lecture 2 the gas laws - chemistry for all…. · lecture 2. the gas laws some fundamental...

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Lecture 2. The GAS LAWS

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.



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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.


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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

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

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Combining the GAS LAWS

How does a bubble-jet printer work?

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

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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

A Hydrogen Gas thermometer is found to have a volume of 100.0 mL when placed in an ice water bath at 0oC. 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?

THE IDEAL GAS LAW: Sample Problem

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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.

THE IDEAL GAS LAW: Sample Problems

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

THE IDEAL GAS LAW: Sample Problem

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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?

THE IDEAL GAS LAW: Sample Problems

GAS STOICHIOMETRY: Sample Problem

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

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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)


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.

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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.

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

……

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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

THE GAS LAWS: Sample Problems

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

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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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REVIEW

Ideal Gases:

V 1/P Boyles’s Law

V T Charles’ Law

V n Avogadro’s Law

V nT/P ; PV = nRT

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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.

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REAL GASES: The van der Waals equation

Why is the molar volume of a gas not zero at 0oK?

-Gases have finite volume.


D. van der Waals proposes a law that accounts for:

- Finite volume of individual molecules

- Attractive forces between molecules.

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(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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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

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 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.

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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

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.

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Condensation of Gases ; Critical State

From Physical Chemistry, R. Chang

Condensation of Gases ; Critical State

From Physical Chemistry, R. Chang

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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

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.

lecture 2 the gas laws - chemistry for all…. · lecture 2. the gas laws some fundamental...

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