Some Fundamental Definitions:

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1 Lecture 2. The GAS LAWS Some Fundamental Definitions: SYSTEM: the part of the universe being the subject of study 1

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.

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

Some Fundamental Definitions: Thermodynamic variables are either extensive or intensive: Intensive variables: independent of the size of the system.

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. 3

The Gas Laws: Boyle s Law Why pressurize the contents

a certain gas (at constant T), Boyle s law can be used

4 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) 4

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.

5 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 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 5

6 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) 6

7 Combining the GAS LAWS How does a bubble-jet printer work? 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 7

8 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 THE IDEAL GAS LAW: Sample Problem A Hydrogen Gas thermometer is found to have a volume of ml when placed in an ice water bath at 0 o C. When the same thermometer is immersed in boiling liquid chorine, the volume of hydrogen at the same pressure is found to be 87.2 ml. What is of the boiling point of chlorine? 8

9 THE IDEAL GAS LAW: Sample Problems 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. THE IDEAL GAS LAW: Sample Problem 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 9

10 THE IDEAL GAS LAW: Sample Problems 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? GAS STOICHIOMETRY: Sample Problem A sample of Nitrogen gas has a volume of 1.75 L at STP. How many moles of N 2 are present? 10

11 GAS STOICHIOMETRY: Sample Problem 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) GAS STOICHIOMETRY: Sample Problem 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. 11

12 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. 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 12

13 THE GAS LAWS: Sample Problems 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 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! 13

14 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 Z < 1 Z > 1 ideal behavior, when P approaches 0 for all gases easier to compress than an ideal gas harder to compress than an ideal gas THE GAS LAWS: REAL GASES 14

15 THE GAS LAWS: REAL GASES REVIEW Ideal Gases: V 1/P Boyles s Law V T Charles Law V n Avogadro s Law V nt/p ; PV = nrt 15

16 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. REVIEW QUESTION: At what conditions of P, V, and T does real gases approaches ideality. 16

17 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. 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. 17

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

18 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 REAL GASES: The van der Waals equation 18

19 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 = REAL GASES: Sample Problem 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

20 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 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. 20

21 Condensation of Gases ; Critical State From Physical Chemistry, R. Chang Condensation of Gases ; Critical State From Physical Chemistry, R. Chang 21

22 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 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. 22

Lecture 2 PROPERTIES OF GASES

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 SOME FUNDAMENTAL