Today…
1) Addressing Some CURIOUS questions
2) Take-up Homework
2) Minds-On-Making Connections to Charles
Law and Gay Lussacs Law
3) Combined Gas law and Dalton’s Law of
Partial Pressures
Celsius and Kelvin Scales
If you double the degrees
Celsius, what happens to
the temperature in Kelvin?
• Graph of four experiments in which the same amount of gas
was used and data were collected at four different pressures
(P1 to P4).
• The solid lines represent actual data, dashed lines represent
extrapolated values.
• All of the plots intersect at −273.15°C.
Why Kelvin and Not Celsius for gas temperature?
Identify the x and
y-intercepts for
each graph.
(A) Using the Celsius temperature scale produces straight-line
graphs that have three different y-intercepts. (not a direct
proportion, doubling temp does not double volume)
(B) Using the Kelvin temperature scale produces straight-line
graphs with the same y-intercept (direct proportion, y-intercept
0, doubling temp doubles the volume)
Combined Gas Laws and
Dalton’s Law of Partial Pressures
The Combined and
Ideal Gas Laws
• All three variables can be changed at the
same time: Temperature, Pressure, and
Volume.
• A combination of Boyle’s and Charles’s
law.
• When the mass (amount) of gas is
constant you can use: P V
PV
1
T1
1
=
2
T2
2
Different forms of Equations
P1V1 = P2V2
T1
T2
V 1 = P 2V 2 T 1
P1T2
T 1 = P 1V 1 T 2
V2 P2
P 1 = P 2V 2 T 1
T2 V1
V 2 = P 1V 1 T 2
T 1 P2
T 2 = P 2V 2 T 1
V 1 P1
P2 = P1V1 T2
T1 V2
pressure and volume of a given amount of
gas are inversely proportional to each other,
and directly proportional to the Kelvin
temperature of the gas.
The Combined Gas law
Sample Problem:
• A weather balloon with a volume of 55.0 L
is filled with hydrogen gas at a pressure of
98.5 kPa and a temperature of 13ºC.
When the balloon is released, it rises to
the stratosphere, where the temperature is
-48ºC and the pressure is 19.7 kPa. What
is the volume of the balloon under these
conditions?
Plan your strategy
Act on your strategy
-None of them remain constant!
-Which law: Combined Gas Law
P1V1/T1 = P2V2/T2
-Isolate the variable you are
looking for (in this case it is V2)
-Remember to convert the
temperatures into Kelvin.
V2 = P1V1T2/P2T1
Plug the numbers (and units) of
the known variables into the
equation.
V2 = (98.5 kPa)(55.0 L)(225
K)/(286 K)(19.7 kPa) = 216 L
Conclusion: The volume at -48ºC and 19.7 kPa is 216 L.
Class work Worksheet: Combining Gas Laws
Dalton’s Law of Partial Pressures
Gas Mixtures:
In a mixture of gases, each gas exerts a pressure.
The pressure exerted by a single gas in a mixture is
called the Partial pressure of the gas.
Dalton observed….
Law of Partial Pressures: The total pressure of a
Mixture of gases is equal to the sum of the partial
pressures of the component gases (if the gases do not
react chemically).
Mathematically this means that if a mixture is made of two
gases, A and B, then:
Pt = PA + PB
Pt = Total pressure
PA = Partial pressure of gas A
PB = Partial pressure of gas B
• When two separate gases originally at the
same temperature are mixed, the
temperature—and thus the average speed
of the gases—does not change. Only the
total number of molecules in the container
increases.
• Therefore there are more molecules
colliding with the walls of the container
and, thus, the pressure is higher.
Pressure of a Gas
• The pressure of a gas in a mixture is also
related to the amount of molecules of that
gas in the mixture. Mathematically this can
be stated as: P = P x n A
A
nA
n total
total
n total
is called the mole fraction of gas A.
Mole Fraction of a Gas
the number of moles of gas A divided by the
total number of moles of ALL gases in the
mixture.
Recap of Key Formulas
PT = PA + PB
PT = Total pressure
PA = Partial pressure of A
PB = Partial pressure of B
_nA_ = mole fraction A
ntotal
nA = moles of gas A
ntotal = Total moles of gas
PA = Pt x nA
ntotal
PA = partial pressure of A
Pt = total pressure
nA = moles of gas A
ntotal = total moles of gas
Partial Pressure Sample Problem
A mixture of 6.0 g of argon gas and 8.0 g of
oxygen gas has a total pressure of 66 kPa.
Calculate the partial pressure exerted by
each gas.
Plan your strategy
Act on your strategy
-This is a partial pressure
problem
PT = PAr + PO2
PAr = Ptotal x nAr/ntotal
PO2 = Ptotal x nO2/ntotal
i) -Convert each mass
into moles and find
ntotal.
i) nAr = 6 g/39.95 g/mol = 0.15 mol
nO2 = 8 g/32 g/mol = 0.25 mol
ntotal = 0.25 mol + 0.15 mol = 0.40 mol
ii) -Find the mole fraction
of each gas.
nA = mole fraction A
ntotal
-To find the partial
pressure of each gas:
PA = Pt x nA
ntotal
ii) nAr = mole fraction Ar
= 0.15 mol/0.40 mol = 0.375 ntotal
nO2 = mole fraction O2
= 0.25 mol/0.40 mol = 0.625
ntotal
PAr = Pt x nAr = 66 kPa x 0.375 = 25 kPa
ntotal
PO2 = Pt x nO2 = 66 kPa x 0.625 = 41 kPa
ntotal
Conclusion: To check, add both partial pressures together. If their sum is equal
to your total pressure (i.e. 66 kPa), then you have done the problem correctly
and successfully!