Combined Gas Laws

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Combined Gas Laws
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• A combination of Boyles and Charles Law.
• Used when pressure and temperature change at the
  same time.
• Solve the equation for any one of the 6 variables

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calculate final volume
final volume
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increases or decreases volume
final volume
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increases or decreases volume
final volume
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A sample of hydrogen occupies 465 ml at STP. If
the pressure is increased to 950 torr and the
temperature is decreased to 15oC, what would be
the new volume?

• Step 1. Organize the given information, putting
  temperature in Kelvins

oC 273 K
0oC 273 273 K
-15oC 273 258 K
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A sample of hydrogen occupies 465 ml at STP. If
the pressure is increased to 950 torr and the
temperature is decreased to 15oC, what would be
the new volume?

• Step 1. Organize the given information, putting
  temperature in Kelvins

P1 760 torr P2 950 torr V1 465 mL V2 ? T1
273 K T2 258 K
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A sample of hydrogen occupies 465 ml at STP. If
the pressure is increased to 950 torr and the
temperature is decreased to 15oC, what would be
the new volume?

• Method A Conversion Factors
• Step 2. Set up ratios of T and P

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A sample of hydrogen occupies 465 ml at STP. If
the pressure is increased to 950 torr and the
temperature is decreased to 15oC, what would be
the new volume?

• Step 3. Multiply the original volumes by the
  ratios

P1 760 torr P2 950 torr V1 465 mL V2 ? T1
273 K T2 258 K
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A sample of hydrogen occupies 465 ml at STP. If
the pressure is increased to 950 torr and the
temperature is decreased to 15oC, what would be
the new volume?

• Method B Algebraic Equation

Step 2. Write and solve the equation for
the unknown V2.
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A sample of hydrogen occupies 465 ml at STP. If
the pressure is increased to 950 torr and the
temperature is decreased to 15oC, what would be
the new volume?

• Step 2 Put the given information into the
  equation and calculate.

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Daltons Law ofPartial Pressures
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• Each gas in a mixture exerts a pressure that is
  independent of the other gases present.

The total pressure of a mixture of gases is the
sum of the partial pressures exerted by each of
the gases in the mixture.
Ptotal Pa Pb Pc Pd .
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A container contains He at a pressure of 0.50
atm, Ne at a pressure of 0.60 atm, and Ar at a
pressure of 1.30 atm. What is the total pressure
in the container?

• Ptotal PHe PNe Par
• Ptotal 0.5 atm 0.6 atm 1.30 atm 2.40 atm

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Collecting a Gas Sample Over Water

• The pressure in the collection container is equal
  to the atmospheric pressure.
• The pressure of the gas collected plus the
  pressure of water vapor at the collection
  temperature is equal to the atmospheric pressure.

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Oxygen collected over water.
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A sample of O2 was collected in a bottle over
water at a temperature of 25oC when the
atmospheric pressure was 760 torr. The vapor
pressure of water at 25oC is 23.8 torr.
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Avogadros Law
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Gay Lussacs Law of Combining Volumes
When measured at the same temperature and
pressure, the ratio of the volumes of reacting
gases are small whole numbers.
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Gay Lussacs Law of Combining Volumes
When measured at the same temperature and
pressure, the ratio of the volumes of reacting
gases are small whole numbers.
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Gay Lussacs Law of Combining Volumes
When measured at the same temperature and
pressure, the ratio of the volumes of reacting
gases are small whole numbers.
O2
?
2H2O

2H2
Figure 12.12
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Avogadros Law
Equal volumes of different gases at the same
temperature and pressure contain the same number
of molecules.
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hydrogen chlorine ? hydrogen chloride
1 volume 1 volume 2 volumes
1 molecule 1 molecule 2 molecules
1 mol 1 mol 2 mol
Each molecule of hydrogen chloride contains at
least 1 atom of hydrogen and 1 atom of chlorine.
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H2 Cl2 ? 2 HCl
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Ideal Gas Equation
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V a
P
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V a
P
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V a
P
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V a
P
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Ideal Gas Constant
V a
P
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A balloon filled with 5.00 moles of helium gas
is at a temperature of 25oC. The atmospheric
pressure is 750. torr. What is the balloons
volume?

• Step 1. Organize the given information.
• Convert temperature to kelvins.

K oC 273
K 25oC 273 298K
Convert pressure to atmospheres.
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A balloon filled with 5.00 moles of helium gas
is at a temperature of 25oC. The atmospheric
pressure is 750. torr. What is the balloons
volume?

• Step 2. Write and solve the ideal gas equation
  for the unknown.

Step 3. Substitute the given data into the
equation and calculate.
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Determination of Molecular Weights Using the
Ideal Gas Equation
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Calculate the molar mass of an unknown gas, if
0.020 g occupies 250 mL at a temperature of 305 K
and a pressure of 0.045 atm.
V 250 mL 0.250 L
g 0.020 g
P 0.045 atm
T 305 K
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The End