Gases. A gas. Difference between gas and vapor: Why Study Gases?

Transcription

1 Gases Chapter 5

2 Gases A gas Uniformly fills any container. Is easily compressed. Mixes completely with any other gas. Exerts pressure on its surroundings. Difference between gas and vapor: A gas is a substance that is normally in the gaseous state at ordinary temperatures and pressures. A vapor is the gaseous form of any substance that is a liquid or a solid at normal temperatures and pressures. At 1 atm and 25 C: water vapor vs. oxygen gas Why Study Gases? An understanding of real world phenomena. An understanding of how science works. 2

3 Pressure One of the most obvious properties of a gas is that it exerts pressure on its surroundings. Pressure (P) is Caused by the collisions of molecules with the walls of a container. Defined as the force (F) that acts on a given area (A). F P A SI unit of pressure is pascal (Pa) 1 Pa = 1 N/m 2 1 N = 1 kg m/s 2 1 bar = 10 5 Pa = 100 kpa Standard atmospheric pressure (1 atm) 1 atm = 101,325 Pa = Pa 1 atm = 760. mmhg = 760. torr = 14.7 psi 3

4 Barometer closed end A barometer (baro = weight, meter = measure) is an instrument for measuring atmospheric pressure and consists of a long glass tube, close at one end & filled with Hg. Mercury (Hg) flows out of the tube until the pressure of the column of Hg standing on the surface of the Hg in the dish is equal to the pressure of the air on the rest of the surface of the Hg in the dish. The normal pressure due to the atmosphere at sea level can support a column of Hg that is 760 mm high. Hg-filled dish 4

5 Manometer A device used to measure the pressure of gases other than the atmosphere. 5

6 The Gas Laws Four variables are needed to define the physical condition (or state) of a gas: Temperature (T, K) Pressure (P, atm) Volume (V, L) Amount (n, mol) The equations that express the relationships among these four variables are known as the gas laws. Four gas laws (A,B,C and I): Avogadro s law Boyle s law Charles s law Ideal-gas law 6

7 The P V Relationship: Boyle s Law The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure: V 1/P A J-tube similar to the one used by Boyle. When mercury is added to the tube, the pressure on the trapped gas is increased, resulting in a decreased volume. 7

8 Boyle s law 8

9 P & V are Inversely Proportional Boyle s law: V 1/P or PV = k (constant) P 1 V 1 = P 2 V 2 (1 initial, 2 final) A plot of V versus P results in a curve. A plot of V versus 1/P will be a straight line. 9

10 EX. 1 A sample of chlorine gas occupies a volume of 946 ml at a pressure of 726 torr. What is the pressure of the gas in torr and atm, respectively, if the volume is reduced at constant temperature to 154 ml? 10

11 The T V Relationship: Charles s Law The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature: V T i.e. V = bt or P = bt (b is a constant) V 1 /T 1 = V 2 /T 2 or P 1 /T 1 = P 2 /T 2 A plot of V versus T will be a straight line 11

12 Charles s Law 12

13 The n V Relationship: Avogadro s Law The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas: V n or V = an (a is a constant) V 1 /n 1 = V 2 /n 2 These ballons each hold 1.0 L gas at 25 C and 1 atm. Each balloon contains mole of gas, or molecules. 13

14 EX. 2 A sample of carbon monoxide gas occupies 3.20 L at 125 C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? 14

15 EX. 3 Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO an H 2 O, respectively, are obtained from one volume of ammonia at the same temperature and pressure? 15

16 The Ideal-Gas Equation So far we ve introduced 3 gas laws: Avogadro s law: V = constant P & T Boyle s law: V = constant n & T Charles law: V = constant n & P Combining these, we can get the ideal gas law: Tn V R P where R is the (universal) gas constant. PV = nrt 16

17 Ideal-Gas Equation Summary PV = nrt P = pressure in atm V = volume in liters n = amount in moles R = proportionality constant ( L atm/mol K) T = temperature in kelvins Ideal gas equation describes the relationship among the four variables P, V, T, and n. Ideal gas equation holds closely at low pressure (1 atm). An ideal gas is a hypothetical gas whose P-V-T behavior can be completely accounted for by the ideal gas equation. 17

18 Q1. Which of these is NOT a unit used to measure gas pressure? a. atmosphere b. torr c. Pascal d. pound Q2. As a helium-filled balloon rises, its volume increases. This is an example of Law. a. Avogadro s b. Boyle s c. Charles s d. Ideal gas law 18

19 EX. 4 What is the volume (in liters) occupied by 49.8 g of HCl at STP? 19

20 Standard Temp and Pressure (STP) The conditions 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, i.e., the molar volume of any gas at STP is L or 22.4 L PV = nrt 20

21 Gas Density (d ) and Molar Mass (M) m d V nm V PM RT m V PV = nrt PM RT d m V n V PM RT P RT where m is the mass of the gas in g and M is the molar mass of the gas. Note: d is the density of the gas in g/l, unlike solids or liguids in g/ml. d PM RT d P M RT M drt P 21

22 Gas Density Density (g/l) mass (g) volume(l) molarmass (g/mol) molarvolume(l/mol) so at STP Density molarmass 22.4L 22

23 EX. 5 A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.0 C. What is the molar mass of the gas? 23

24 Q3. Standard temperature and pressure (STP) equals (X) atmosphere(s) and (Y) degrees Celsius. a. X = 0, Y = 25 b. X = 1, Y = 0 c. X = 1, Y = 25 d. X = 0, Y = 0 Q4. A sample of 16.0 grams of methane (CH 4 ) gas at STP occupies a volume of liters. a. 5.6 b c d

25 Dalton s Law of Partial Pressures The total pressure of a mixture of gases is just the sum of the pressure that each gas would exert if it were present alone. For a mixture of gases in a container, P T = P 1 + P 2 + P This is particularly useful in calculating the pressure of gases collected over water. P 1 P 2 P total = P 1 + P 2 25

26 Dalton s Law of Partial Pressures (cont d) 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 P T = P A + P B = T RT V where n T = n A + n B. mole fraction (X i ) = n i n T n A is the number of moles of A n B is the number of moles of B X A = n A n A + n B X B = 1 = X A + X B n B n A + n B P i = X i P T P A = X A P T P B = X B P T 26

27 Apparatus for Collecting Gas over Water 2KClO 3 (s) 2KCl(s) + 3O 2 (g) P P P T O2 H2O 27

28 Kinetic Molecular Theory of Gases 1. The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero). (a) One mole of N 2 (l) has a volume of approximately 35 ml and a density of 0.81 g/ml. (b) One mole of N 2 (g) has a volume of L (STP) and a density of g/l. Thus the ratio of the volumes of gaseous N 2 (g) and liquid N 2 (l) is 22.42/0.035 = 640, and spacing of the molecules is 9 times farther apart in N 2 (g). 28

29 Kinetic Molecular Theory of Gases 2. The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. 3. The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other. 4. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. 29

30 Kinetic Molecular Theory 30

31 Application of KMT to Gas Laws Compressibility of Gases (Postulate 1) Boyle s Law P collision rate with wall Collision rate number density Number density 1/V P 1/V Charles s Law (Postulate 4) P collision rate with wall Collision rate average kinetic energy of gas molecules Average kinetic energy T P T 31

32 Application of KMT to Gas Laws Avogadro s Law P collision rate with wall Collision rate number density Number density n P n Dalton s Law of Partial Pressures (Postulate 3) Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas P T = P i 32

33 Molecular View of Boyle s Law 33

34 Molecular View of Charles s Law 34

35 Molecular View of the Ideal Gas Law 35

36 Gas effusion Is the process by which gas under pressure escapes from one chamber of a container to another by passing through a tiny orifice. The rate (r) of effusion measures the speed at which the gas is transferred into the chamber. Graham s law of effusion: r r 1 2 M M 2 1 where M 1 and M 2 represent the molar masses of the gases. 36

37 Effusion 37

38 Gas Diffusion Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. The rate (r) of diffusion is the rate of gas mixing. Diffusion always proceeds from a region of higher concentration to one of lower concentration. Graham's Law of Diffusion The diffusion rate (r) of a gas is inversely proportional to the square root of its molar mass (M). For two gases, 1 and 2, we have. r r 1 2 M M 2 1 U rms 3RT M 38

39 Demonstration of Gas Diffusion 39

40 Demonstration of Gas Diffusion HCl(g) + NH 3 (g) NH 4 Cl(s) (above left) A demonstration of the relative diffusion rates of NH 3 (17 g/mol) and HCl (36 g/mol) molecules through air. Two cotton plugs, on dipped in HCl(aq) and one dipped in NH 3 (aq), are simultaneously inserted into the ends of the tube. Gaseous NH 3 and HCl vaporizing from the cotton plugs diffuse toward each other, and where they meet, react to form NH 4 Cl(s). (Above right) When HCl(g) and NH 3 (g) meet in the tube, a white ring of NH 4 Cl(s) forms. 40

41 Deviations from Ideal Behavior In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure. For an ideal gas, PV nrt 1 (idealgas) For real gases, PV 1 (real gas@ highp) nrt The effect of pressure on the behavior of several real gases. 41

42 Nonideal Gases vs. Ideal Gases Characteristics of an ideal gas Molecules are points, i.e., gas molecules individually have no volume. Molecules do not attract each other. Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important). Volume occupied by the gas molecules. Intermolecular attractive forces between gas molecules. The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account. 42

43 Van der Waals Eqn (for nonideal gases) Ideal Gas Equation: PV = nrt Van der Waals equation: P an V 2 2 V nb nrt 43

44 Q5. A gas sample with a mass of 88.0 mg occupies 50.0 ml at 750 Torr and 27 degrees Celsius. The gas is a. CO b. CO 2 c. SO 2 d. SF 6 Q6. The partial pressure of each gas in a mixture of gases is proportional to the of the gas. a. mass b. molecular weight c. square root of the molecular weight d. mole fraction 44

45 Q7. Neon gas undergoes effusion krypton gas does. a. slower than b. at the same rate as c. twice as fast as d. four times as fast as Q8. Which gas below has the greatest density at STP? a. Ne b. Ar c. Kr d. Xe 45