phy210 ch5

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Chapter 5

GAS LAWS AND

KINETIC THEORY

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Boyles‟, Charles and Gay-Lussacs‟ Law

GAS LAW

Gases are a state of matter characterized bytwo properties which are lack of exact volumeand lack of exact shape.

There are three properties of gases: Volume, V Pressure, P Temperature, T

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The Gas Laws and Absolute Temperature

The relationship between the volume,pressure, temperature, and mass of a gas iscalled an equation of state.

The gases law that we will cover for thischapter including: Boyle`s law

Charles`s law Pressure law or Gay-Lussac law

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BOYLE‟S LAW

The volume of a gas depends on the pressure exerted onit. When you pump up a bicycle tire, you push down on ahandle that squeezes the gas inside the pump. You cansqueeze a balloon and reduce its size (the volume itoccupies).

In general, the greater the pressure exerted on a gas,the less its volume and vice versa.

This relationship is true only if the temperature of thegas remains constant while the pressure is changed.

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Pressure is

inversely proportionalto the volume.

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Boyle‟s law definition:

..’The volume of a given

amount of gas is inversely proportional to the absolute

pressure as long as thetemperature is constant ’..

We can see that the data fit into apattern called a hyperbola.

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If, however weplot pressure against 1/volumewe get a linear (straight line)graph.

PV = constant

P1V1 = P2V2

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• Charles‟s law definition:

..’ the volume of a givenamount of gas is directly

proportional to the absolutetemperature (Kelvin) when the

pressure is kept constant ’..

Charles‟s law

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V/T = constant

V1 /T1 = V2 /T2

• By extrapolating, the volume becomes zero at−273.15°C; this temperature is called absolute

zero (refer figure).

• Therefore, absolute temperature:

T(K) = T(C) + 273.15

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• Definition:

..’The absolute pressure of a given amount of gas is

directly proportional to the absolute temperature (K)when the volume is kept constant ’..

P/T = constant

Thus; P1 /T1 = P2 /T2

Gay-Lussacs‟ law

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Absolute Temperature andIdeal Gas Law

Absolute Temperature

Known as the Kelvin scale. Degrees are samesize as Celcius scale.

Absolute zero = 0°C = 273.15 K

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At standard atmospheric pressure :

Room temperature is about 293 K (20°C)

Standard temperature is 273 K

Water freezes at 273.15 K and boils at 373.15 K.

T (K) = T (°C) + 273.15

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Note:If any gas could be cooled to -273°C, the volume would

be zero.

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• This three gas laws can be combined to produced a singlemore general relation between absolute pressure, volumeand absolute temperature; that is:

Where PV/T = constant

P1V1 /T1 = P2V2 /T2

The Ideal Gas Law

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• Now we are looking to a simple experiment where theballoon is blown up at a constant pressure and temperature(figure below).

• It is found that, the volume, V of a gas increases in directproportion to the mass, m of a gas present:

Hence we can write:

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• A mole (mol) is defined as the number of grams of asubstance that is numerically equal to the molecular mass of the substance.

Example:

i. 1 mol H2 has a mass of 2 g.

ii. 1 mol Ne has a mass of 20 g.

iii. 1 mol CO2 has a mass of 44 g; where the molecularmass for CO2 = [12 + (2 x 16)] = 44 g/mol

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• Where the number of moles in a certain mass of materialis given as:

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• From proportion the equation for ideal gaslaw can be written as:

• Where n is the number of moles and R is the universal gasconstant and its value is given as:

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• The ideal gas law often refers to “standard conditions” orstandard temperature and pressure (STP). Where at STP:

T = 273 K

P = 1.00 atm

= 1.013 x 105 N/m2

= 101.3 kPa

Note:1 mol STP gas has:i. Volume = 22.4Lii. No. of molecule/moles = 6.023 x 1023 molecules

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When using and dealing with all this three gas laws and alsoideal gas law; the temperature must in Kelvin (K) and the

pressure must always be absolute pressure, not gaugepressure.

Absolute pressure = gauge pressure + atmospheric pressure

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1. Determine the volume of 1.00 mol of any gas, assumingit behaves like an ideal gas, at STP.

(ans: 0.0224 m3)

2. An automobile tire is filled to a gauge pressure of 200kPa at 10°C. After a drive of 100 km, the temperaturewithin the tire rises to 40°C. What is the pressure withinthe tire now?

(ans: 333 kPa)

Exercises:

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• Since the gas constant is universal, the number of moleculesin one mole is the same for all gases. That number is calledAvogadro‟s number:

• The number of molecules in a gas is the number of molestimes Avogadro‟s number:

Ideal Gas Law in Terms of Molecules:Avogadro‟s Number

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Therefore we can write:

Where k is called Boltzmann‟s constant

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Kinetic Theory and the MolecularInterpretation of Temperature

The force exerted on the wall by the collision of onemolecule is:

Then the force due to all molecules colliding with thatwall is:

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Figure 13.16:(a)Molecules of a gas moving about

in a rectangular container.

(a) Arrows indicate the momentumof one molecules as it reboundsfrom the end wall.

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The averages of the squares of the speeds in all threedirections are equal:

So the pressure is:

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Rewriting;

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The average translational kinetic energy of themolecules in an ideal gas is directly proportional to thetemperature of the gas.

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We can invert this to find the average speed of molecules in a gas as a function of temperature:

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Distribution of Molecular Speeds

These two graphs show the distribution of speeds of molecules in a gas, as derived by Maxwell. The mostprobable speed, v P, is not quite the same as the rmsspeed.

Note:vrms is not at the peak of the curve because the curve is skewed to the right (not symmetrical).vp is called the „most probable speed.

Figure 13.17: Distribution of speeds of molecules in an ideal gas.

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As expected, the curves shift to the right with temperature.

Figure 13.18: Distribution of molecular speeds for two different temperature

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• The ideal gas law equation is given as;

• The term of “ideal” refers to characteristics/behavior of gaswhere at “ideal”, the pressure of gas is too high and thetemperature of gas close/near the liquefaction point (boilingpoint).

Real Gases

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• However, at pressures less than an atmosphere or so (nottoo high), and when temperature is not close to the boilingpoint of the gas, it is refers to behavior of real gases.

• Figure below is the curve of P vs V at temperatureconstant for ideal gas (Boyle`s law).

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• And figure below is the curves represent the behavior of thegas at different temperatures (not constant) for real gases.Where TA TB TC TD

• It is found that, the cooler (temperature decrease @ fartherfrom boiling point) it gets, the further the gas is from ideal.

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Below the critical temperature (the gas can liquefy if thepressure is sufficient; above it, no amount of pressurewill suffice):

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• The dashed curve A` and B`represents the behavior of a gas aspredicted by the ideal gas law (Boyle`slaw) for several different values of the

temperature.• We see that, the behavior of gasdeviates even more from the curvespredicted by ideal gas law (curves Aand B), and the deviation is greater

when the gas is closer to liquid-vaporregion (curve C and D).

Figure 13.19: PV diagram forreal substance

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• In curve D, the gas becomes liquid; it begins condensingat (b) and is entirely liquid at (a).

• Curve C represent the behavior of the substance at its

critical temperature, and the point (c) is called the criticalpoint.

• At temperature less than the critical temperature, a gaswill change to the liquid phase if sufficient pressure isapplied.

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• The behavior of a substance can be diagrammed not onlyon a PV diagram but also on a PT diagram.

• A PT diagram is called a phase diagram; it shows allthree phases of matter:

i. The solid-liquid transition (in equilibrium) is meltingor freezing

ii. The liquid-vapor transition is boiling or condensing

iii. The solid-vapor transition is sublimation. Wheresublimation refers to the process whereby at lowpressures a solid changes directly into the vaporphase without passing through the liquid phase.

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• The intersection of the three curves is called the triplepoint. Where it is only at triple point that the three phasescan exist together in equilibrium.

Figure 13.20: Phase diagram of water.

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Figure 13.21: Phase diagram of carbon dioxide.

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phy210 ch5

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