Unit 8 - Gases

```Unit 8
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
Characteristics of Gas
Pressure
 Partial Pressures
 Mole Fractions

Boyles Law
Charles Law
Avogadro’s Law
Guy-Lussac’s Law
Ideal Gas Law
Ideal Gases
Real Gases
Density of Gases
Volumes of Gases
 Standard molar volume
 Gas stoichiometry
Gas Laws
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Effusion/Diffusion
 Graham’s Law
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Expansion – gases expand to fill their containers
Compression – gases can be compressed
Fluids – gas particles flow past each other
Density – gases have low density
 1/1000 the density of the equivalent liquid or solid

Gases effuse and diffuse
1.
Gases consist of large numbers of tiny particles that are
far apart relative to their size.
2.
Collisions between gas particles and between particles
and container walls are elastic.

Elastic collision – collision in which there is no net loss of
kinetic energy
3.
Gas particles are in continuous, rapid, random motion.
They therefore possess kinetic energy.
4.
There are no forces of attraction between gas particles.
5.
The temperature of a gas depends on the average kinetic
energy of the particles of the gas.

At the same conditions of temperature, all
gases have the same average kinetic energy
KE 
1
2
mv
2
m = mass
v = velocity
At the same temperature, small molecules
move FASTER than large molecules
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V = velocity of molecules
M = molar mass
R = gas constant
T = temperature

A force that acts on a given area
Force
Pressure =
Area

The first device for
measuring atmospheric
pressure was developed
by Evangelista Torricelli
during the 17th century
 Called a barometer

The normal pressure due
to the atmosphere at sea
level can support a
column of mercury that
is 760 mm high

1 atmosphere (atm)
 760 mm Hg (millimeters of mercury)
 760 torr
 1.013 bar
 101300 Pa (pascals)
 101.3 kPa (kilopascals)
 14.7 psi (pounds per square inch)

Standard Temperature and Pressure (STP)
 1 atmosphere
 273 K
Partial pressure – pressure exerted by particular
component in a mixture of gases
 Dalton’s Law states that the total pressure of a gas
mixture is the sum of the partial pressures of the
component gases

Pt = P1 + P2 + P3+…

Mole fraction – expresses the ratio of the number of moles of
one component to the total number of moles in the mixture
P1 =
Pt or P1 = X1Pt
X1 = mole fraction of gas 1
Example: The mole fraction of N2 in air is 0.78 (78% of air is
nitrogen). What is the partial pressure of nitrogen in mmHg?
PN2 = (0.78)(760 mmHg) = 590 mmHg
Gas collected by water
displacement is always
mixed with a small
amount of water vapor
 Must account for the
vapor pressure of the
water molecules

Ptotal = Pgas + PH2O
Note: The vapor pressure of water varies with temperature
Robert Boyle
Jacques Charles
Amadeo Avogadro
Joseph Louis Gay-Lussac
Pressure is inversely proportional to volume
when temperature is held constant.
P1V1  P2V 2
The volume of a gas is directly proportional to
temperature.
(P = constant)
V1
T1

V2
T2
Temperature MUST be in
KELVINS!
The pressure and temperature of a gas are
directly related, provided that the volume
remains constant.
P1
T1

P2
T2
Temperature MUST be in
KELVINS!
Expresses the relationship between pressure, volume
and temperature of a fixed amount of gas
P1V1
T1

P2V 2
T2
For a gas at constant temperature and
pressure, the volume is directly proportional
to the number of moles of gas (at low
pressures).
V = constant × n
V = volume of the gas
n = number of moles of gas
For example,
doubling the moles
will double the
volume of a gas

Imaginary gases that perfectly fit all of the
assumptions of the kinetic molecular theory
PV = nRT
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P = pressure
V = volume
n = moles
R = ideal gas constant
T = temperature (Kelvin)
Numerical Value of R
Units
0.0821
(atm∙L)/(mol∙K)
8.314
J/(mol∙K)
62.4
(mmHg∙L)/(mol∙K)
Note: 1 J = 1 Pa∙m3

STP of 1 mole of gas = 1 atm and 273K
PV = nRT
(1atm)(V) = (1mol)(.0821)(273)
V = 22.4 L

Volume of 1 mole of gas at STP = 22.4 liters

Real Gas – does not behave completely
according to the assumptions of the kinetic
molecular theory

At high pressure (smaller volume) and low
temperature gases deviate from ideal
behavior
 Particles will be closer together so there is
insufficient kinetic energy to overcome attractive
forces

The Van der Waals Equation adjusts for nonideal behavior of gases (p. 423 of book)
2

 n  
 Pobs  a    x (V  nb )  nR T
 V  

corrected pressure
Pideal
corrected volume
Videal
… so at STP…


Combine density with the ideal gas law
(V = p/RT)
M = Molar Mass
P = Pressure
R = Gas Constant
T = Temperature in Kelvins
If reactants and products are at the same conditions
of temperature and pressure, then mole ratios of
gases are also volume ratios.
3 H2(g)
3 moles H2
3 liters H2
+ N2(g)

2NH3(g)
+ 1 mole N2

2 moles NH3
+ 1 liter N2

2 liters NH3
How many liters of ammonia can be produced when
12 liters of hydrogen react with an excess of
nitrogen?
3 H2(g) + N2(g)  2NH3(g)
12 L H2
2 L NH3
3 L H2
=
8.0 L NH3
How many liters of oxygen gas, at STP, can be
collected from the complete decomposition of 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
22.4 L O2
2 mol KClO3
1 mol O2
= 13.7 L O2
How many liters of oxygen gas, at 37.0C and 0.930
atmospheres, can be collected from the complete
decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s)  2 KCl(s) + 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
122.55 g KClO3
V
nRT
P

2 mol KClO3
(0.612 mol)(0.082
1
L  atm
mol  K
0.930 atm
=
0.612
mol O
2
)(310 K)
= 16.7 L
Spontaneous mixing of two
substances caused by the
random motion of particles
 The rate of diffusion is the
rate of gas mixing
 The rate of diffusion
increases with temperature
 Small molecules diffuse
faster than large molecules

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Process by which gas particles pass through a
tiny opening

Rate of effusion of gases at the same temperature and
pressure are inversely proportional to the square roots
of their molar masses.
M1 = Molar Mass of gas 1
M2 = Molar Mass of gas 2
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