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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

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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:

SOME FUNDAMENTAL DEFINITIONS:

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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.

SOME FUNDAMENTAL DEFINITIONS:

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

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THE THREE STATES OF MATTER

Figure 5.2 Effect of atmospheric pressure on objects at Earth’s surface.

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A mercury barometer.

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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:

P1V1 = P2V2 (at constant gas mass and T)

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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

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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: V1/T1 = V2/T2 and P1/T1 = P2/T2

THE GAS LAWS: Charles’ Law

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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)

THE GAS LAWS: Avogadro’s Law

Combining the GAS LAWS

How does a bubble-jet printer work?

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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 = 0.080206 L atm K-1 mol-1

R = 8.314 N m K-1 mol-1

The Gas Laws: THE IDEAL GAS LAW; PV = nRT

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THE STANDARD TEMPERATURE AND PRESSURE

By international agreement the standard temperature and pressure (STP) are:

0.00 oC (273.15 K) 1.00 atm (760.0 torr)

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?

SAMPLE PROBLEM 2.01

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A sample of nitrogen occupies 117 mL at 100oC. At what temperature in oC would it occupy 234 mL if the pressure did not change?

SAMPLE PROBLEM 2.02

A sample of neon occupies 105 liters at 27oC under a pressure of 985 torr. What volume would it occupy at STP?

SAMPLE PROBLEM 2.03

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A gas-filled weather balloon with a volume of 65.0 L is released at sea level conditions of 745 torr and 25oC. The balloon can expand to a maximum volume of 835 L. When the balloon rises to an altitude at which the temperature is -5oC and the pressure is 0.066 atm, will it reach its maximum volume?

- From Silberberg, Chemistry, Molecular Nature of Matter and Change.

SAMPLE PROBLEM 2.04

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 SO2 per day. If this gas is emitted at 800oC and at 1 atm, what volume of gas is emitted?

- From Atkin’s Physical Chemistry, 8th, Oxford Press

SAMPLE PROBLEM 2.05

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A 2.50 g sample of XeF4 gas is placed into an evacuated 3.00 liter container at 80oC. What is the pressure in the container?

SAMPLE PROBLEM 2.06

A sample of Nitrogen gas has a volume of 1.75 L at STP. How many moles of N2 are present?

SAMPLE PROBLEM 2.07

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Density =

n =

The Density of a Gas

PV = nRT PV = RT

m/V = d =

• The density of a gas is directly proportional to its molar mass.

• The density of a gas is inversely proportional to the temperature.

M x P RT

m M

m V

m M

Nitric acid, a very important industrial chemical, is made by dissolving the gas nitrogen dioxide, NO2, in water. Calculate the density of NO2 gas in g/L at 1.24 atm and 50oC.

SAMPLE PROBLEM 2.08

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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 25oC. A.  To what pressure must the hydrogen be compressed? B.  What would be the density of the high-pressure hydrogen?

SAMPLE PROBLEM 2.09

MOLAR MASS OF A GAS / DENSITY

The molar mass of a gas was measured at 1.5 atm and 27oC and found to be 1.95 g/L. Calculate the molar mass of the gas.

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MOLECULAR WEIGHTS AND FORMULAS FOR GASEOUS COMPOUNDS

A 120. mL flask contained 0.345 g of gaseous compound at 100oC 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?

SAMPLE PROBLEM 2.10

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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.

PT = (n1 + n2 +……nn) RT/V

P1 = x1PT where x1 is the mole fraction of gas 1

P2 = x2PT where x2 is the mole fraction of gas 2

Pn = xnPT where xn is the mole fraction of gas n

……

A 10.0 L flask contains 0.200 mole of methane, 0.300 mole of hydrogen, and 0.400 mole of nitrogen at 25oC. A.  What is the pressure inside the flask? B.  What is the partial pressure of each component in the flask?

SAMPLE PROBLEM 2.11

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What is the mole fraction of each gas in a mixture having the partial pressures of 0.467 atm of He, 0.317 atm of Ar and 0.277 atm of Xe?

SAMPLE PROBLEM 2.12

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 25oC and 1.0 atm and 12 L of O2 at 25oC 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 25oC.

- From Atkin’s Physical Chemistry, 8th, Oxford Press

SAMPLE PROBLEM 2.13

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STOICHIOMETRY IN REACTIONS INVOLVING GASES

Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate (CaCO3). Calculate the volume of CO2 at STP produced from the decomposition of 152 g of CaCO3 by the reaction:

CaCO3(s) → CaO(s) + CO2(g)

SAMPLE PROBLEM 2.14

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A sample of methane gas having a volume of 2.8 L at 25oC and 1.65 atm was mixed with a sample of oxygen gas having a volume 35.0 L at 31oC and 1.25 atm. The mixture was then ignited to form carbon dioxide and water. Calculate the volume of CO2 formed at a pressure of 2.5 atm and a temperature of 125oC.

SAMPLE PROBLEM 2.15

If 36.0 g of C3H8 and 112 g of O2 are placed in a closed container and the mixture is ignited, the reaction products are CO2 and H2O. If 61.6 g of CO2 are actually produced in the reaction, what is the percent yield of CO2?

SAMPLE PROBLEM 2.16

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LAW OF COMBINING VOLUMES

At constant temperature and pressure, the volumes of reacting gases can be expressed as a ratio of simple whole numbers. H2(g) + Cl2(g) 2 HCl(g) 1 volume + 1 volume = 2 volumes

If 36.0 L of C4H10 and 112 L of O2 are placed in a closed container and the mixture is ignited, what is the maximum volume of CO2 that could be produced at the same temperature and pressure? The other product of the reaction is water.

SAMPLE PROBLEM 2.17

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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

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

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THE GAS LAWS: REAL GASES

THE GAS LAWS: REAL GASES

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REVIEW

Ideal Gases: V ∝ 1/P 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.

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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 0oK?

- Gases have finite volume.

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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 + an2/V2)(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 + an2/V2) - pressure of corrected for intermolecular forces

(V-nb) - nb represents the total effective volume of the gas

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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 NH3 suggests strong interaction: value of 0.0341 for He represent a negligible interaction

The constant b reflects the physical size of the gas molecule:

b for He; 0.0237 CO2 = 0.0427

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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 25oC based on a) the ideal gas equation and b) van der Waals equation. For oxygen a = 1.364 li2 atm mol-2, b = 3.19 X10-2 li mol-1.

SAMPLE PROBLEM 2.17

REAL GASES: The Virial Equation of State

Another way of expressing the non-ideal behavior of gases:

Z = 1 + B/V + C/V2 + D/V3 + ……

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

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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 -0.042 L mol-1. Compare your result with that obtained using the ideal-gas equation.

Condensation of Gases ; Critical State

From Physical Chemistry, R. Chang

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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 Pc and Vc

a = 3Pc(Vc/n)2 b = Vc/3n

As a function of Pc and Tc

a = 27R2Tc2/64Pc b = RTc/8Pc

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Critical State: Sample problem

The critical constants for methane are Pc = 45.6 atm, Vc = 0.098.7 li/mol and Tc = 190.6 K. Calculate the van der Waals parameters of the gas.