Lecture 2 PROPERTIES OF GASES
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1 Lecture 2 PROPERTIES OF GASES Reference: Principles of General Chemistry, Silberberg Chapter 6 SOME FUNDAMENTAL DEFINITIONS: SYSTEM: the part of the universe being the subject of study 1
2 SOME FUNDAMENTAL DEFINITIONS: State of the System: condition of a system at any given time as defined by the experimental variables such as pressure, volume, temperature and composition. Surroundings: portion of the universe outside of the system and that interacts with the system Process: is an occurrence that changes the state of the system. SOME FUNDAMENTAL DEFINITIONS: 2
3 SOME FUNDAMENTAL DEFINITIONS: Thermodynamic variables are either extensive or intensive: Intensive variables: independent of the size of the system. Pressure, density and temperature. Extensive variables: variables that depend on the size of the system. Volume, mass, internal energy and entropy. THE DISTINCTION OF GASES FROM LIQUIDS AND SOLIDS 1. Gas volume changes greatly with pressure. 2. Gas volume changes greatly with temperature 3. Gases have relatively low viscosity 4. Most gases have relatively low densities under normal conditions. 5. Gases are miscible 3
4 6/23/14 THE THREE STATES OF MATTER Figure 5.2 Effect of atmospheric pressure on objects at Earth s surface. 4
5 A mercury barometer. 5
6 THE GAS LAWS: Boyle s Law Why pressurize the contents of gas canister? The effect of pressure on gas volume Robert Boyle (1662) discovered that: pv = constant (Boyle s Law) For a certain gas (at constant T), Boyle s law can be used to predict when its volume changes and vice versa: P 1 V 1 = P 2 V 2 (at constant gas mass and T) 6
7 THE GAS LAWS: Charles Law Why does a hot air balloon float? The effect of temperature on gas volume Small burner at the heart of the balloon heats the canvas hood of the balloon. Density of the gas inside the balloon decreases with heating ( since mass is assumed constant, the decreased in density must have been due to increase in volume. The balloon floats because the voluminous air inside has a lower density than the air outside. Balloon descends back to earth when the air it contains cools down 7
8 THE GAS LAWS: Charles Law J. A. Charles: at constant pressure, the volume of the gas expands when heated and contracts when cooled. V T ; V/T = constant (Charles Law) An alternative is that at constant volume; P T; P/T = constant Volume-temperature and pressure-temperature values of a gas in states 1 and 2: V 1 /T 1 = V 2 /T 2 and P 1 /T 1 = P 2 /T 2 8
9 THE GAS LAWS: Avogadro s Law Proposed by Amedeo Avogadro in 1811: Equal volumes of gases at the same temperature and pressure contains the same number of molecules. V n ; V/n = constant (at constant T, P) Combining the GAS LAWS How does a bubble-jet printer work? 9
10 The Gas Laws: THE IDEAL GAS LAW; PV = nrt The volume of a gas is dependent on the temperature, pressure and the number of moles: at constant T and n: V 1/P Boyles Law at constant P and n: V T Charles Law at constant T and P: V n Avogadro s Law Therefore: V nt/p V = nrt/p The Gas Laws: THE IDEAL GAS LAW; PV = nrt The values of R: R = L atm K -1 mol -1 R = N m K -1 mol -1 10
11 THE STANDARD TEMPERATURE AND PRESSURE By international agreement the standard temperature and pressure (STP) are: 0.00 o C ( K) 1.00 atm (760.0 torr) SAMPLE PROBLEM 2.01 A sample of gas occupies 12.0 L under a pressure of 1.2 atm. What would be its volume if the pressure were increased to 2.4 L? 11
12 SAMPLE PROBLEM 2.02 A sample of nitrogen occupies 117 ml at 100 o C. At what temperature in o C would it occupy 234 ml if the pressure did not change? SAMPLE PROBLEM 2.03 A sample of neon occupies 105 liters at 27 o C under a pressure of 985 torr. What volume would it occupy at STP? 12
13 SAMPLE PROBLEM 2.04 A gas-filled weather balloon with a volume of 65.0 L is released at sea level conditions of 745 torr and 25 o C. The balloon can expand to a maximum volume of 835 L. When the balloon rises to an altitude at which the temperature is -5 o C and the pressure is atm, will it reach its maximum volume? - From Silberberg, Chemistry, Molecular Nature of Matter and Change. SAMPLE PROBLEM 2.05 Atmospheric pollution is a problem that has received much attention. Not all pollution, however, comes from industrial sources. Volcanic eruptions can be significant source of air pollution. The Kilauea volcano in Hawaii emits on the average 250 tons of SO 2 per day. If this gas is emitted at 800 o C and at 1 atm, what volume of gas is emitted? - From Atkin s Physical Chemistry, 8 th, Oxford Press 13
14 SAMPLE PROBLEM 2.06 A 2.50 g sample of XeF 4 gas is placed into an evacuated 3.00 liter container at 80 o C. What is the pressure in the container? SAMPLE PROBLEM 2.07 A sample of Nitrogen gas has a volume of 1.75 L at STP. How many moles of N 2 are present? 14
15 The Density of a Gas m Density = V m n = M PV = nrt PV = m M RT m/v = d = M x P RT The density of a gas is directly proportional to its molar mass. The density of a gas is inversely proportional to the temperature. SAMPLE PROBLEM 2.08 Nitric acid, a very important industrial chemical, is made by dissolving the gas nitrogen dioxide, NO 2, in water. Calculate the density of NO 2 gas in g/l at 1.24 atm and 50 o C. 15
16 SAMPLE PROBLEM 2.09 A chemist is preparing to carry out a reaction at high pressure that requires 36.0 mol of hydrogen gas. The chemist pumps the hydrogen into a 12.3 Liters rigid steel container at 25 o C. A. To what pressure must the hydrogen be compressed? B. What would be the density of the high-pressure hydrogen? MOLAR MASS OF A GAS / DENSITY The molar mass of a gas was measured at 1.5 atm and 27 o C and found to be 1.95 g/l. Calculate the molar mass of the gas. 16
17 MOLECULAR WEIGHTS AND FORMULAS FOR GASEOUS COMPOUNDS SAMPLE PROBLEM 2.10 A 120. ml flask contained g of gaseous compound at 100 o C and 1.00 atm pressure. What is the molecular weight of the compound? Additional analysis of the gaseous compound showed that it contained 54.5% C, 9.10% H, and 36.4% O by mass. What is its molecular formula? 17
18 DALTON s LAW of Partial Pressures For a system containing two or more different gases, the total pressure is the sum of the individual pressures that each gas would exert if it were alone and occupied the same volume. P T = (n 1 + n 2 + n n ) RT/V P 1 = x 1 P T where x 1 is the mole fraction of gas 1 P 2 = x 2 P T where x 2 is the mole fraction of gas 2 P n = x n P T where x n is the mole fraction of gas n SAMPLE PROBLEM 2.11 A 10.0 L flask contains mole of methane, mole of hydrogen, and mole of nitrogen at 25 o C. A. What is the pressure inside the flask? B. What is the partial pressure of each component in the flask? 18
19 SAMPLE PROBLEM 2.12 What is the mole fraction of each gas in a mixture having the partial pressures of atm of He, atm of Ar and atm of Xe? SAMPLE PROBLEM 2.13 Mixtures of helium and oxygen can be used in scuba diving tanks to prevent the bends. For a particular dive, 46 L of He at 25 o C and 1.0 atm and 12 L of O 2 at 25 o C and 1.0 atm were pumped into a tank with volume of 5.0 L. Calculate the partial pressure of each gas and total pressure in the tank at 25 o C. - From Atkin s Physical Chemistry, 8 th, Oxford Press 19
20 STOICHIOMETRY IN REACTIONS INVOLVING GASES SAMPLE PROBLEM 2.14 Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate (CaCO 3 ). Calculate the volume of CO 2 at STP produced from the decomposition of 152 g of CaCO 3 by the reaction: CaCO 3 (s) CaO(s) + CO 2 (g) 20
21 SAMPLE PROBLEM 2.15 A sample of methane gas having a volume of 2.8 L at 25 o C and 1.65 atm was mixed with a sample of oxygen gas having a volume 35.0 L at 31 o C and 1.25 atm. The mixture was then ignited to form carbon dioxide and water. Calculate the volume of CO 2 formed at a pressure of 2.5 atm and a temperature of 125 o C. SAMPLE PROBLEM 2.16 If 36.0 g of C 3 H 8 and 112 g of O 2 are placed in a closed container and the mixture is ignited, the reaction products are CO 2 and H 2 O. If 61.6 g of CO 2 are actually produced in the reaction, what is the percent yield of CO 2? 21
22 LAW OF COMBINING VOLUMES At constant temperature and pressure, the volumes of reacting gases can be expressed as a ratio of simple whole numbers. H 2 (g) + Cl 2 (g) 2 HCl(g) 1 volume + 1 volume = 2 volumes SAMPLE PROBLEM 2.17 If 36.0 L of C 4 H 10 and 112 L of O 2 are placed in a closed container and the mixture is ignited, what is the maximum volume of CO 2 that could be produced at the same temperature and pressure? The other product of the reaction is water. 22
23 THE GAS LAWS: REAL GASES IDEAL GAS: Gas molecules have negligible volume. There are no attractive nor repulsive interaction between molecules. No such gases exist! THE GAS LAWS: REAL GASES When gases are compressed, molecules are brought closer together, gases will deviate from ideal behavior! Measure of deviation from ideality: compressibility factor, Z Z = PV/nRT Z = 1 ideal behavior, when P approaches 0 for all gases Z < 1 easier to compress than an ideal gas Z > 1 harder to compress than an ideal gas 23
24 THE GAS LAWS: REAL GASES THE GAS LAWS: REAL GASES 24
25 Ideal Gases: V 1/P REVIEW Boyles s Law V T Charles Law V n Avogadro s Law V nt/p ; PV = nrt REVIEW Real Gases: - are not just points of mass; they have definite volumes - gas molecules interacts (attractive or repulsive) with each other. Compressibility factor is a measure for non-ideality of gases. 25
26 REVIEW QUESTION: At what conditions of P, V, and T does real gases approaches ideality. REAL GASES: The van der Waals equation Why is the molar volume of a gas not zero at 0 o K? - Gases have finite volume. 26
27 REAL GASES: The van der Waals equation D. van der Waals proposes a law that accounts for: - Finite volume of individual molecules - Attractive forces between molecules. REAL GASES: The van der Waals equation (P + an 2 /V 2 )(V-nb) = nrt Introduces two new constants to the ideal gas law: b - the finite volume of the non ideal gas and a - attractive forces between the gas molecules. (P + an 2 /V 2 ) - pressure of corrected for intermolecular forces (V-nb) - nb represents the total effective volume of the gas 27
28 REAL GASES: The van der Waals equation REAL GASES: The van der Waals equation The constant a reflects the strength of interaction between gas molecules: - a value of 4.25 for NH 3 suggests strong interaction: value of for He represent a negligible interaction The constant b reflects the physical size of the gas molecule: b for He; CO 2 =
29 SAMPLE PROBLEM 2.17 Cylinders of compressed gas are typically filled to pressures of 200 atm. For oxygen, how many kg of this gas can be stored in a 50-liter cylinder at this pressure and 25 o C based on a) the ideal gas equation and b) van der Waals equation. For oxygen a = li 2 atm mol -2, b = 3.19 X10-2 li mol -1. REAL GASES: The Virial Equation of State Another way of expressing the non-ideal behavior of gases: Z = 1 + B/V + C/V 2 + D/V 3 + Where B, C, D are virial coefficients and are T dependent. Alternatively, a series expansion in terms of pressure Z = 1 + B P + C P2 + D P3 +.. when B >> C >> D Z = 1+ B P 29
30 REAL GASES: Sample Problem Calculate the molar volume of methane at 300K and 100 atm, given that the second virial coefficient (B) of methane is L mol-1. Compare your result with that obtained using the ideal-gas equation. Condensation of Gases ; Critical State From Physical Chemistry, R. Chang 30
31 Condensation of Gases ; Critical State From Physical Chemistry, R. Chang Van de Waals Equation and the Critical State Relationship between critical constants and a and b in van der Waals equation: As a function of P c and V c a = 3P c (V c /n) 2 b = V c /3n As a function of P c and T c a = 27R 2 T c2 /64P c b = RT c /8P c 31
32 Critical State: Sample problem The critical constants for methane are P c = 45.6 atm, V c = li/mol and T c = K. Calculate the van der Waals parameters of the gas. 32
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