The Combined
&
Ideal Gas Laws
The Combined Gas Law
• The combined gas law takes the relationships described by
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Boyle’s, Charles’ and Gay-Lussac’s Laws and expresses
them together in one formula.
It is important to note that the amount of the gas (moles)
is held constant throughout any calculations involving the
combined gas law.
The formula for the combined gas law is:
P1V1 = P2V2
T2
T1
• If you cross multiply, you can rearrange the formula into
the following which may be easier to manipulate when
finding a missing value.
P1V1T2 = P2V2T1
Molar Volume of Ideal Gases
• We have discussed two sets of conditions that act as
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standards when describing gases – STP and SATP.
STP = 101.3kPa & 273K (0°C)
SATP = 100kPa & 298K (25°C)
Each of these sets of standards has a standard
molar volume associated with it. The molar
volume is the amount of space that one mole of
the gas would take up if it were in one of the sets of
conditions- STP or SATP.
For STP, any gas will take up 22.4L/mol. A single
morel takes up 22.4L of space.
For SATP, any gas will take up 24.8L/mol. A single
mole takes up 24.8L of space.
The Ideal Gas Law
• The ideal gas law illustrates the relationship between
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pressure, volume , temperature and moles. Remember,
moles was always held at a constant previous to this.
The formula for the ideal gas law is:
• In this formula:
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–
–
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PV = nRT
P = Pressure
V = Volume
n = Moles
T = Temperature
R = The Ideal Gas Constant
• The “R” is new to you – it is the Ideal Gas Constant
and it has a value of 8.31 kPa·L/K·mol.
The Ideal Gas “R” Value
• The “R” in the Ideal Gas Law is a constant and has
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a value of 8.31 kPa·L/K·mol. Notice it has all of
the units of the other four parts of the law – this is
so it can be used to cancel out three of those parts
when solving for the fourth. (You’ll see what I
mean shortly.)
Where does it come from?
When this formula was developed, the chemists
used SATP values as the starting point.
– P = 100kPa
– T = 298K (25°C)
– V = 24.8L/mol (This value is the molar volume of any gas
at SATP.)
• Now we need to use the combined gas law…
Calculating the “R” Value
• Using the combined gas law we know that the
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relationship between P, V & T is…
P1V1
T1
If we plug in our SATP values in this formula, we
will get…
(100kPa)(24.8L/mol)
(298K)
We will work the rest of this out on the board –
watch carefully and the Ideal Gas Constant will
magically appear before your eyes.
Now…go forth and solve the many issues
concerning ideal gases everywhere.
THE END