Gas Laws
A review
Important Information
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What is STP?
Standard Temperature and Pressure.
1 atm pressure and 273 Kelvin
What are standard conditions?
Pressure is still 1 atm, but the
temperature is 25 degrees C or 298 K
Units
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Units are very important in this chapter.
One must be consistent or be incorrect.
All temperature must be in Kelvin.
°C + 273 = Kelvin
Pressure may be in one of these choices:
1 atm
760 mmHg
760 torr
101.3 kPa
Effusion and Diffusion
Effusion
• The passage of a gas
through a tiny orifice.
Diffusion
• The rate at which a gas
moves from area of high
concentration to low
concentration
Boyles Law
• http://en.wikipedia.org/wiki/Boyle's_law
• Pressure and Volume are inversely
proportional when temperature is constant.
• As Pressure increases, Volume decreases
and visa versa.
• P V =P V
• If a system with a pressure of 5 atm and
45 ml is compressed to 30 ml, what is the
new pressure?
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Boyle’s Law
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P
V=
P V
5 atm 45 ml = X 30 ml
X=(5atm*45ml)/30ml
X= 7.5 atm
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Charles’ Law
• http://en.wikipedia.org/wiki/Charles's_law
• Volume and Temperature are directly
proportional when pressure is constant.
• As Volume increases, so does Temperature.
• V1 = V2
• T1 T2
• What happens to a 1 liter balloon at 25
degrees Celsius if the temperature is
reduced to 0 degrees Celsius?
Charles’ Law
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V1 1 liter
= V2 X
T1 25°C
T2 0°C
Temperature must be in Kelvin!!!! C+ 273=K
V1 1 liter
= V2 X
T1 298 K
T2 273 K
X= (1 L*273 K)/298K
X=0.916 L new volume
Gay-Lussac’s Law
• Pressure and
Temperature are
directly proportional
when the volume
remains constant.
• The pressure
increases as the
temperature in kelvin
increases.
Gay-Lussac’s Law
• What is the new pressure if a ridged
container at 1 atm and 25 °C is heated to
75° C?
• P1 1 atm
= P2 X
• T1 25°C
T2 75°C
• Temperature must be in Kelvin!!!! C+ 273=K
• P1 1 liter
= P2 X
• T1 298 K
T2 348 K
Gay-Lussac’s Law
• X= (1 L*348 K)/298K
• X= 1.17 L
Combined Gas Law
• Pressure and volume are inversely
proportional. Both Pressure and Volume
are directly proportional to temperature.
• We can combine Charles’, Boyle’s and GayLussac’s Law to form the Combined gas law.
Combined Gas Law
• You have an expandable syringe holding a
volume of 20ml at STP.
• What is the new volume at Standard
Conditions?
• P1=1 atm * V1 =20mL
P2=1 atm * V2 =X
• T1 = 273 K
= T2 = 298 K
• X= 21.8 ml
Ideal Gas Law
• The main difference with the ideal gas law
is that now we take the number of moles
of gas into consideration.
• All previous gas laws had a constant
amount of gas.
• In the ideal gas law, the number of moles
of a gas is also a variable.
• To do this the equation requires a
conversion factor called, R.
Ideal Gas Law
• PV=nRT
• Pressure times Volume equals the number
of moles times the gas constant times the
Temperature in Kelvin.
• There are many versions of the Gas
constant, R. We will use only two.
• R= 0.0821 (L*atm)/(mol*Kelvin)
• R= 8.31 (L*kPa)/(mol*Kelvin)
Units and the Ideal Gas Law
• The units of your problem must match the
units in your gas constant, R.
• If they do not you need to convert those
units that do not match.
• Example:
• I have 20 grams of neon gas at 760 mmHg
and 0° C. What is the volume of this gas?
Answer
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Which R?
I chose R=0.08206 (L*atm)/(mole*Kelvin)
First we need moles of gas not grams
20 g/(20g/mol)=1 mole of Neon
Pressure from mmHg to atm
760 mmHg*(1 atm/760 mmHg)= 1 atm
Temperture from Celsius to Kelvin
0° C +273=273 Kelvin
Answer continued
• PV=nRT
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1atm(V)= [1 mol*0.0821(L*atm)/(mol*K)]273K
V=[1mol*0.0821 (L*atm/mol*K)*273K]/1atm
Cancel your units and do the math:
V=0.0821 L/273
V= 22.4 L
In fact, all gases at STP occupy 22.4 L/mol
How to determine which to use
• Ideal or Combined?
• Does the problem mention a change in
either Temperature, Pressure or Volume?
• Combined Gas Law!
• Does the problem give or ask for the
number of grams of a gas or the number of
moles of a gas?
• Ideal Gas law!
Dalton’s Law of Partial
Pressures
• In a mixture of gases, each gas has its own
partial pressure. The total pressure in the
container is the sum of the partial
pressures.
• P =P +P +P …Pn
• It is important that all the pressures are
in the same units before adding them
together!
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Graham’s Law of Effusion
• Larger molecules will
migrate slower than a
smaller molecule under
a constant
temperature.
• This is in direct
violation of the KMT.
• REAL GASES have
significant size
Graham’s Law
• Which of these gases will effuse faster,
He, Ne, Xe?
• When all gases are at the same
temperature, they have the same kinetic
energy. Therefore the smallest gas,
Helium, will effuse faster.