Gas Laws

1. Gas Laws
Chapter 14

2. Opening thoughts…
Have you ever:
Seen a hot air balloon?
Had a soda bottle spray all over you?
Baked (or eaten) a nice, fluffy cake?
These are all examples of gases at work!
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3. Properties of Gases
You can predict the behavior of gases
based on the following properties:
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Pressure
Volume
Amount (moles)
Temperature
Lets review each of these briefly…

4. NEXTPREVIOUS
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Pressure
Volume
Amount (moles)
Temperature
You can predict the behavior of gases
based on the following properties:

5. Pressure
Pressure is defined as the force the gas
exerts on a given area of the container in
which it is contained. The SI unit for
pressure is the Pascal, Pa.
• If you’ve ever inflated a tire,
you’ve probably made a
pressure measurement in
pounds (force) per square inch
(area).
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6. NEXTPREVIOUS
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Pressure
Volume
Amount (moles)
Temperature
You can predict the behavior of gases
based on the following properties:

7. Volume
Volume is the three-dimensional space inside
the container holding the gas. The SI unit for
volume is the cubic meter, m3
. A more common
and convenient unit is the liter, l.
Think of a 2-liter bottle of soda to get
an idea of how big a liter is.
(OK, how big two of them are…)
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8. NEXTPREVIOUS
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Pressure
Volume
Amount (moles)
Temperature
You can predict the behavior of gases
based on the following properties:

9. Amount (moles)
Amount of substance is tricky. As we’ve already
learned, the SI unit for amount of substance is the mole,
mol. Since we can’t count molecules, we can convert
measured mass (in kg) to the number of moles, n, using
the molecular or formula weight of the gas.
By definition, one mole of a substance contains
approximately 6.022 x 1023
particles of the
substance. You can understand why we use mass
and moles!
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10. NEXTPREVIOUS
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Pressure
Volume
Amount (moles)
Temperature
You can predict the behavior of gases
based on the following properties:

11. Temperature
Temperature is the measurement with which you’re
probably most familiar (and the most complex to
describe completely). For these lessons, we will be
using temperature measurements in Kelvin, K.
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The Kelvin scale starts at Absolute 0, which
is -273.15°C. To convert Celsius to Kelvin,
add 273.15.

12. How do they all relate?
Some relationships of gases may be easy to
predict. Some are more subtle.
Now that we understand the factors that
affect the behavior of gases, we will study
how those factors interact.
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13. How do they all relate?
Some relationships of gases may be easy to
predict. Some are more subtle.
Now that we understand the factors that
affect the behavior of gases, we will study
how those factors interact.
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Let’s go!

14. Properties of GasesProperties of Gases
Gas properties can be modeledGas properties can be modeled
using math. Model depends onusing math. Model depends on
——
• V = volume of the gas (L)V = volume of the gas (L)
• T = temperature (K)T = temperature (K)
– ALL temperatures in theALL temperatures in the
entire chapter MUST be inentire chapter MUST be in
Kelvin!!! No Exceptions!Kelvin!!! No Exceptions!
• n = amount (moles)n = amount (moles)
• P = pressureP = pressure
(atmospheres)(atmospheres)

15. Pressure and Volume: Boyle’s Law
How is the pressure applied to a gas related to its volume?
Piston
Gas molecules
Piston
Gas molecules
Boyle’s Law: P1V1 = P2V2
Volume is inversely proportional to applied pressure.

16. The Harder we Push
the smaller the gas
volume gets!
Boyle’s Law: P1V1 = P2V2

17. 340 kPa
Sample Problem 1:
If the pressure of helium gas in a balloon
has a volume of 4.0 L at 210 kPa, what will
the pressure be at 2.5 L?
P1 V1 = P2 V2

18. Temperature and Volume: Charles’s Law
How is the volume of a gas related to its temperature?
gas molecules
moveable mass
(constant pressure)
What happens if heat is applied to the gas?

19. Temperature and Volume: Charles’s Law
How is the volume of a gas related to its temperature?
gas molecules
moveable mass
(constant pressure)
Why did the volume change?
What happens to the average
speed of the gas molecules?
.

20. Temperature and Volume: Charles’s Law
How is the volume of a gas related to its temperature?
gas molecules
moveable mass
(constant pressure)
The volume of a gas is directly proportional to its
Temperature (temperature must be in Kelvin)
Charles’s Law: V1/T1 = V2/T2

21. V1 = V2
T1 T2
Sample Problem 2:
A gas sample at 40 o
C occupies a volume
of 2.32 L. If the temperature is increased
to 75 o
C, what will be the final volume?
2.58 L

22. E. Gay-Lussac’s Law
1. Volume held CONSTANT
2. Found direct relationship
between temperature & pressure
3. P1 = P2
T1 T2
http://www.marymount.k12.ny.us/marynet/06stwbwrk/06gas/1amcslussac/amcsgaylussac.html

23. P1 = P2
T1 T2
Sample Problem 3:
The pressure of a gas in a tank is 3.2 atm
at 22 o
C. If the temperature rises to 60o
C,
what will be the pressure in the tank?
3.6 atm

24. A. The Combined Gas Law
1. Amount of Gas held CONSTANT
2. P1 V1 = P2 V2
T2T1
http://kids.earth.nasa.gov/archive/air_pressure/balloon.html
3. This law combines
which 3 laws?

25. Combined Gas Law (Boyle and Charles):
T
VP
T
VP
2
22
1
11
= T must be in Kelvin
Can be rearranged to:
P1V1T2 = P2V2T1
A combined gas law problem can be recognized by
having two sets of conditions.
Note: if one set of parameters is unchanged that term
will cancel on each side.

26. Sample Problem 4:
A gas at 110 kPa and 30 o
C fills a
container at 2.0 L. If the temperature
rises to 80o
C and the pressure
increases to 440 kPa, what is the new
volume? 0.58 L

27. A. The Ideal Gas Law
1. Contains ALL variables
2. P V = n R T
3. Where
P = pressure (depends on R)
n = amount of gas (moles)
R = ideal gas constant (depends on
pressure)
T = temperature (Kelvin)
V = volume (liters)

28. R = ideal gas constant (depends on
pressure)
Pressure R value
mm Hg
torr
62.4
kPa 8.314
atm 0.0821

29. Sample Problem 6:
Calculate the volume of a gas at STP
with 2.80 moles.
62.8 L
Sample Problem 7:
Calculate the moles of a gas at STP
with a volume of 238 L.
10.6 mol

30. Sample Problem 8:
Calculate the number of moles of gas
contained in a 3.0 L vessel at 27 o
C
with a pressure of 1.50 atm.
0.18 mol

31. B. Dalton’s Law of Partial Pressure
1. Contains only pressure
3. Ptotal = P1 + P2 + P3 + . . .
2. Where pressure must be in the
same units

32. 4. Sample Problem 9:
If the total pressure of a mixture of oxygen
& nitrogen gases was 820 mmHg, how
much pressure would nitrogen exert if
oxygen had 580 mmHg?
240 mmHg

33. C. Graham’s Law of Effusion
1. Contains rates & masses of gases
2. Rate A = Mass B
Rate B Mass A
3. Where
Rate is measured in m/s
Mass is measured in grams

34. Sample Problem 8:
If neon travels at 400. m/s, estimate
the average speed of butane (C4H10) at
the same temperature.
235 m/s
Sample Problem 9:
Chlorine has a velocity of 0.0380 m/s.
What is the average velocity of sulfur
dioxide under the same conditions?
0.0400 m/s

35. Question 1
Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law
(p*V=n*R*T), when the number of moles (n) and temperature
(T) are held constant, pressure and volume are:
a. Inversely proportional: if one goes up, the other comes
down.
b. Directly proportional: if one goes up, the other goes up.
c. Not related
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36. Question 1 is Correct!
Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law
(p*V=n*R*T), when the number of moles (n) and temperature
(T) are held constant, pressure and volume are:
a. Inversely proportional: if one goes up, the other
comes down.
Decreasing volume increases
pressure. Increasing volume
decreases pressure.
pressure
volume
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37. Try Question 1 again…
Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law
(p*V=n*R*T), when the number of moles (n) and temperature
(T) are held constant, pressure and volume are:
a. Inversely proportional: if one goes up, the other comes
down.
b. Directly proportional: if one goes up, the other goes up.
c. Not related
You selected b. While pressure and volume are related,
it is not a direct proportion. Try again!
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38. Try Question 1 again…
Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law
(p*V=n*R*T), when the number of moles (n) and temperature
(T) are held constant, pressure and volume are:
a. Inversely proportional: if one goes up, the other comes
down.
b. Directly proportional: if one goes up, the other goes up.
c. Not related
You selected c. Pressure and volume are related. Is
the relationship inverse or direct?
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AGAIN
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39. Question 2
Based on Charles’ Law (V / T = constant) or the Ideal Gas
Law (p*V=n*R*T), when the number of moles (n) and pressure
(p) are held constant, volume and temperature are:
a. Inversely proportional: if one goes up, the other comes
down.
b. Directly proportional: if one goes up, the other goes up.
c. Not related
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40. Try Question 2 again…
Based on Charles’ Law (V / T = constant) or the Ideal Gas
Law (p*V=n*R*T), when the number of moles (n) and pressure
(p) are held constant, volume and temperature are:
a. Inversely proportional: if one goes up, the other comes
down.
b. Directly proportional: if one goes up, the other goes up.
c. Not related
You selected a. While volume and temperature are
related, it is not an inverse proportion. Try again!
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AGAIN
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41. Question 2 is Correct!
Based on Charles’ Law (V / T = constant) or the Ideal Gas
Law (p*V=n*R*T), when the number of moles (n) and pressure
(p) are held constant, volume and temperature are:
b. Directly proportional: if one goes up, the other goes
up.
Increasing temperature
increases volume. Decreasing
temperature decreases
volume.
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volume
temperature

42. Try Question 2 again…
Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law
(p*V=n*R*T), when the number of moles (n) and temperature
(T) are held constant, pressure and volume are:
a. Inversely proportional: if one goes up, the other comes
down.
b. Directly proportional: if one goes up, the other goes up.
c. Not related
You selected c. Pressure and volume are related. Is
the relationship inverse or direct?
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AGAIN
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43. Question 3
Lets put the Ideal Gas Law (p*V=n*R*T) to some practical
use. To inflate a tire of fixed volume, what is the most
effective way to increase the pressure in the tire?
a. Increase the force pressing on the outside of the tire.
b. Increase the temperature of the gas (air) in the tire.
c. Increase the amount (number of moles) of gas in the tire.
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44. Try Question 3 again…
Lets put the Ideal Gas Law (p*V=n*R*T) to some practical
use. To inflate a tire of fixed volume, what is the most
effective way to increase the pressure in the tire?
a. Increase the force pressing on the outside of the tire.
b. Increase the temperature of the gas (air) in the tire.
c. Increase the amount (number of moles) of gas in the tire.
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TRY
AGAIN
While increasing the load in the car might increase the
force on the tires, it would prove to be a difficult way to
adjust tire pressure. Try again!

45. Try Question 3 again…
Lets put the Ideal Gas Law (p*V=n*R*T) to some practical
use. To inflate a tire of fixed volume, what is the most
effective way to increase the pressure in the tire?
a. Increase the force pressing on the outside of the tire.
b. Increase the temperature of the gas (air) in the tire.
c. Increase the amount (number of moles) of gas in the tire.
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TRY
AGAIN
Increasing the temperature of the air in the tire would definitely increase
pressure. That is why manufacturers recommend checking air pressures
when the tires are cold (before driving). But how would you increase
temperature without damaging the tire? Is there a more practical
solution?

46. Question 3 is Correct!
Lets put the Ideal Gas Law (p*V=n*R*T) to some practical
use. To inflate a tire of fixed volume, what is the most
effective way to increase the pressure in the tire?
a. Increase the force pressing on the outside of the tire.
b. Increase the temperature of the gas (air) in the tire.
c. Increase the amount (number of moles) of gas in the tire.
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When you inflate a tire with a pump, you are adding air, or
increasing the amount of air in the tire. This will often result
in a slight increase in temperature because a tire is not a
controlled environment. Such deviations and quirks will be
discussed in class!
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