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Gas Laws

Joseph Louis Gay-LussacAmadeo Avogadro

Robert Boyle Jacques Charles

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The Combined Gas Law

The combined gas law expresses therelationship between pressure, volume andtemperature of a fixed amount of gas.

2

22

1

11

T

VP

T

VP

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Boyles Law

Pressure is inversely proportional tovolume when temperature is heldconstant.

2211 VPVP

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Charless LawThe volume of a gas is directly proportionalto temperature, and extrapolates to zero atzero Kelvin.

(P= constant)

Temperature MUST be in KELVINS!

2

2

1

1

T

V

T

V

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Gay Lussacs LawThe pressure and temperature of a gas aredirectly related, provided that the volumeremains constant.

Temperature MUST be in KELVINS!

2

2

1

1

T

P

T

P

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Avogadros Law

For a gas at constant temperature andpressure, the volume is directlyproportional to the number of moles ofgas (at low pressures).

V = an

a= proportionality constant

V= volume of the gas

n= number of moles of gas

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Ideal Gas Law

PV= nRTP= pressure in atmV= volume in litersn= molesR= proportionality constant

= 0.08206 L atm/ molKT= temperature in Kelvins

Holds closely at P< 1 atm

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Real Gases

corrected pressure corrected volume

Pideal Videal

At high pressure (smaller volume) and lowtemperature (attractive forces becomeimportant) you must adjust for non-idealgas behavior using van der Waals equation.

2

( )obsn

P a x V nb nRTV

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Gas Density

so at STP

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Density and the Ideal Gas Law

Combining the formula for density with theIdeal Gas law, substituting and rearrangingalgebraically:

M = Molar MassP = Pressure

R = Gas Constant

T = Temperature in Kelvins

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Gas Stoichiometry #2

How many liters of ammonia can beproduced when 12 liters of hydrogen reactwith an excess of nitrogen?

3 H2(g) + N

2(g) 2NH

3(g)

12 L H2

L H2= L NH3

L NH3

3

28.0

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Gas Stoichiometry #3How many liters of oxygen gas, at STP, can

be collected from the complete decompositionof 50.0 grams of potassium chlorate?

2 KClO3(s) 2 KCl(s) + 3 O2(g)

50.0 g KClO3 1 mol KClO3

122.55 g KClO3

3 mol O2

2 mol KClO3

22.4 L O2

1 mol O2

= 13.7 L O2

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Gas Stoichiometry #4How many liters of oxygen gas, at 37.0Cand 0.930 atmospheres, can be collectedfrom the complete decomposition of 50.0grams of potassium chlorate?

2KClO3(s) 2KCl(s) + 3O2(g)

50.0 g KClO3 1 mol KClO3

122.55 g KClO3

3mol O2

2mol KClO3=

mol O2

= 16.7 LP

nRTV

atm0.930

K))(310Kmol

atmL1mol)(0.082(0.612

0.612

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Daltons Law of Partial Pressures

For a mixture of gases in acontainer,

PTotal = P1 + P2 + P3 + . . .

This is particularly useful in calculatingthe pressure of gases collected overwater.