1 P PV = constant Increase P 12

13 Charles Law: relation of T and V The volume of a fixed amount of gas at a constant pressure is directly proportional to the temperature of the gas V T V = T constant Increase T 13

14 Charles Law: relation of T and V Absolute zero: the temperature at which a gas is predicted to have no volume T = C = 0K (ml) of gas volume temperature (degrees C) S. Ensign, S. Ensign, Chem. gases

15 Gay-Lussac s Law: relation of T and P The pressure of a fixed amount of gas at a constant volume is directly proportional to the temperature of the gas P T P = T constant 15

16 Avogadro s Law: relation of V and n Equal volumes of gases at the same T and P have equal numbers of molecules V n V constant n = 10molN molHe molCO molAr

17 For a chemical reaction involving gases where P and T are kept constant, the stoichiometric coefficients in the balanced chemical equation can represent either moles of reactants and products, or volumes of reactants and products, because n V 2H 2 + O 2 2H 2 O 2 molecules H molecule O 2 2 molecules H 2 O 2 mol H mol O 2 2 mol H 2O 2 L H L O 2 2 L H 2 O 17

18 The ideal gas law Boyle: V 1 P Charles: V T Avogadro: V n 18

19 What is the numerical value of the constant R? 19

20 One mole of any ideal gas will have the same volume at a given temperature Gas N 2 He CO 2 CH 4 Volume (L) Moles Mass (g) Molecules 602x x x x

21 Using the ideal gas law to solve for an unknown quantity (n, V, P, or T) 21

22 Using the ideal gas law to solve for an unknown quantity (n, V, P, or T) What volume will 2 mols of a gas occupy at 37 C and 649 torr of pressure? 22

23 Using the ideal gas law to solve for an unknown quantity (n, V, P, or T) What temperature will be required to have a pressure of 100 atm in a 10 liter vessel containing 4 mols of a gas?? 23

24 Using the ideal gas law to interconvert t volume, mols and mass Molar Avogadro s mass mass moles number molecules mass Molar mass moles PV = nrt gas data(p,v) 24

25 The airbag in an automobile is rapidly inflated in the event of an accident by the explosion of sodium azide (NaN 3 ) which produces N 2 gas according to the following equation: 2NaN 3 (s) 2Na(s) + 3N 2 (g) You want to design an airbag that will contain 50 liters of gas at a pressure of 1.3 atm. and at a temperature t of 22 C when inflated. How much NaN 3 (in grams) will you need for your airbag? 25

26 2NaN 3 (s) 2Na(s) + 3N 2 (g) You want to design an airbag that will contain 50 liters of gas at a pressure of 1.3 atm. and at a temperature of 22 C when inflated. How much NaN 3 (in grams) will you need for your airbag? 26

27 Using the ideal gas law for calculations where a change in 1 or more variables occurs PV T = 1 P V Initial conditions Final conditions 1 T 2 27

28 Helium balloons are used as instruments for weather forecasting. You have a weather balloon with a volume of 4190 liters which is launched when the temperature is 22.5 C and atmospheric pressure is 754 torr. At it s final altitude of 20 miles, the temperature is -33 C and the atmospheric pressure is 76 torr. What is the volume of the balloon at this altitude? 28

29 You decide to throw a surprise birthday party for your chemistry professor. You want to have helium filled ballons for the festivity. You have a 44 liter cylinder of helium at a pressure of 2000 psi. How many balloons can you fill for your beloved professor?? Assume each balloon will contain 5 liters of He at a pressure of 2 atm. 1 atm. = 14.7 psi 29

30 Density of gases Molar mass (M) is the mass of one mole of a substance and has units of g/mol 30

31 Law of partial pressures for gas mixtures The pressure of a mixture of gases is equal to the sum of the pressures of the different components of the gas mixture Each component s pressure = a partial pressure n t = n 1 + n 2 + n 3 + P t = P 1 + P 2 + P

32 You have a 12.2 liter vessel that contains 2.34 g CO 2, 1.73 g SO 2, and 3.33 g Ar at 42 C. What is the total pressure in the vessel in torr? 32

33 Mol fraction The ratio of the number of mols of one component in a mixture to the total number of mols in the mixture n x = 1 1 n t x t = x 1 + x 2 + x 3 + = 1 P 1 = x 1 P T 33

34 You have a 12.2 liter vessel that contains 2.34 g CO 2, 1.73 g SO 2, and 3.33 g Ar at 42 C. What is the total pressure in the vessel in torr? What is the mol fraction of Ar in this mixture? 34

35 Stoichiometric relations Molar mass Stoich. relation Molar mass mass a moles a moles b mass b PV = PV = nrt nrt gas data(p,v) a gas data(p,v) b 35

36 A 10.0 gram sample of dry ice (solid CO 2 ) is placed in a container initially at 1 atm. pressure that has a volume of 4.6 liters and a temperature of 24.0 C. The container is then sealed. Calculate the pressure inside the container after all the dry ice is converted to gas. 36

37 What volume of hydrogen gas can be produced from the electrolysis of a gallon of sea water at 25 Cand1atm.P? atm. 2H 2 O (l) 2H 2(g) + O d 2(g) H2 O = 1g/ml 1 gallon = 3.78 liters S. Ensign, S. Ensign, Chem. gases

38 What volume of hydrogen gas can be produced from the electrolysis of a gallon of sea water at 25 Cand1atm.P? atm. 2H 2 O (l) 2H 2(g) + O d 2(g) H2 O = 1g/ml 1 gallon = 3.78 liters 38

39 Kinetic-molecular theory The volume occupied by gas molecules is much less than the volume in which they reside Molecules of gases are in continual random motion Attractive/repulsive forces between gas molecules are negligible Gas molecules collide with each other and walls of container without loss of energy The average kinetic energy of a gas molecule is proportional to the temperature 39

40 Distribution of molecular speeds for N 2 at 300K olecules n of mo fraction molecular speed (m/s) 40

41 Note that the distribution of molecular speeds is not symmetric fraction of mo olecules Symmetric distribution ib ti in red Actual speeds in blue molecular speed (m/s) 41

42 Note that the distribution of molecular speeds is not symmetric fraction of mo olecules Root mean square speed: the speed of a molecule possessing average kinetic energy Ek E k = mv molecular speed (m/s) 42

43 Distribution of molecular speeds for N 2 at different temperatures fractio on of mo olecule s 300K 600K 900K 1200K Higher temperatures gives higher average kinetic energies molecular speed (m/s) 43

44 Distributions of molecular speeds for noble gases at 300K of mole ecules fraction All gases have the same average kinetic energy at a given temperature Kr Ar Ne fhe Ek = 1 mv molecular speed (m/s) 44

45 Deviations of gases from ideal behavior Under what conditions will a gas begin to deviate from gas-like behavior? Kinetic-molecular l theory The volume occupied by gas molecules is much less than the volume in which they reside Molecules of gases are in continual random motion Attractive/repulsive forces between gas molecules are negligible Gas molecules collide with each other and walls of container without loss of energy The average kinetic energy of a gas molecule is proportional to the temperature re 45

46 Gas molecule ( a pea) Volume that belongs to the gas molecule ( a basketball) 46