The Gaseous State of Matter

Transcription

1 The Gaseous State of Matter Chapter 12 Hein and Arena Version 1.1 Dr. Eugene Passer Chemistry Department Bronx Community 1 College John Wiley and Company

2 The Kinetic- Molecular Theory 2

3 The Kinetic-Molecular Theory KMT is based on the motions of gas particles. A gas that behaves exactly as outlined by KMT is known as an ideal gas. While no ideal gases are found in nature, real gases can approximate ideal gas behavior under certain conditions of temperature and pressure. 3

4 Principle Assumptions of the KMT 1. Gases consist of tiny particles with mass but negligible volume. 2. The distance between particles is large compared with the size of the particles themselves. 3. Gas particles have no attraction for one another. 4

5 Principle Assumptions of the KMT 4. Gas particles move in straight lines in all directions, colliding frequently with one another and with the walls of the container. 5. No energy is lost by the collision of a gas particle with another gas particle or with the walls of the container. All collisions are perfectly elastic. 5

6 Principle Assumptions of the KMT 6. The average kinetic energy for particles is the same for all gases at the same temperature, and its value is directly proportional to the Kelvin temperature. 6

7 Kinetic Energy 1 KE = mv 2 2 7

8 Standard Temperature and Pressure 8

9 Standard Temperature and Pressure Selected common reference points of temperature and pressure. Standard Conditions Standard Temperature and Pressure STP K or 0.00 o C 1 atm or 760 torr or 760 mm Hg 9

10 Mole-Mass-Volume Relationships 10

11 Volume of one mole of any gas at STP = 22.4 L L at STP is known as the molar volume of any gas (i.e L/mol.). 11

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13 The density of neon at STP is g/l. What is the molar mass of neon? g 22.4 L g = 20.2 mol 1 L 1 mol 13

14 Ideal Gas Equation 14

15 nrt nt PV V a= nrt P 15

16 atmospheres nrt nt PV V a= nrt P 16

17 liters nrt nt PV V a= nrt P 17

18 moles nrt nt PV V a= nrt P 18

19 Kelvin nrt nt PV V a= nrt P 19

20 Ideal Gas Constant L-atm mol-k nrt nt PV V a= nrt P 20

21 A balloon filled with 5.00 moles of helium gas is at a temperature of 25 o C. The atmospheric pressure is 750. torr. What is the balloon s volume? Step 1. Organize the given information. P = 750. torr Convert temperature to kelvins. K = o C K = 25 o C = 298K Convert pressure to atmospheres. 1 atm x 760 torr = atm 21

22 A balloon filled with 5.00 moles of helium gas is at a temperature of 25 o C. The atmospheric pressure is 750. torr. What is the balloon s volume? Step 2. Write and solve the ideal gas equation for the unknown. nrt PV = nrt V = P Step 3. Substitute the given data into the equation and calculate. (5.00 mol) ( L atm/mol K)(298 K) V = = 124 L (0.987 atm) 22

23 Determination of Molecular Weights Using the Ideal Gas Equation g molar mass = mol M = molar mass PV = nrt grt M = PV g mol = molar mass g n = mol = M PV = g M RT 23

24 Calculate the molar mass of an unknown gas, if g occupies 250 ml at a temperature of 305 K and a pressure of atm. V = 250 ml = L g = g T = 305 K grt M = PV P = atm M = (0.020 g) (0.082 L atm/mol K)(305 K) (0.045 atm)(0.250 L) g = mol

25 Gas Stoichiometry 25

26 Gas Stoichiometry Primary conversions involved in stoichiometry. 26

27 What volume of oxygen (at STP) can be formed from mol of potassium chlorate? The problem can be solved in one continuous calculation. 2 KClO 3 2KCl + 3 O 2 3 mol O2 (0.500 mol KClO 3) 2 mol KClO L 1 mol = 16.8 L O 2 27

28 nrt nt PV V a= nrt P 28

29 What volume of hydrogen, collected at 30.0 o C and 700. torr, will be formed by reacting 50.0 g of aluminum with hydrochloric acid? 2 Al(s) + 6 HCl(aq) 2AlCl 3 (aq) + 3 H 2 (g) Step 1 Calculate moles of H 2. grams Al moles Al moles H g Al 1 mol Al g Al 3 mol H 2 2 mol Al = 2.78 mol H 2 29

30 What volume of hydrogen, collected at 30.0 o C and 700. torr, will be formed by reacting 50.0 g of aluminum with hydrochloric acid? 2 Al(s) + 6 HCl(aq) 2AlCl 3 (aq) + 3 H 2 (g) Step 2 Calculate liters of H 2. Convert o C to K: 30. o C = 303 K Convert torr to atm: 700 torr 1 atm 760 torr = atm 30

31 What volume of hydrogen, collected at 30.0 o C and 700. torr, will be formed by reacting 50.0 g of aluminum with hydrochloric acid? Solve the ideal gas equation for V PV = nrt V = nrt V = P (2.78 mol H 2) ( L-atm)(303 K) (0.921 atm) (mol-k) = 75.1 L H 2 31

32 Real Gases 32

33 Real Gases Deviations from the gas laws occur at high pressures and low temperatures. At high pressures the volumes of the real gas molecules are not negligible compared to the volume of the gas At low temperatures the kinetic energy of the gas molecules cannot completely overcome the intermolecular attractive forces between the molecules. 33

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