Behavior of
Gases
Example of Importance of Gases
Airbags fill with N2 gas in an accident.
Gas is generated by the decomposition of sodium azide
Gas molecules save your life!
2 NaN3 ---> 2 Na + 3 N2
Kinetic Molecular Theory (KMT)

Particles in an ideal gas…
have no volume.
 have elastic collisions.
 are in constant, random, straight-line motion.
 don’t attract or repel each other.
 have an avg. KE directly related to Kelvin
temperature.

Real Gases

Particles in a REAL gas…



have their own volume
attract each other
Gas behavior is most ideal…




at low pressures
at high temperatures
when very small in size
when nonpolar
PLIGHT
Characteristics of Gases

Gases expand to fill any container uniformly.


Are in random motion, have no attraction
Gases have very low densities.

Particles have no volume = lots of empty space
Characteristics of Gases

There is a lot of “free” space in a gas.

Gases can be compressed.

no volume = lots of empty space

Gases undergo diffusion & effusion.
Are always in random motion
 Smaller and lighter gas particles do this faster

Gas Pressure
force
pressure 
area
Which shoes create the most pressure?
What Causes Pressure?
 http://www.chm.davidson.edu/vce/kineticm
oleculartheory/Pressure.html

Factors Affecting Gas Pressure

Number of Moles (Amount of gas)
 As # of particles increase, the number of
collisions with the container wall increases.

Volume
 Smaller the volume, the greater the pressure
exerted on the container.

Temperature
 As temp. increases, KE increases, this increases
frequency of collisions making pressure
increase.
Measuring Gas Pressure

Barometer
measures atmospheric pressure
 (developed by Torricelli in 1643)

Aneroid Barometer
Mercury Barometer

Standard Pressure (Sea Level)
101.3 kPa (kilopascal)
1 atm
760 mm Hg (also called torr)
You may be asked to convert between units of pressure!
Hg rises in tube until force of
Hg (down) balances the force
of atmosphere (pushing up).
(Just like a straw in soft drink)
Column height measures
pressure of atmosphere
1 standard atmosphere (atm)
= 760 mm Hg (or torr)
Measuring Gas Pressure

Manometer

measures contained gas pressure
U-tube Manometer
The Gas Laws
Working
with
Formulas
Temperature

Always use absolute temperature (Kelvin)
when working with gases.
ºC
-273
0
100
K
0
273
373
K = ºC + 273
Gas properties can be modeled using math.
Model depends on:

V = volume of the gas (L)

T = temperature (K)
 ALL
temperatures MUST be in Kelvin!!!

n = amount (moles)

P = pressure (atmospheres or kPa)
STP
Standard Temperature & Pressure
0°C
273 K
-OR-
1 atm
101.325 kPa
760 mmHg
Boyle’s Law

Robert Boyle
(1627-1691). Son
of Earl of Cork,
Ireland.
The pressure and volume of a
gas are inversely related

at constant mass & temp
PV = k
P
V
Boyle’s Law

Since P x V is always a constant:
P1 x V1 = P2 x V2
Pressure and
Volume Relationship
http://www.chm.david
son.edu/vce/kineticm
oleculartheory/PV.htm
l
If Mass and Temp are Constant
Boyle’s Law
Balloon
in a
Vacuum
Charles’ Law

Jacques Charles
(1746-1823). Isolated
boron and studied
gases. Balloonist.
The volume and absolute
temperature (K) of a gas are
directly related

V
T
at constant mass & pressure
V
k
T
Charles’ Law

Since V/T is always a constant:
V1
T1
=
V2
T2
If Mass and Pressure are Constant
Charles’ Law
Pour Liquid
Nitrogen on
Balloon!!
http://group.chem.iastate.edu/Greenbowe/sections/projectfolder/flas
hfiles/gaslaw/charles_law.html
http://www.pinnaclescience.com/demo.htm
Gay-Lussac’s Law

The pressure and absolute
temperature (K) of a gas are
directly related

at constant mass & volume
P
k
T
P
T
Gay – Lussac’s Law

Since P/T is always a constant:
P1
T1
=
P2
T2


Pressure and Temperature Relationship
http://www.chm.davidson.edu/vce/kineticmoleculartheory
/PT.html
Review of 3 Gas Laws
Summary of Changing Variables
http://www.mhhe.com/physsci/chemistry/es
sentialchemistry/flash/gasesv6.swf
Combined Gas Law (on Ref Table)
The good news is that you don’t have to remember all three gas laws!
We can combine them into a single equation.
If you should only need one of the other gas laws, you can cover up the
item that is constant and you will get that gas law!
P 1V 1
T1
=
P 2V 2
T2
P 1 V 1T 2 = P 2V 2 T 1
Example
A sample of helium gas has a volume of
0.180 L, a pressure of 0.800 atm and a
temperature of 29°C.
What is the new temperature (°C) of the
gas at a volume of .090 L and a pressure
of 3.20 atm?
Set up Data Table
P1 = 0.800 atm
P2 = 3.20 atm
V1 = .180 L
V2= .090 L
T1 = 302 K
T2 = ??
Gas Law Problems

A gas occupies 473 ml at 36°C. Find its
volume at 94°C.
CHARLES’ LAW
GIVEN: T V
V1 = 473 ml
T1 = 36°C = 309K
V2 = ?
T2 = 94°C = 367K
WORK:
P1V1T2 = P2V2T1
(473 ml )(367 K)=V2(309 K)
V2 = 562 ml
Gas Law Problems

A gas occupies 100. mL at 150. kPa. Find
its volume at 200. kPa.
BOYLE’S LAW
GIVEN: P V
V1 = 100. mL
P1 = 150. kPa
V2 = ?
P2 = 200. kPa
WORK:
P1V1T2 = P2V2T1
(150.kPa)(100.mL)=(200.kPa)V2
V2 = 75.0 mL

Gas Law
A gas occupies
7.84 mlProblems
at 71.8 kPa & 25°C.
Find its volume at STP.
COMBINED GAS LAW
GIVEN: P T V WORK:
V1 = 7.84 ml
P1V1T2 = P2V2T1
P1 = 71.8 kPa
(71.8 kPa)(7.84 ml)(273 K)
T1 = 25°C = 298 K
=(101.325 kPa) V2 (298 K)
V2 = ?
P2 = 101.325 kPa V2 = 5.09 ml
T2 = 273 K
Gas Law Problems

A gas’ pressure is 765 torr at 23°C. At
what temperature will the pressure be 560.
torr?
GAY-LUSSAC’S LAW
GIVEN: P T WORK:
P1 = 765 torr
P1V1T2 = P2V2T1
T1 = 23°C = 296K (765 torr)T2 = (560. torr)(309K)
P2 = 560. torr
T2 = 226 K = -47°C
T2 = ?
Dalton’s Law of Partial Pressures

Ptotal = P1+P2+….
Total pressure of a mixture of gases in a
container is the sum of the individual
pressures (partial pressures) of each gas,
as if each took up the total space alone.
 This is often useful when gases are
collected “over water”

Dalton’s Law of
Partial Pressures

The total pressure of a mixture of
gases equals the sum of the partial
pressures of the individual gases.
Ptotal = P1 + P2 + ...
Patm = PH2 +
PH2O
Dalton’s
Law
 Hydrogen gas is collected over water at
22.5°C. Find the pressure of the dry gas if the
atmospheric pressure is 94.4 kPa.
The total pressure in the collection bottle is equal to atmospheric
pressure and is a mixture of H2 and water vapor.
GIVEN:
PH2 = ?
Ptotal = 94.4 kPa
PH2O = 2.72 kPa
Look up water-vapor pressure
on for 22.5°C.
WORK:
Ptotal = PH2 + PH2O
94.4 kPa = PH2 + 2.72 kPa
PH2 = 91.7 kPa
Sig Figs: Round to least number
of decimal places.

Dalton’s Law
A gas is collected over water at a temp of 35.0°C when
the barometric pressure is 742.0 torr. What is the partial
pressure of the dry gas?
The total pressure in the collection bottle is equal to barometric
pressure and is a mixture of the “gas” and water vapor.
DALTON’S LAW
GIVEN:
Pgas = ?
Ptotal = 742.0 torr
PH2O = 42.2 torr
Look up water-vapor pressure
for 35.0°C.
WORK:
Ptotal = Pgas + PH2O
742.0 torr = PH2 + 42.2 torr
Pgas = 699.8 torr
Sig Figs: Round to least number
of decimal places.
Graham’s Law

Diffusion


Spreading of gas molecules throughout a
container until evenly distributed.
Effusion

Passing of gas molecules through a tiny
opening in a container
Graham’s Law

Speed of diffusion/effusion

Kinetic energy is determined by the
temperature of the gas.

At the same temp & KE, heavier molecules
move more slowly.
Avogadro’s Principle

Equal volumes of gases contain
equal numbers of moles


at constant temp & pressure
true for any gas
Equal volumes of gases at the same T and P have the
same number of molecules.
V
k
n
V
n