1 Lecture 6 Gases Properties of Gases Gas Pressure Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

2 Kinetic Theory of Gases Assumptions about the behavior of gases:  Gas particles are in constant motion and move rapidly in straight lines until they collide  Gas particles are very far apart.  Gases have no volume or very small volume (true if pressure is low)  As the temperature of gas increases, the speed of the gas particles increase (Kinetic energy increases).  The size of the gas molecule will not affect the properties of the gas Ideal Gas: one that obeys all of the above criteria Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

3 Properties of Gases  Gases are described in terms of four properties: pressure (P), volume (V), temperature (T), and amount (n). TABLE 7.1 Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

4 Gas pressure: the force acting on a specific area. Pressure (P) = force area  Has units of atm, mm Hg, torr, lb/in. 2 and kilopascals (kPa). 1 atm = 760 mm Hg (exact) 1 atm = 760 torr 1 atm = 14.7 lb/in. 2 1 atm = kPa Gas Pressure

5 A. What is 475 mm Hg expressed in atm? 1) 475 atm 2) atm 3) 3.61 × 10 5 atm B. The pressure of a tire is 2.00 atm. What is this pressure in mm Hg? 1) 2.00 mm Hg 2) 1520 mm Hg 3) mm Hg Learning Check

6 Atmospheric Pressure Atmospheric pressure  Is the pressure exerted by a column of air from the top of the atmosphere to the surface of the Earth. Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

7 Atmospheric Pressure Atmospheric pressure  Is about 1 atmosphere at sea level.  Depends on the altitude and the weather.  Is lower at high altitudes where the density of air is less.  Is higher on a rainy day than on a sunny day. Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

8 Barometer A barometer  Measures the pressure exerted by the gases in the atmosphere.  Indicates atmospheric pressure as the height in millimeters of the mercury column. Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

9 Relationship Between Properties of Gases  Pressure and Volume (Boyle’s Law)  Temperature and Volume (Charle’s Law)  Temperature and Pressure (Gay-Lussac’s Law)  The Combined Gas Law  Volume and Moles (Avogadro’s Law)  Partial Pressures (Dalton’s Law)

10 Pressure and Volume (Boyle’s Law) Boyle’s Law states that or PV = K The pressure of a gas is inversely related to its volume when T and n are constant.  If the pressure increases, volume decreases. Robert Boyle, * Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings *

11 In Boyle’s Law  The product P x V is constant as long as T and n do not change. P 1 V 1 = 8.0 atm x 2.0 L = 16 atm L P 2 V 2 = 4.0 atm x 4.0 L = 16 atm L P 3 V 3 = 2.0 atm x 8.0 L = 16 atm L  Boyle’s Law can be stated as P 1 V 1 = P 2 V 2 (T, n constant) PV Constant in Boyle’s Law

12 Solving for a Gas Law Factor The equation for Boyle’s Law can be rearranged to solve for any factor. P 1 V 1 = P 2 V 2 Boyle’s Law To solve for V 2, divide both sides by P 2. P 1 V 1 = P 2 V 2 P 2 P 2 V 1 xP 1 = V 2 P 2

13 Freon-12, CCl 2 F 2, is used in refrigeration systems. What is the new volume (L) of a 8.0 L sample of Freon gas initially at 550 mm Hg after its pressure is changed to 2200 mm Hg at constant T? Conditions 1Conditions 2 P 1 = 550 mm HgP 2 = 2200 mm Hg V 1 = 8.0 LV 2 = Calculation with Boyle’s Law ?

14 Learning Check For a cylinder containing helium gas indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant): 1) Pressure decreases 2) Pressure increases Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

15 Learning Check If a sample of helium gas has a volume of 120 mL and a pressure of 850 mm Hg, what is the new volume if the pressure is changed to 425 mm Hg ? 1) 60 mL 2) 120 mL3) 240 mL

16 Learning Check A sample of helium gas in a balloon has a volume of 10. L at a pressure of 0.90 atm. At 1.40 atm (T constant), is the new volume represented by A, B, or C? Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

17 Temperature and Volume: Charles’ Law In Charles’ Law  The Kelvin temperature of a gas is directly related to the volume.  P and n are constant.  When the temperature of a gas increases, its volume increases. Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings Jaques Alexander Cedar Charles ( )* *

18  For two conditions, Charles’ Law is written V 1 = V 2 (P and n constant) T 1 T 2  Rearranging Charles’ Law to solve for V 2 T 2 xV 1 = V 2 x T 2 T 1 T 2 V 2 = V 1 x T 2 T 1 Charles’ Law: V and T

19 Learning Check Solve Charles’ Law expression for T 2. V 1 = V 2 T 1 T 2

20 A balloon has a volume of 785 mL at 21°C. If the temperature drops to 0°C, what is the new volume of the balloon (P constant)? Set up data table: Conditions 1Conditions 2 V 1 = 785 mLV 2 = ? T 1 = 21°C = 294 KT 2 = 0°C = 273 K Be sure to use the Kelvin (K) temperature in gas calculations. Calculations Using Charles’ Law

21 A sample of oxygen gas has a volume of 420 mL at a temperature of 18°C. At what temperature (in °C) will the volume of the oxygen be 640 mL (P and n constant)? 1) 443°C 2) 170°C 3) - 82°C Learning Check

22 Use the gas laws to complete with 1) Increases 2) Decreases A. Pressure _______, when V decreases. B. When T decreases, V _______. C. Pressure _______ when V changes from 12 L to 24 L D.Volume _______when T changes from 15 °C to 45°C Learning Check

23 Gay-Lussac’s Law: P and T In Gay-Lussac’s Law,  The pressure exerted by a gas is directly related to the Kelvin temperature.  V and n are constant. P 1 = P 2 T 1 T 2 Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

24 A gas has a pressure at 2.0 atm at 18°C. What is the new pressure when the temperature is 62°C? (V and n constant) Calculation with Gay-Lussac’s Law

25 Vapor Pressure and Boiling Point Vapor pressure is the  Pressure of gas molecules above the surface of a liquid.  At the boiling point, the vapor pressure becomes equal to the external pressure. Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

26  The combined gas law uses Boyle’s Law, Charles’ Law, and Gay-Lussac’s Law (n is constant). P 1 V 1 =P 2 V 2 T 1 T 2 Combined Gas Law

27 A sample of helium gas has a volume of L, a pressure of atm and a temperature of 29°C. At what temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n constant)? Combined Gas Law Calculation

28 A gas has a volume of 675 mL at 35°C and atm pressure. What is the volume(mL) of the gas at -95°C and a pressure of 802 mm Hg (n constant) Learning Check

29 Avogadro's Law: Volume and Moles Avogadro’s Law states that  The volume of a gas is directly related to the number of moles (n) of gas.  T and P are constant. V 1 = V 2 n 1 n 2 Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

30 Learning Check If 0.75 mole helium gas occupies a volume of 1.5 L, what volume will 1.2 moles helium occupy at the same temperature and pressure? 1) 0.94 L 2)1.8 L 3) 2.4 L

31 The volumes of gases can be compared at STP, (Standard Temperature and Pressure) when they have  The same temperature. Standard temperature (T) 0°C or 273 K  The same pressure. Standard pressure (P) 1 atm (760 mm Hg) STP

32 Molar Volume The molar volume of a gas  Is measured at STP (standard temperature and pressure).  Is 22.4 L for 1 mole of any gas.. Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

33 Molar Volume as a Conversion Factor The molar volume at STP can be used to form conversion factors L and 1 mole 1 mole 22.4 L

34 Using Molar Volume What is the volume occupied by 2.75 moles N 2 gas at STP? The molar volume is used to convert moles to liters moles N 2 x 22.4 L = 61.6 L 1 mole Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

35 A. What is the volume at STP of 4.00 g of CH 4 ? 1) 5.60 L2) 11.2 L3) 44.8 L B. How many grams of He are present in 8.00 L of Hes at STP? 1) 25.6 g2) g3) 1.43 g Learning Check

36 Gases in Chemical Reactions The volume or amount of a gas at STP in a chemical reaction can be calculated from  STP conditions.  Mole factors from the balanced equation.

37 STP and Gas Equations What volume (L) of O 2 gas is needed to completely react with 15.0 g of aluminum at STP? 4Al(s) + 3O 2 (g) 2Al 2 O 3 (s) Plan: g Al mole Al mole O 2 L O 2 (STP) What volume (L) of O 2 gas is needed to completely react with 15.0 g of aluminum at STP? 4Al(s) + 3O 2 (g) 2Al 2 O 3 (s) Plan: g Al mole Al mole O 2 L O 2 (STP 22.4 L/1 mole)

38 What mass of Fe will react with 5.50 L O 2 at STP? 4Fe(s) + 3O 2 (g) 2Fe 2 O 3 (s) Learning Check

39  The relationship between the four properties (P, V, n, and T) of gases can be written equal to a constant R. PV = R nT  Rearranging this expression gives the expression called the ideal gas law. PV = nRT Ideal Gas Law

40 The universal gas constant, R  Can be calculated using the molar volume of a gas at STP.  Calculated at STP uses 273 K,1.00 atm, 1 mole of a gas, and a molar volume of 22.4 L. P V R = PV = (1.00 atm)(22.4 L) nT (1 mole) (273K) n T = L atm mole K Universal Gas Constant, R

41 Another value for the universal gas constant is obtained using mm Hg for the STP pressure. What is the value of R when a pressure of 760 mm Hg is placed in the R value expression? Learning Check

42 Dinitrogen oxide (N 2 O), laughing gas, is used by dentists as an anesthetic. If a 20.0 L tank of laughing gas contains 2.86 moles N 2 O at 23°C, what is the pressure (mm Hg) in the tank? Learning Check Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

43 Learning Check A cylinder contains 5.0 L of O 2 at 20.0°C and 0.85 atm. How many grams of oxygen are in the cylinder? Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

44 The partial pressure of a gas  Is the pressure of each gas in a mixture.  Is the pressure that gas would exert if it were by itself in the container. Partial Pressure (Dalton’s Law)

45 Dalton’s Law of Partial Pressures indicates that  Pressure depends on the total number of gas particles, not on the types of particles.  The total pressure exerted by gases in a mixture is the sum of the partial pressures of those gases. P T = P 1 + P 2 + P Dalton’s Law of Partial Pressures

46 Dalton’s Law of Partial Pressures Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

47  For example, at STP, one mole of a pure gas in a volume of 22.4 L will exert the same pressure as one mole of a gas mixture in 22.4 L. V = 22.4 L Gas mixtures Total Pressure 0.5 mole O mole He 0.2 mole Ar 1.0 mole 1.0 mole N mole O mole He 1.0 mole 1.0 atm

48 Scuba Diving  When a scuba diver dives, the increased pressure causes N 2 (g) to dissolve in the blood.  If a diver rises too fast, the dissolved N 2 will form bubbles in the blood, a dangerous and painful condition called "the bends".  Helium, which does not dissolve in the blood, is mixed with O 2 to prepare breathing mixtures for deep descents. Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

49 Learning Check A scuba tank contains O 2 with a pressure of atm and He at 855 mm Hg. What is the total pressure in mm Hg in the tank? Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

50 For a deep dive, a scuba diver uses a mixture of helium and oxygen with a pressure of 8.00 atm. If the oxygen has a partial pressure of 1280 mm Hg, what is the partial pressure of the helium? 1) 520 mm Hg 2) 2040 mm Hg 3) 4800 mm Hg Learning Check

51 Gases We Breathe The air we breathe  Is a gas mixture.  Contains mostly N 2 and O 2 and small amounts of other gases. TABLE 7.7 Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings

52 A.If the atmospheric pressure today is 745 mm Hg, what is the partial pressure (mm Hg) of O 2 in the air? 1) ) 156 3) 760 B. At an atmospheric pressure of 714, what is the partial pressure (mm Hg) N 2 in the air? 1) 557 2) 9.143) Learning Check