Gas Laws

Charles, Boyle, Gay- Lussac, Combined and The Ideal Gas Law

The Nature of a Gas

Gases have mass.Its easy to compress gases.Gases fill their containers completely.Different gases can move through each other quite rapidly.Gases exert pressure.The pressure of a gas depends on its temperature.

Kinetic-Molecular TheoryA gas consists of very small particles, with mass.The distances between gas particles are relatively large.Gas particles are in constant, random motion.Collisions between gas particles are perfectly elastic.Average KE of particles depends only on the temperature of the gas.There is no attractive force between particles of a gas.

Variables That Effect GasesMoles (n) – the amount of gas. Volume (V) – the size of the container that holds the gas in liters (L).Temperature (T) – the speed or kinetic energy of the particles in kelvin (oC +273)Pressure (P) – The outward push of gas particles on their container in atmospheres (atm) or millimeters of mercury (mm Hg)*Think of pressure as the number of collisions between gas particles and their container.

STP

The behavior of a gas depends on its temperature and the pressure at which the gas is held. So far we have only dealt with gases at STP. Standard Temperature and Pressure.

• 273 kelvins and 1 atm.

The Gas Laws

Boyle’s LawCharles’s LawGay-Lussac’s LawThe Combined Gas LawThe Ideal Gas Law

Boyle’s LawThe Pressure-Volume RelationshipThe pressure and volume of a sample of gas at constant temperature are inversely proportional to each other.(As one goes up, the other goes down)P1V1 =P2V2

If 3 of the variables are known, the fourth can be calculated.

Boyle’s Law

The gas in a 20.0mL container has a pressure of 2.77atm. When the gas is transferred to a 34.0mL container at the same temperature, what is the new pressure of the gas.P1 V1 =P2 V2

2

112

VVPP =

mLatmmLP

0.34)77.2(0.20

2 =

atmP 63.12 =

Boyle’s LawSo, does it make sense?If a set amount of gas is transferred into a larger container, would the pressure go up or down?Would there be more collisions, or fewer collisions with the container holding the gas?More volume (space) means fewer collisions with the container, therefore pressure goes down. (From 2.77 atm to 1.63 atm)

Charles’s Law

The temperature-volume relationshipAt constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature.

2

2

1

1

TV

TV =

If 3 of the variables are known, the fourth can be calculated.

Charles’s Law

What will be the volume of a gas sample at 355K if its volume at 273K is 8.57L?

2

2

1

1

TV

TV =

1

212

TTVV =

kelvinkelvinLV

273)355(57.8

2 =

LV 1.112 =

Charles’s LawDoes it make sense?If the temperature of a given quantity of gas is increased, what will happen to the volume it occupies? (In an elastic container?)Gas particles moving faster would have more collisions with the container and exert more force to enlarge the volume of the elastic container.In this case, from 8.57L to 11.1L.

Pressure ReviewDetermined by the number of collisions between the particles of a gas and their containerforce exerted per unit of areaMeasured in pascals (pa)

Review: To analyze the behavior of a gas:1. Pressure (P)

Related to the number of collisions2. Temperature (T)

Related to the speed of the particles3. Volume (V)

The amount of space a gas occupies4. Mass (M) can relate to density (M/V)

Number of gas particles(Usually expressed in moles of gas)

Behavior of a Gas

If the amount and temperature of a gas remains constant, and the pressure increases, the volume of the gas will decrease. If P increases then V decreases.

Behavior of a Gas

If the amount and volume of a gas remains constant and the temperature increases, the pressure will increase.If T increases then P increases.

Behavior of a Gas

If the pressure and amount of gas remains the same and the temperature increases, the volume increases. If T increases then V increases.

Gay-Lussac’s Law

The Temperature-Pressure RelationshipIf a volume of a sample of gas remains constant, the temperature of a fixed amount of gas is directly proportional to its pressure.

2

2

1

1

TP

TP =

If you know 3 of the variables, you can calculate the 4th.

Gay-Lussac’s Law

The gas left in a used aerosol can is at a pressure of 2.03atm at 25oC. If this can is thrown onto a fire, what is the pressure of the gas when its temperature reaches 928oC?

2

2

1

1

TP

TP =

1

212

TTPP =

KKatmP

298)1201(03.2

2 =

atmP 18.82 =

Gay-Lussac’s Law

Does it make sense?If the temperature of a fixed amount of gas goes up, the particles will have more collisions. More collisions means the pressure will increase.In this case, when the temp went up the pressure increased from 2.03atm to 8.18atm.

The Combined Gas Law

If more than one variable changes, a different equation is needed to analyze the behavior of the gas.

2

22

1

11

TVP

TVP =

5 of the variables must be known to calculate the 6th.

The Combined Gas Law

The volume of a gas-filled balloon is 30.0L at 40oC and 1.75atm of pressure. What volume will the balloon have at standard temperature and pressure?

2

22

1

11

TVP

TVP =

12

2112

TPTPVV =

)313(00.1)273)(75.1(0.30

2Katm

KatmLV =

LV 8.452 =

The Combined Gas LawDoes it make sense?You have a fixed volume of gas. The temperature decreases which would cause fewer collisions and the pressure decreases which causes fewer collisions as well. What can you do to volume to make the pressure decrease???Increase it. More space means fewer collisions.

The Ideal Gas LawDescribes the physical behavior of an ideal gas in terms of the pressure, volume, temperature and the number of moles of gas.Ideal – a gas as it is described by the kinetic-molecular theory postulates.All gases are REAL gases… which behave like ideal gases only under most ordinary conditions.

The Ideal Gas Law

Only at very low temperatures and very high pressures do real gases show significant non-ideal behavior.We will assume that gases are close to ideal and that the ideal gas equation applies.

Ideal Gas Equation- Can Crush mini-lab

PV=nRTP-pressureV-volumen-number of moles of gasR-ideal gas constant (universal gas constant) 0.0821 atm.L/mol.Kor 62.396 torr.L/mol.KT-temperature

Ideal Gas Equation

What is the volume occupied by 9.45g of C2H2 at STP?

nRTPV =

PnRTV =

First, calculate amountof gas in moles.

22

2222 03788.26

145.9 HgCHmolCHgCn =

223629328.0 HmolCn =

Ideal Gas Law

LV 1345217.8=

LV 13.8=

PnRTV =

atmkKmolLatmmolV

00.1273)/0821.0(3629328.0 ⋅⋅=

Ideal Gas Law

How many moles of a gas at 100oC does it take to fill a 1.00L flask to a pressure of 1.5atm?

RTPVn =

nRTPV =

)373(/0821.0)00.1(5.1

kKmolLatmLatmn⋅⋅

=

moln 0490.0=

Lifting Power of Gases

For a gas to be used to inflate lighter-than-air craft like balloons and blimps, the gas must have a density lower than air.The lower the density, the greater the lifting power.

Lifting Power of Gases

The density of a gas depends on its pressure, temperature and molar mass.Each of these variables is part of the ideal gas law.Therefore, we should be able to adjust each of these variables to give low density.

Lifting Power of GasesHowever, if the pressure of the gas within a balloon or blimp were significantly less than the atmospheric pressure, the balloon or blimp would be crushed.Therefore, only two factors can be manipulated to lower the density of a gas: molar mass and temperaturehttp://www.metacafe.com/watch/1702972/mythbusters_floating_on_invisible_water/Mini hot air balloons.http://home.earthlink.net/~quade/lawnchair.html

Molar Mass

Gases with low density can be corrosive, combustible, flammable or chemically active in some way. These gases would make poor choices to fill blimps and balloons.Helium, due to its small molar mass and chemical inactivity is the primary choice for balloons and blimps.

TemperatureHelium is relatively rare and very expensive, so hot air is often preferable.As the temperature of a gas is increased, the particles increase the number of collisions and increase the pressure inside the balloon. The volume of the balloon increases and becomes less dense and rises.Hot air does not have the same lifting power as helium, but it is much cheaper.

Gas EffusionThe movement of atoms or molecules through a hole so tiny that they do not stream through but instead pass through one particle at a time. Explains why helium balloons deflate slowly over a period of a few hours.The lower the mass of the gas, the greater the speed of its particles.Hydrogen effuses faster than helium. Helium effuses faster than oxygen.