ANNOUNCEMENTS. Exam 3 Score will update soon. Chapter 9 home work due Dec. 7th. Chapter 10 and 11 home work due Dec. 14th.

Transcription

1 ANNOUNCEMENTS Exam 3 Score will update soon. Chapter 9 home work due Dec. 7th. Chapter 10 and 11 home work due Dec. 14th. Final exam is on Dec 15th, 7:30-9:30 pm

2 LECTURE OBJECTIVES Chapter Describe the unique properties of gasses. Quantify measurements of pressure. Define the ideal gas law relationships. Calculate the density of ideal gasses. Define standard temperature, and pressure. Calculate partial pressures of gasses in a mixture.

3 LECTURE OBJECTIVES Chapter Describe the unique properties of gasses. Quantify measurements of pressure. Define the ideal gas law relationships. Calculate the density of ideal gasses. Define standard temperature, and pressure. Calculate partial pressures of gasses in a mixture.

4 GASES ARE STRANGE... Compared to solids & liquids, gasses behave in very strange ways: Gas volume varies dramatically with changes in pressure and temperature. Gases have low viscosities (flow freely) Gases have low densities (mostly empty) Gases are miscible (mix perfectly in all proportions) The physical behavior of gases does not depend on the chemical identity (ideally)

5 MEASURING PRESSURE A cylindrical tube (~1 m long) containing Hg(l) is inverted into a dish of Hg(l). The Hg(l) in the tube descends until the pressure of the atmosphere on the external Hg(l) equals the downward force of the column of Hg(l). At sea level this is usually about 76 cm.

6 COMMON UNITS OF PRESSURE Unit Atmospheric pressure Scientific field pascal (Pa); kilopascal (kpa) Pa kpa SI unit; physics & chemistry atmosphere 1 atm chemistry millimeters of mercury (Hg) 760 mm Hg chemistry, medicine, biology torr 760 torr chemistry pounds per square inch (psi or lb/in 2 ) bar 14.7 lb/in 2 engineering bar meteorology, chemistry, physics

7 THE KINETIC-MOLECULAR THEORY OF GASES A gas consists of a large collection of individual particles that are very small (no volume). Gas particles are in constant, random, straight-line, motion (except for collisions) Collisions between particles are elastic - their total kinetic energy (Ek) is constant. Between collisions, the gas particles do not influence each other in any way (act independently).

8 MODEL OF A GAS SAMPLE empty space very small particle gas pressure from collisions

9 THE IDEAL GAS LAW An ideal gas physical behavior can be completely described by only four variables: Pressure (P) Temperature (T) Volume (V) Amount (moles, n) PV = nrt R = Universal gas constant = L atm/mol K

10 QUESTION What is the volume of 2.00 mol of helium gas at 27.0 C and at 3.00 atm? Answer A B C D E L 1.48 L 16.4 L 36.9 L 44.8 L R = L atm/mol K

11 CHANGING CONDITIONS The Ideal Gas Law can also explain the manner in which a gas changes when conditions change (e.g. increase P, decrease T...): P1V1 n1t1 = P2V2 n2t2 = R Subscript 1: Initial conditions Subscript 2: Final conditions

12 QUESTION What is the effect of increasing the pressure by a factor of four on an ideal gas, if the number of moles and temperature are held constant? Answer A - B - C - D - The volume increases by a factor of four The volume decreases by a factor of four The volume remains the same The volume doubles

13 UNDERSTANDING THE IDEAL GAS LAW Initially discovered through observations of gas behavior - the changing of gas volumes. Macroscopic behavior of gases explained by Kinetic-Molecular Theory.

14 BOYLE S LAW The volume of an ideal gas is inversely proportional to the external pressure - at a fixed T and n: P1V1 P2V2 = P1V1 = P2V2 n1t1 n2t2 V2 = (P1/P2)V1

15 MOLECULAR VIEW OF BOYLE S LAW Pext increased T, n constant volume decreases More frequent collisions (force) over a smaller surface area.

16 CHARLES LAW The volume of an ideal gas is directly proportional to the temperature of the gas - at a fixed P and n. P1V1 = P2V2 V1 = V2 n1t1 n2t2 T1 T2 V2 = (T2/T1)V1

17 MOLECULAR VIEW OF CHARLES LAW

18 CHARLES LAW V2 = (T2/T1)V1

19 CHARLES LAW AND ABSOLUTE ZERO Celsius scale - arbitrary zero point 3! T vs. V Kelvin scale (K) - absolute temperature scale; 0 K is the lowest possible temperature C = 0 K Volume (L)! 2! 1! At 0 K - molecular motion stops; zero volume for gases 0! -200! 0! 200! 400! Temperature ( C)!

20 QUESTION What is the effect of increasing the temperature by a factor of two and increasing the pressure by a factor of two on an ideal gas, if the number of moles of the gas is held constant? Answer A - B - C - The volume increases by a factor of four The volume increases by a factor of two The volume remains the same D -The volume decreases by a factor of two E - The volume decreases by a factor of four

21 AVOGADRO S LAW The volume of an ideal gas is directly proportional to the amount of gas - at fixed P and T. P1V1 = P2V2 V1 = V2 n1t1 n2t2 n1 n2 V2 = (n2/n1)v1 At a fixed P and T, equal volumes of an ideal gas contain an equal number of particles.

22 MOLECULAR VIEW OF AVOGADRO S LAW

23 QUESTION Magnesium metal (0.100 mol) and 1 L of M hydrochloric acid are combined and react to completion. How many liters of hydrogen gas, measured at K and 1.00 atm are produced? Mg(s) + 2HCl(aq) MgCl2(aq) + H2(g) Answer: 2.24 L of H2 A 4.48 L of H2 B 5.60 L of H2 C 11.2 L of H2 D 22.4 L of H2 E

24 STOICHIOMETRIC RELATIONSHIPS BETWEEN GASEOUS REAGENTS P, V, T of moles of moles of P, V, T of gas A gas A gas B gas B Ideal gas law Molar ratio from balanced equation Ideal gas law

25 AN EXAMPLE IN THE BOOK

26 GAS DENSITY AND MOLAR MASS The ideal gas law (PV=nRT) can be used to determine the density (d) and/or molecular weight (MW) of the gas. The MW of a gas will always remain the same, as it is based on the mass of the atoms of the gas. The density of a gas will change with pressure, and temperature. n = mass MW n = PV RT MW = (mass)rt PV d = mass V MW = drt P

27 PROBLEM A 0.50 L bottle contains an unknown gas under a pressure of 3.0 atm at T = 300.K. The mass of the container is g when evacuated and g when filled with the gas. Which of the following could be the identity of the gas? nitrogen oxygen fluorine argon carbon dioxide

28 STANDARD MOLAR VOLUME Standard Temperature and Pressure (STP) = 0 C ( K) and 1.00 atm One mole of any idea gas will occupy 22.4 L at standard temperature and pressure. The difference will be in the mass of the gas (and the density of the gas).

29 QUESTION List the following gases in order of increasing density. Assume temperature and pressure are constant. Answer: A B C D E Cl2<Kr<SO2 Kr<SO2<Cl2 SO2<Cl2<Kr SO2<Kr<Cl2 Cl2<SO2<Kr

30 DALTON S LAW OF PARTIAL PRESSURES When there is a mixture of gases, the total pressure of the mixture is due to the sum of the individual gas pressures. These are termed partial pressures - the amount of pressure produced by each individual type of gas. Ptotal = P1 + P2 + P3 + P Pair = Pnitrogen + Poxygen + Pcarbon dioxide + Pargon +... Py = Xy Ptotal Xy = mole fraction of gas y = (moles of y) (total moles)

31 PROBLEM A 5.63 g sample of methane (CH4) is combusted with a stoichiometric amount of oxygen. The gas produced from the combustion is captured in a 6.48 L canister and is at a temperature of 126 C. What is the pressure inside the cylinder? CH4(g) + 2O2(g) CO2(g) + 2H2O(g)