Section 13.1 Describing the Properties of Gases Steven S. Zumdahl Susan A. Zumdahl Donald J. DeCoste Gretchen M. Adams University of Illinois at Urbana-Champaign Chapter 13 Gases

Section 13.1 Describing the Properties of Gases 1.To learn about atmospheric pressure and how barometers work 2.To learn the units of pressure 3.To understand how the pressure and volume of a gas are related 4.To do calculations involving Boyle’s Law 5.To learn about absolute zero 6.To understand how the volume and temperature of a gas are related 7.To do calculations involving Charles’s Law 8.To understand how the volume and number of moles of a gas are related 9.To do calculations involving Avogadro’s Law Objectives

Section 13.1 Describing the Properties of Gases A. Pressure Barometer – device that measures atmospheric pressure  Invented by Evangelisti Torricelli in 1643 Measuring Pressure

Section 13.1 Describing the Properties of Gases A. Pressure  Changing weather conditions Atmospheric Pressure

Section 13.1 Describing the Properties of Gases A. Pressure  Changing altitude Atmospheric Pressure

Section 13.1 Describing the Properties of Gases A. Pressure 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr = 101,325 Pa Units of Pressure

Section 13.1 Describing the Properties of Gases The pressure of a gas is measured as 2.5 atm. Represent this pressure in both torr and pascals. Pressure Conversions: An Example

Section 13.1 Describing the Properties of Gases A. Pressure Units of Pressure A manometer measures the pressure of a gas in a container.

Section 13.1 Describing the Properties of Gases Robert Boyle’s experiment B. Pressure and Volume: Boyle’s Law

Section 13.1 Describing the Properties of Gases B. Pressure and Volume: Boyle’s Law

Section 13.1 Describing the Properties of Gases Graphing Boyle’s results B. Pressure and Volume: Boyle’s Law

Section 13.1 Describing the Properties of Gases B. Pressure and Volume: Boyle’s Law This graph has the shape of half of a hyperbola with an equation: Volume and pressure are inversely proportional.  If one increases the other decreases. PV = k

Section 13.1 Describing the Properties of Gases B. Pressure and Volume: Boyle’s Law Another way of stating Boyle’s Law is P 1 V 1 =P 2 V 2 (constant temperature and amount of gas)

Section 13.1 Describing the Properties of Gases Exercise A sample of helium gas occupies 12.4 L at 23°C and atm. What volume will it occupy at 1.20 atm assuming that the temperature stays constant? 9.88 L

Section 13.1 Describing the Properties of Gases Graphing data for several gases C. Volume and Temperature: Charles’s Law

Section 13.1 Describing the Properties of Gases It is easier to write an equation for the relationship if the lines intersect the origin of the graph. C. Volume and Temperature: Charles’s Law  Use absolute zero for the temperature.

Section 13.1 Describing the Properties of Gases These graphs are lines with an equation: C. Volume and Temperature: Charles’s Law Volume and pressure are directly proportional.  If one increases the other increases. Another way of stating Charles’s Law is V = bT (where T is in kelvin) V 1 = V 2 T 1 T 2 (constant pressure and amount of gas)

Section 13.1 Describing the Properties of Gases Exercise Suppose a balloon containing 1.30 L of air at 24.7°C is placed into a beaker containing liquid nitrogen at –78.5°C. What will the volume of the sample of air become (at constant pressure)? L

Section 13.1 Describing the Properties of Gases D. Volume and Moles: Avogadro’s Law

Section 13.1 Describing the Properties of Gases D. Volume and Moles: Avogadro’s Law Volume and moles are directly proportional.  If one increases the other increases V = an (constant temperature and pressure) Another way of stating Avogadro’s Law is V 1 = V 2 n 1 n 2 (constant temperature and pressure)

Section 13.1 Describing the Properties of Gases Exercise If 2.45 mol of argon gas occupies a volume of 89.0 L, what volume will 2.10 mol of argon occupy under the same conditions of temperature and pressure? 76.3 L

Section 13.2 Using Gas Laws to Solve Problems 1.To understand the ideal gas law and use it in calculations 2.To understand the relationship between the partial and total pressure of a gas mixture 3.To do calculations involving Dalton’s law of partial pressures 4.To understand the molar volume of an ideal gas 5.To learn the definition of STP 6.To do stoichiometry calculations using the ideal gas law Objectives

Section 13.2 Using Gas Laws to Solve Problems A. The Ideal Gas Law Boyle’s Law V = k (at constant T and n) P Charles’s Law V = bT (at constant P and n) Avogadro’s Law V = an (at constant T and P) We can combine these equations to get

Section 13.2 Using Gas Laws to Solve Problems A. The Ideal Gas Law Rearranging the equation gives the ideal gas law: PV = nRT R = L∙ atm mol∙K

Section 13.2 Using Gas Laws to Solve Problems Exercise An automobile tire at 23°C with an internal volume of 25.0 L is filled with air to a total pressure of 3.18 atm. Determine the number of moles of air in the tire mol

Section 13.2 Using Gas Laws to Solve Problems Exercise What is the pressure in a L tank that contains kg of helium at 25°C? 114 atm

Section 13.2 Using Gas Laws to Solve Problems Exercise At what temperature (in °C) does 121 mL of CO 2 at 27°C and 1.05 atm occupy a volume of 293 mL at a pressure of 1.40 atm? 696°C

Section 13.2 Using Gas Laws to Solve Problems What happens to the pressure of a gas as we mix different gases in the container? B. Dalton’s Law of Partial Pressures

Section 13.2 Using Gas Laws to Solve Problems Dalton’s law of partial pressures B. Dalton’s Law of Partial Pressures For a mixtures of gases in a container, the total pressure exerted is the sum of the partial pressures of the gases present. P total = P 1 + P 2 + P 3

Section 13.2 Using Gas Laws to Solve Problems B. Dalton’s Law of Partial Pressures The pressure is independent of the nature of the particles. The pressure of the gas is affected by the number of particles.

Section 13.2 Using Gas Laws to Solve Problems Two crucial things we learn from this are: B. Dalton’s Law of Partial Pressures the volume of the individual particles is not very important the forces among the particles must not be very important

Section 13.2 Using Gas Laws to Solve Problems Exercise Consider the following apparatus containing helium in both sides at 45°C. Initially the valve is closed.  After the valve is opened, what is the pressure of the helium gas? 2.00 atm 9.00 L 3.00 atm 3.00 L

Section 13.2 Using Gas Laws to Solve Problems Exercise 27.4 L of oxygen gas at 25.0°C and 1.30 atm, and 8.50 L of helium gas at 25.0°C and 2.00 atm were pumped into a tank with a volume of 5.81 L at 25°C. Calculate the new partial pressure of oxygen atm Calculate the new partial pressure of helium atm Calculate the new total pressure of both gases atm

Section 13.2 Using Gas Laws to Solve Problems Collecting a gas over water B. Dalton’s Law of Partial Pressures Total pressure is the pressure of the gas + the vapor pressure of the water.

Section 13.2 Using Gas Laws to Solve Problems Collecting a gas over water B. Dalton’s Law of Partial Pressures How can we find the pressure of the gas collected alone?

Section 13.2 Using Gas Laws to Solve Problems Molar Volume C. Gas Stoichiometry Molar volume of an ideal gas at STP 22.4 L Standard temperature and pressure (STP)  0 o C and 1 atm For one mole of a gas at STP

Section 13.2 Using Gas Laws to Solve Problems Exercise A sample of oxygen gas has a volume of 2.50 L at STP. How many grams of O 2 are present? 3.57 g

Section 13.3 Using a Model to Describe Gases 1.To understand the relationship between laws and models (theories) 2.To understand the postulates of the Kinetic Molecular Theory 3.To understand temperature 4.To learn how the Kinetic Molecular Theory explains the gas laws 5.To describe the properties of real gases Objectives

Section 13.3 Using a Model to Describe Gases A. Laws and Models: A Review

Section 13.3 Using a Model to Describe Gases A. Laws and Models: A Review A model can never be proved absolutely true. A model is an approximation and is destined to be modified.

Section 13.3 Using a Model to Describe Gases B. The Kinetic Molecular Theory of Gases

Section 13.3 Using a Model to Describe Gases C. The Implications of the Kinetic Molecular Theory Meaning of temperature – Kelvin temperature is directly proportional to the average kinetic energy of the gas particles Relationship between Pressure and Temperature – gas pressure increases as the temperature increases because the particles speed up Relationship between Volume and Temperature – volume of a gas increases with temperature because the particles speed up

Section 13.3 Using a Model to Describe Gases Concept Check You are holding two balloons of the same volume. One contains helium, and one contains hydrogen. Complete each of the following statements with “different” or “the same” and be prepared to justify your answer. He H2H2

Section 13.3 Using a Model to Describe Gases Concept Check Complete the following statement with “different” or “the same” and be prepared to justify your answer. The pressures of the gas in the two balloons are __________. He H2H2

Section 13.3 Using a Model to Describe Gases Concept Check Complete the following statement with “different” or “the same” and be prepared to justify your answer. The temperatures of the gas in the two balloons are __________. He H2H2

Section 13.3 Using a Model to Describe Gases Concept Check Complete the following statement with “different” or “the same” and be prepared to justify your answer. The numbers of moles of the gas in the two balloons are __________. He H2H2

Section 13.3 Using a Model to Describe Gases Concept Check Complete the following statement with “different” or “the same” and be prepared to justify your answer. The densities of the gas in the two balloons are __________. He H2H2

Section 13.3 Using a Model to Describe Gases Concept Check Sketch a graph of: I.Pressure versus volume at constant temperature and moles.

Section 13.3 Using a Model to Describe Gases Concept Check Sketch a graph of: II.Volume vs. temperature (  C) at constant pressure and moles.

Section 13.3 Using a Model to Describe Gases Concept Check Sketch a graph of: III.Volume vs. temperature (K) at constant pressure and moles.

Section 13.3 Using a Model to Describe Gases Concept Check Sketch a graph of: IV.Volume vs. moles at constant temperature and pressure.

Section 13.3 Using a Model to Describe Gases Concept Check Which of the following best represents the mass ratio of Ne:Ar in the balloons? 1:1 1:2 2:1 1:3 3:1 Ne Ar V Ne = 2V Ar

Section 13.3 Using a Model to Describe Gases Concept Check You have a sample of nitrogen gas (N 2 ) in a container fitted with a piston that maintains a pressure of 6.00 atm. Initially, the gas is at 45  C in a volume of 6.00 L. You then cool the gas sample.

Section 13.3 Using a Model to Describe Gases Concept Check Which best explains the final result that occurs once the gas sample has cooled? a)The pressure of the gas increases. b)The volume of the gas increases. c)The pressure of the gas decreases. d)The volume of the gas decreases. e)Both volume and pressure change.

Section 13.3 Using a Model to Describe Gases Concept Check The gas sample is then cooled to a temperature of 15  C. Solve for the new condition. (Hint: A moveable piston keeps the pressure constant overall, so what condition will change?) 5.43 L

Section 13.3 Using a Model to Describe Gases Gases do not behave ideally under conditions of high pressure and low temperature. Why? D. Real Gases

Section 13.3 Using a Model to Describe Gases At high pressure the volume is decreased.  Molecule volumes become important.  Attractions become important. D. Real Gases