OBJECTIVES:
OB
ECT VE :
Unit 9
Section 12.4
The Ideal Gas Law
Calculate the amount of gas at any
specific conditions of: a) pressure, b)
volume, and c) temperature.
„ Distinguish between ideal and real
gases.
„
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We’ve Seen:
1. Boyle’s Law:
P1V1 = P2V2
2 Charles’
2.
Ch l ’ LLaw:
V1/T1 = V2/T2
3. Gay Lussac Law:
P1/T1 = P2/T2
4. Combined Gas Law:
P1V1/T1 = P2V2/T2
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Ideal Gases
What is Ideal Gas?
We are going to assume the gases
behave “ideally”
“ideally”-- obeys the Gas
Laws under all temp. and pres.
„ An ideal gas does not really exist,
exist
but it makes the math easier and is
a close approximation.
„
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GHS Honors Chem
Ideal Gases
Assumptions for Ideal Gases
1.
2.
3.
Ideal Gas Model assumes that
particles have no volume.
Ideal Gas Model assumes that
there are no attractive forces
between particles.
The Ideal Gas Law assumes that
the collisions between the gas
particles are elastic.
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There are no gases for which this is
true; however,
„ Real gases behave this way at high
temperature
p
and low p
pressure.
„
„
„
High Temperature: minimizes attractive
forces between gas particles
Low Pressure: Volume of gas sample is large.
Volume of the individual particles is
minimized relative to the entire sample.
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The Ideal Gas Law #1
The Ideal Gas Law #1
Equation: P x V = n x R x T
Equation: P x V = n x R x T
Pressure times Volume equals the
number of moles times the Ideal Gas
Constant (R) times the temperature in
Kelvin.
„ R is the Ideal Gas Constant:
„
„
„
R = 8.31 (L x kPa) / (mol x K)
R = 8.31 J / (mol x K)
„ R = 0.0821 (L x atm) / (mol x K)
„
We now have a way to relate the number
of moles, or quantity, of a gas to pressure,
temperature, and volume,
volume, at conditions
other than STP.
This equation can be rearranged to solve
for any of the variables, including:
n=
„
GHS Honors Chem
GHS Honors Chem
The Ideal Gas Law #1
Let’s Try Some Ideal Gas Law
Problems
Equation: P x V = n x R x T
„
PxV
RxT
When Calculating the variables in the
Ideal Gas Law, the units are
dependent on the R value used.
R = 8.31 (L x kPa) / (mol x K)
„ R = 8.31 J / (mol x K)
„ R = 0.0821 (L x atm) / (mol x K)
„
How many moles of air are there in a
2.0 L bottle at 19 ºC and 747 mm
Hg?
Answer: 0.082 moles
„
Otherwise Temp = K, Volume = Liters
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„
What is the pressure exerted by 1.8 g
of H2 gas in a 4.3 L balloon at 27 ºC?
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Answer: 5.16 atm
Ideal Gas Law Sample
Ideal Gas Law Sample
At what temperature will 5.00 grams Cl2
exert a pressure of 151 kPa at a volume
of 0.753 Liters?
How many moles are contained in 2.44L
sample of gas at 25.0°
25.0°C and 202 kPa?
Answer:
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194 oK
Answer:
0.2 moles
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What if we Stretch the Limit of this
Ideal Gas Law, to include other
variables?
mxRxT
M
„ Allows LOTS of calculations!
„ m = mass, in grams
„ M = molar mass, in g/mol
„ Molar mass = m R T
PV
„
PxV=
GHS Honors Chem
2.
3.
D= Mass/Volume
„ Since the Molar mass = m R T
PV
„ D = m/V
„ So, the Molar mass = D R T
P
„ And finally, Density = P x Mmass
RT
„
GHS Honors Chem
So We Have 3 Flavors of
the Ideal Gas Law
1.
Could We Consider “Ideal Gazz”
Density?
Some More Problems
„
PV = n R T
Molar mass = m R T
PV
Density = P x Mmass
RT
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Answer:
Determine the mass of sulfur dioxide,
SO2, with a volume of 2.7 L, at 303 kPa
and 303 K.
Answer:
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5.23 g/L
GHS Honors Chem
Some More Problems
„
Determine the density of an unknown
gas with a molar mass of 64 grams, at
2.0 atm and 20.0 C.
Some More Problems
„
Calculate the number of molecules in a
nitrogen gas sample that occupies a
volume of 10.0 liters at a temperature of
60.0 C and a pressure of 5.0
atmospheres.
t
h
20.8 grams
Answer:
1.10 x 1024 molecules
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So What About REAL Gases?
Ideal Gases don’t exist
Molecules do take up space
„ There are attractive forces
„ Without Attractive Forces, how would
liquids form??
„
Real Gases behave like Ideal
Gases...
„
„
„
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Real Gases behave like Ideal
gases when...
„
When molecules are moving fast
„
At high temperatures
Collisions are harder and faster.
faster
„ Molecules are not next to each other
very long.
„ Attractive forces can’t play a role.
„
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When the molecules are
far apart, they do not
take up as big a
percentage
t
off th
the space
We can ignore their
volume.
This is at low pressure
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Gas Laws
W kh 2
Worksheet
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