UNIT X - GAS LAWS
1
I. Boyle’s Law - relates pressure with volume for a gas in a closed container at constant temperature
* apparatus:
piston
manometer
enclosed
gas
Using the computer setup, obtain pressures at the following volumes, then print a graph of your results:
Volume (cm3)
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
GRAPH:
Pressure (
)
P*V
UNIT X - GAS LAWS
2
Conclusion questions
1) Calculate the PV product and record it in the third column of your data table. What do you notice?
2) Is the graph linear? _______ Is it directly proportional? _________ Is it inversely proportional? _________
The mathematical equation is known as Boyle’s Law, and in words it says: at constant temperature, the pressure
and volume of a gas are inversely proportional. The equation for this is:
PV = K
or more commonly:
P1V1 = P2V2
T. A sample of a gas under a pressure of 722.0 mmHg has a volume of 301 cm3. If the pressure is increased to
900.0 mmHg with no change in temperature, what will the new volume be?
S. If you have a 2.00 dm3 balloon at standard pressure, and you increase its pressure to 350.0 kPa, what will its new
volume be? Assume the temperature is constant.
UNIT X - GAS LAWS
3
II. Charles’ Law – at constant pressure, the volume and temperature of a gas are directly proportional.
V
=K
T
V1 V2
=
T1 T2
* NOTE: ROOM TEMPERATURE:
25oC = ____ K
* NOTE: TEMPERATURE MUST BE IN KELVIN!!!!
Here’s something interesting:
He
6
5
CH4
4
Volume (L)
3
H 2O
2
H2
1
N 2O
-300
0
300
Temperature (oC)
What is this temperature?
T. If you have a balloon under constant pressure whose volume is 0.543 mL at room temperature, and you put it in
some boiling water, what will the new volume be? Assume pressure is constant.
S.
1) A sample of a gas has a volume of 155 cm3 when its temperature is 10.0oC. What will the volume be at a temperature of 45.0oC? Assume pressure is constant.
UNIT X - GAS LAWS
4
III. Combined Gas Law:
PV
PV
1 1
= 2 2
T1
T2
You can use this to find:
- Boyle’s Law:
- Charles’ Law:
- P vs. T Law:
* Standard Temperature and Pressure (STP): T: 273K
P: 1 atm, 76θ Torr, 76θ mmHg, or 101.3 kPa
T. If I have a 30.0 L container at STP, what will the volume be at 255oC and 133 kPa?
S.
1) If I have a 15.0 L container at STP, what will the pressure be at 52oC if the container expands to 25.3 dm3?
2) A sample of oxygen gas has a volume of 205 cm3 when its temperature is 22oC and its pressure is 30.8 kPa.
What volume will the gas occupy at STP?
UNIT X - GAS LAWS
5
V. The Ideal Gas Law
* Avogadro’s Law - under constant temperature and pressure, equal volumes of any two gases will contain
the same number of particles
- mole - a “number word” 6.02 x 1023
like dozen (12), score (20), gross (144)
602,000,000,000,000,000,000,000 OR 600 billion trillions
22.4 L
22.4 L
22.4 L
carbon
dioxide
helium
hydrogen
- each of these boxes of gas contain 6.02 x 1023 molecules of the gas
- another wording: the volume of a gas is directly proportional to the number of moles of particles
V = kn
k - constant
n - number of moles of particles
* Ideal Gas Law - a state equation (does not require change to calculate)
PV = nRT
R - universal gas constant
atm⋅ L
kPa⋅ L
R = 0.0821 mol
⋅ K = 8.31 mol ⋅ K
T.
1) A sample of hydrogen gas has a volume of 8.56 L at a temperature of 0oC and a pressure of 1.5 atm. How many
moles of hydrogen molecules are in this container?
2) If you had a 3.50 L container with 0.980mol of helium gas (He) in it, what pressure will it exert at room
temperature?
UNIT X - GAS LAWS
6
S.
1) What volume will 1.00 mole of methane (CH4) occupy at STP?
2) A 1.25mol sample of methane gas occupies a 50.0 dm3 container when 123 kPa of pressure is exerted on
it. What is the temperature of the sample?
3) If you collect 45.3 mL of hydrogen gas at a pressure of 754 mmHg and a temperature of 19oC, how many
moles of hydrogen (H2) gas did you collect?
4) Look at the reaction for the decomposition of sodium chloride under electrolysis:
2 NaCl(s) 2 Na(s) + Cl2(g)
If you begin this reaction with 15.04g of sodium chloride, and it produces 0.128 moles of chlorine gas,
what volume of chlorine gas would be produced if the reaction was performed at 99.8 kPa of pressure and a
temperature of 19oC?
UNIT X - GAS LAWS
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VI. Dalton’s Law of Partial Pressures - in a mixture of gases, the total pressure of the mixture is equal to the sum of
the pressures that each gas would exert by itself in the same volume.
1 liter container
1 liter container
1310
Torr
550
Torr
760
Torr
* mathematical:
1 liter container
Ptot = P1 + P2 + ... OR
Ptot = X1Ptot + X2Ptot + ....
X - mole fraction (% of total)
S.
1) If you have a 441 L container with nitrogen gas under a pressure of 88.3 kPa and you add some oxygen gas until
the total pressure of the mixture is 213.9 kPa, what is the partial pressure of oxygen?
2) If you have a mixture made up of 25.6% helium gas, 31.2% argon gas, and 43.2% neon gas which exerts a
pressure of 1.54 atm in a 3.0 L container, what are the partial pressures of each gas?
* When a gas is collected in a lab, it is usually bubbled through, and contained by, water. Under normal conditions, water evaporates in an amount directly proportional to its temperature. As a result, any gas collected over water will be a mixture of the desired gas and water vapor. This water vapor exerts a pressure
on the container known as the vapor pressure. Vapor pressure is directly proportional to the temperature
of the water in degrees Celsius.
3)
The equation that describes the reaction is as follows:
Mg(s) + 2 HCl(aq) MgCl2(aq) + H2(g)
If you began with 0.543g of magnesium ribbon, and reacted it with excess HCl, collecting it over water
at a temperature of 21oC and an atmospheric pressu re of 99.6 kPa, and 0.02234 moles of hydrogen gas was
produced what volume should you expect? The vapor pressure of water at 21oC is 2.48 kPa.
UNIT X - GAS LAWS
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VII. Graham’s Law of Diffusion and Effusion - under constant temperature and pressure, gases diffuse at a rate
inversely proportional to the square roots of their densities.
v1
= rr =
v2
FM 2
FM1
(can use densities also)
* diffusion – the process through which two or more different gases spontaneously mix with each other
* effusion – the process through which a gas in a closed container escapes through a small opening
* Basic Rule: lighter gases diffuse and effuse more quickly than heavier gases
T.
1) What is the relative rate of diffusion for Neon (FM = 20.2 g/mol) vs. Argon (FM = 40.0 g/mol)?
Which gas travels faster?
2) If a mystery gas diffuses 1.48 times faster than carbon dioxide (FM = 44.0 g/mol), what is the molecular mass of
the mystery gas?
S.
1) What is the relative rate of diffusion for Helium (FM = 4.00 g/mol) vs. Radon (FM = 222 g/mol)?
Which gas travels faster?
2) If helium diffuses 4.21 times faster than a mystery gas, what is the molecular mass of the gas?
UNIT X - GAS LAWS
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VIII. Kinetic Theory of the Gas Laws - can we explain why they work the way they do?
* ideal gas – any gas which follows the five assumptions below
- i.e. any gas that obeys the mathematical models perfectly
- some gases are more ideal than others
* 5 assumptions:
1) Gases are composed of tiny particles of negligible volume separated by lots of space
2) Gas particles travel in a straight-line motion until a collision occurs.
3) All collisions are elastic.
4) Particles display no attractive or repulsive forces for each other.
5) All particles have different velocities, but the average of the velocities remains the same unless
the temperature changes.
Temperature α ave.KE
* Explain, using Kinetic theory why:
- Boyle’s Law
- Charles’ Law
UNIT X - GAS LAWS
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- Guy-Lussac’s (P-T) Law
- Dalton’s Law
+
=
- Graham’s Law
vs.
IX. When do gases not behave ideally?
- extremely high pressures
- extremely low temperatures
- vander Waal’s Equation