= let’s build it… = if the temperature of the gases in the soda increase, what happens to the...
TRANSCRIPT
THE IDEAL GAS LAW
IT ALL STARTS WITH A FORMULA
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Let’s Build It…
IT ALL STARTS WITH A FORMULA
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If the temperature of the gases in the soda increase, what happens to the pressure inside the can?
IT ALL STARTS WITH A FORMULA
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So Pressure and Temperature are __________ related
IT ALL STARTS WITH A FORMULA
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So Pressure and Temperature are directly related
IT ALL STARTS WITH A FORMULA
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They must go on opposite sides of the equation. “If one increases, the other must increase”.
P T
IT ALL STARTS WITH A FORMULA
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If the temperature of the gas in the balloon decreases, what happens to the volume of the balloon?
P T
IT ALL STARTS WITH A FORMULA
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So Volume and Temperature are __________ related
P T
IT ALL STARTS WITH A FORMULA
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So Volume and Temperature are directly related
P T
IT ALL STARTS WITH A FORMULA
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They must go on opposite sides of the equation. “If one decreases, the other must decrease”.
P TV
IT ALL STARTS WITH A FORMULA
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If you add moles of gas to the tire, what happens to the volume and the pressure in the tire?
P TV
IT ALL STARTS WITH A FORMULA
=P TV
So Volume and Pressure are __________ related to Moles
IT ALL STARTS WITH A FORMULA
=P TV
So Volume and Pressure are directly related to Moles
IT ALL STARTS WITH A FORMULA
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They must go on opposite sides of the equation. “If one increases, the other must increase”.
P TV n
IT ALL STARTS WITH A FORMULA
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There is also a “constant” of proportionality in the equation
P TV n
IT ALL STARTS WITH A FORMULA
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It is called “R”, the “Universal Gas Law Constant”
P TV n R
THE IDEAL GAS LAW FORMULA
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This law is valid under most normal conditions so don’t break it!
P TV n R
THE UNITS FOR EACH VARIABLE
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Volume is measured in Liters (L)
P TV n R
THE UNITS FOR EACH VARIABLE
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Amount is measured in Moles (mol)
P TV n R
THE UNITS FOR EACH VARIABLE
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Temperature is measured in Kelvins (K)
P TV n R
THE UNITS FOR EACH VARIABLE
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Pressure has many units. The S.I. unit for pressure is the Pascal (Pa)
P TV n R
*See the notes on “Pressure” to learn more
THE UNITS FOR EACH VARIABLE
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“R” has 4 units.Rearrange this equation to solve it for “R”
P TV n R
THE UNIVERSAL GAS LAW CONSTANT
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See why it has 4 units, now?
P TV n R
THE UNIVERSAL GAS LAW CONSTANT
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“R” has units of pressure
PTV
nR
THE UNIVERSAL GAS LAW CONSTANT
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“R” has units of pressure, volume
PTV
nR
THE UNIVERSAL GAS LAW CONSTANT
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“R” has units of pressure, volume, moles
PTV
nR
THE UNIVERSAL GAS LAW CONSTANT
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“R” has units of pressure, volume, moles and temperature
PTV
nR
THE UNIVERSAL GAS LAW CONSTANT
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To get the numerical value of “R”, you must substitute in all the standard values:
PTV
nR
(1 atm)(22.4L) (1mol)(273K)R = atm L
mol K= 0.0821
THE UNIVERSAL GAS LAW CONSTANT
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There are many different standard pressure units you could plug in:
PTV
nR
(760mmHg)(22.4L) (1mol)(273K)R = mmHg L
mol K= 62.4
THE UNIVERSAL GAS LAW CONSTANT
=
There are many different standard pressure units you could plug in:
PTV
nR
(101.3kPa)(22.4L) (1mol)(273K)R = kPa L
mol K= 8.31
EXAMPLE #1
What is the volume of 2.3 moles of hydrogen gas at a pressure of 1.2 atm
and a temperature of 20 oC?
If PV=nRT, then V =
nRT P
EXAMPLE #1
What is the volume of 2.3 moles of hydrogen gas at a pressure of 1.2 atm
and a temperature of 20 oC?
V =
(2.3 mol)
0.0821 atm L mol K
(293 K)
(1.2 atm)
EXAMPLE #1
V =
(2.3 mol)
0.0821 atm L mol K
(293 K)
(1.2 atm)
This “R”
value has atmin it
EXAMPLE #1
V =
(2.3 mol)
0.0821 atm L mol K
(293 K)
(1.2 atm)
This “R”
value has atmin it
which cancels with units of “P”
EXAMPLE #1
V =
(2.3 mol)
0.0821 atm L mol K
(293 K)
(1.2 atm)
Every unit cancels except “L” which is good because we are solving for volume!
EXAMPLE #1
What is the volume of 2.3 moles of hydrogen gas at a pressure of 1.2 atm
and a temperature of 20 oC?
V =
46 L
EXAMPLE #2
What is the temperature of 2.50 moles of helium gas at a pressure of 795 mmHg
in a 3.25 liter container?
If PV=nRT, then T =
PVnR
EXAMPLE #2
What is the temperature of 2.50 moles of helium gas at a pressure of 795 mmHg
in a 3.25 liter container?
If you want to use 0.0821 atm L for “R”, mol Kyou have to convert 795 mmHg to atm so they will cancel
EXAMPLE #2
What is the temperature of 2.50 moles of helium gas at a pressure of 795 mmHg
in a 3.25 liter container?
795 mmHg x
1 atm =760 mmHg
1.05 atm
EXAMPLE #2
What is the temperature of 2.50 moles of helium gas at a pressure of 795 mmHg
in a 3.25 liter container?
T =
(2.50 mol)
0.0821 atm L mol K
(3.25 L)(1.05 atm)
EXAMPLE #2
T =
(2.50 mol)
0.0821 atm L mol K
(3.25 L)(1.05 atm)
Every unit cancels except “K” which is good because we are solving for temperature!
EXAMPLE #1
What is the temperature of 2.50 moles of helium gas at a pressure of 795 mmHg
in a 3.25 liter container?
T =
16.6 K
WHAT IS AN “IDEAL” GAS?
A gas that behaves according to the Kinetic Molecular Theory*
(It obeys all the postulates of KMT)
*See KMT Notes for more information
WHEN IS A GAS “IDEAL”?
Never!!!!Ideal gases don’t exist
However, real gases act like “ideal” gases at most normal conditions of temperature and pressure
HUH?
Real gases follow the Kinetic Molecular Theory until…….
The temperature gets extremely lowORThe pressure gets extremely high
KMT FAILS AT LOW TEMPERATURES
The KMT says particles don’t attract or repel each other, but at very low temperatures, gas particles move very slowly and this
allows particles to attract each other when they get close
If no attractive forces, the particles will spread out
If attractive forces are present,The particles would clump together
KMT FAILS AT LOW TEMPERATURES
The KMT says particles don’t attract or repel each other, but at very low temperatures, gas particles move very slowly and this
allows particles to attract each other when they get close
If no attractive forces, the particles will spread out
And the volume would be smallerThan our gas law would predict
KMT FAILS AT HIGH PRESSURES
The KMT says particles have negligible volume, but at very high pressures, the
gas particles are smashed close together thus reducing the empty
space between them, but NOT to zero volume because the particles
themselves have some volume.
KMT FAILS AT HIGH PRESSURES
The KMT says particles have negligible volume, but at very high pressures, the
gas particles are smashed close together thus reducing the empty
space between them, but NOT to zero volume because the particles
themselves have some volume.
WHY USE THE KMT IF IT IS NOT TRUE?
Because it is a useful “model” that helps us understand and predict what gases
will do under most conditions
The KMT only breaks down under extremely low temperatures and
extremely high pressures