THREE STATES OF MATTER
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1 CHAPTER 9.1 Gases
2 THREE STATES OF MATTER
3 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)
4 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
5 UNDERSTANDING THE IDEAL GAS LAW PV = nrt Initially discovered through observations of gas behavior - the changing of gas volumes. Macroscopic behavior of gases explained by Kinetic- Molecular Theory.
6 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
7 MOLECULAR VIEW OF BOYLE S LAW Pext increased T, n constant volume decreases More frequent collisions (force) over a smaller surface area.
8 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
9 MOLECULAR VIEW OF CHARLES LAW
10 CHARLES LAW V2 = (T2/T1)V1
11 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 Volume (L)! 2! 1! C = 0 K At 0 K - molecular motion stops; zero volume for gases 0! -200! 0! 200! 400! Temperature ( C)!
12 QUESTION 9.1 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
13 QUESTION 9.1 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
14 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.
15 MOLECULAR VIEW OF AVOGADRO S LAW
16 QUESTION 9.2 If a you are inflating several balloons in a room at some ambient temperature (and constant pressure). What do you think the relationship is between the volume of the balloon (V) and the amount of gas (n = number of moles) in it? Answer A B C D - V is directly proportional to n. - V is the square of n. - V is inversely proportional to n. - There is no relationship between V and n.
17 QUESTION 9.2 If a you are inflating several balloons in a room at some ambient temperature (and constant pressure). What do you think the relationship is between the volume of the balloon (V) and the amount of gas (n = number of moles) in it? Answer A B C D - V is directly proportional to n. - V is the square of n. - V is inversely proportional to n. - There is no relationship between V and n.
18 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
19 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.
20 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
21 QUESTION 9.3 What is the volume of 2.00 mol of helium gas at 27 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
22 QUESTION 9.3 What is the volume of 2.00 mol of helium gas at 27 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
23 STANDARD MOLAR VOLUME Standard Temperature and Pressure = 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).
24 THE IDEAL GAS LAW PV = nrt V = nrt P R = PV nt 1 atm L = = 1 mol K atm L mol K Fixed n & T Fixed n & P Fixed P & T Boyle s Law Charles Law Avogadro s Law V = const./p V = const. T V = const. n
25 CALCULATION QUESTION 9.3 A 30.0 L balloon is filled with gas at K and has a pressure of 1.2 atm. How many moles of gas are in the balloon? Does it matter if the gas in the balloon is air, helium, nitrogen or methane...?
26 QUESTION 9.4 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
27 QUESTION 9.4 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
28 QUESTION 9.5 A bicycle tire can be inflated to a pressure of 7.00 atm at 20.0 C using a cartridge containing 16.0 g of compressed CO2(g). What is the volume of a road Answers: A L B L C L D L E L bicycle tire? R = L atm/mol K
29 QUESTION 9.5 A bicycle tire can be inflated to a pressure of 7.00 atm at 20.0 C using a cartridge containing 16.0 g of compressed CO2(g). What is the volume of a road Answers: A L B L C L D L E L bicycle tire? R = L atm/mol K
30 QUESTION 9.6 Which of the following statements correctly completes the sentence: If equal masses of of F2 and N2 are placed in identical containers at the same temperature....both containers have the same number of molecules...the pressure is greater in the container with F2 gas...the pressure will be the same in both containers...the N2 gas is denser than the F2 gas...there are more molecules in the container of N2 gas Answer: A B C D E
31 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)
32 DALTON S LAW PROBLEM 9.7 What is the total pressure (in atm) when 1.00 mol of Ar, mol of He, and 1.60 mol of N2 gases are injected into a 9.12 L flask at 0.00 C? What is the pressure of each gas in the mixture? 32
33 DENSITY OF AN IDEAL GAS The density of an ideal gas depends on its chemical identity (molar mass). X moles of ideal gas H2(g) will occupy the same volume as X moles of CH4(g). Yet X moles of H2(g) has less mass than CH4(g). density = (molar mass)p RT Gases are compressible: density will vary greatly with changes in T and P
34 LAKE NYOS - CAMEROON Crater lake on the flank of an inactive volcano. Upper levels of the lake are warm water, lower levels are cold. Lake water is saturated with CO2 - dead lake. On August 21, 1986 the lake experienced a disruption which caused the CO2 to erupt from the lake. ~ kg of CO2 was released. 50 m high wave of CO2, moving at km/h for ~23 km. Deaths: 1,700 people & 3,500 livestock.
35 THE MOLAR MASS OF A GAS n = mass M n = PV RT M = (mass)rt PV d = mass V d = density M = drt P
36 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
37 QUESTION 9.8 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
38 QUESTION 9.8 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
39 GAS STOICHIOMETRY 9.9 The ideal gas law can be used to determine the amount of a gas present for a stoichiometry calculation: PV = nrt n = PV RT Problem Aluminum reacts with hydrochloric acid to produce aqueous aluminum chloride and hydrogen gas. If 3.75 g of aluminum reacts with an excess of hydrochloric acid, what volume of hydrogen gas is generated at 25.0 C at 1 atm?
40 QUESTION 9.10 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
41 QUESTION 9.10 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
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