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Standard Temp and Pressure, STP
• For gases, chemists have defined a standard set of conditions: standard temperature and pressure or STP.
• STP is defined as 1.00 atm pressure and 0°C or
273.15K.
• If a 1.00 mol sample of ANY gas is at STP, then the volume which this sample occupies is 22.414L.
• This means that at STP, we have another conversion factor: 1mol = 22.414L
• Problem: A 12.37L sample of gas is at STP. How many moles are in this sample?
2

Using PV=nRT to find density
• Density of gases is given as mass/volume or g/L.
•
But in PV = nRT, this is very close to n/V or mol/volume.
•
•
Then we have: n
=
V
P
RT
•
But we really want g/L, not mol/L.
•
How can we get from n in mol to g?
3

Using PV=nRT to find density
•
We know that: n = g/MW where MW is the molar mass (really mol. mass)
•
Now we substitute in n = g/MW in the above to get:
• Problem: Find the density of helium at STP and at
30°C and 1.00atm.
4

Using PV=nRT to find MW
• This is similar to the above:
5

Dalton’s Law of Partial Pressures
• When we have a mixture of 2 or more gases, they act essentially independently of each other.
•
This means that they each exert their own pressure, or partial pressure.
•
Therefore, the total pressure of the gas mixture is equal to the sum of the partial pressures of the individual gases in the mixture.
• This is stated thus:
P
T
= P
1
+ P
2
+....
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Dalton’s Law of Partial Pressures
•
We also use mol fractions, X i
:
X i
= n i and X
1
+ X
2
+ ... = 1 n
T but P and n are
so P i
= X i
P
T
•
If the partial pressure of water vapor is
23.756 torr at 25°C, what is the mol fraction of oxygen if atmospheric pressure is 765 torr?
7

RMS Speed of Gas Particles
•
For gas particles, we talk about the rootmean square speed (RMS speed) of particles instead of the average speed:
RMS = m
so KE = 0.5m
m
2 but it is true for 1 mol of gas: KE = 3
2 so solving for m
gives:
RT m
=
3RT
MW
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RMS Speed of Gas Particles
•
What does this mean?
•
That heavy gases move slower than light ones!
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Graham’s Law of Effusion
• Effusion is when gas particles escape through pinholes.
•
Diffusion is when gas particles mix throughout a container.
•
The speed or rate of effusion is related to the molar mass or molecular weight as seen above.
r
1
MW
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Graham’s Law of Effusion
• More importantly, we can compare the rates of
2 gases: r r
1
2
=
3RT
MW
1
=
3RT
MW
2
MW
2
MW
1
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Graham’s Law of Effusion
• Again, this tells us what we already knew (or would have guessed intuitively): lighter gases effuse faster.
•
However, this difference in the rate of effusion is actually used to separate gases with different molecular weights.
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Gas Stoichiometry
• We can use PV = nRT or the fact that at STP 1 mol =
22.414 L to solve gas stoichiometry problems.
• Let’s look at the rxn of hydrogen gas with oxygen gas to produce liquid water:
• How many g of water can be produced from 5.72 L of hydrogen gas at STP?
•
If 17.9 g of water is produced at 25°C and 1.00 atm, how many liters of oxygen were consumed?
13

Deviations from the Ideal Gas Law
• The Ideal Gas Law, PV = nRT is based on some assumptions.
1) Gases have negligible volume!
–
Wrong! Particularly for high pressures, the volume of gas particles may take up as much as 10% of the total volume of the container.
–
This means that gas particles exert a greater pressure, or P real
> P ideal
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Deviations from the Ideal Gas Law
• Next wrong assumption:
2) Gas particles have no interactions!
– Wrong! They do interact to some extent.
– When they do interact, the pressure decreases, or
P real
< P ideal
• So these 2 factors tend to cancel each other out, and for pressures below around 4 atm, they pretty much do!
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Deviations from the Ideal Gas Law
• So if the pressure is below 4 atm, we ignore deviations from ideal gas behavior.
•
For intermediate pressures the gas particle interactions are more important, so P real
P ideal
.
<
•
For high pressures the particles are closer and closer together, so the volume effect is much greater, or P real
> P ideal
.
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Deviations from the Ideal Gas Law
• These 2 deviation may be seen in the Van der
Waals equation (don’t need to memorize or use):
æ
ææ
P + n
2 a
V
2
æ
ææ
(
V - nb
)
= nRT
OR nRT
P real
=
V-nb
- n
2 a
V
2
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Deviations from the Ideal Gas Law
• What’s really important about deviations?
•
What conditions favor deviations?
–
High Pressures (favors high volume)
–
Low temperatures (favors interactions)
18

Deviations from the Ideal Gas Law
•
What type of molecular or atomic properties lead to higher deviations?
–
The higher the mass or the larger the size, the larger the deviation (so for He,
Ne, Ar, Kr, and Xe, Xenon would have the highest deviation.)
–
The more polar the substance, the larger the deviation. So water would deviate more than methane.
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