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1. COMBINED GAS
LAW

2. STP: you need to memorize this
Standard Temperature & Pressure
0°C 273 K
1 atm or 101.325 kPa
1atm = 760 torr

3. 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.

4. Boyle’s Law
This lesson introduces Boyle’s Law, which
describes the relationship between pressure and
volume of gases.
P
V
P1V1 = P2V2

5. Boyle’s Law
 This law is named for Charles Boyle, who
studied the relationship between pressure,
p, and volume, V, in the mid-1600s.
 Boyle determined that for the same amount
of a gas at constant temperature, results in
an inverse relationship:
when one goes up, the other
comes down.
pressure
volume

6. Charles’ Law
This lesson introduces Charles’ Law, which
describes the relationship between volume
and temperature of gases.
V
T
V1
T1
=
V2
T2

7. Charles’ Law
 This law is named for Jacques Charles, who
studied the relationship volume, V, and
temperature, T, around the turn of the 19th
century.
 This defines a direct relationship:
With the same amount of gas he found that
as the volume increases the temperature
also increases. If the temperature
decreases than the volume also
decreases.
volume
temperature

8. Gay-Lussac’s Law
The pressure and absolute temperature
(K) of a gas are directly related at constant
mass & volume.
P
T
P1
T1
=
P2
T2

9. What does it mean?
 For a gas at constant mass and
volume, the pressure and temperature
are directly related.
pressure
temperature

10. Combined Gas Law
The combined gas law
combines Boyle’s Law and
Charles’ Law

11. Combined Gas Law
 Boyle’s Law:
 Charles’ Law:
 Gay-Lussac’s Law:

12. Avogadro’s Principle
 Equal volumes of gases contain equal numbers
of moles
 at constant temp & pressure
 true for any ideal gas
V
n
V1
n1
=
V2
n2

13. IDEAL GAS
PV = nRT
1. Ideal gas molecules do not attract or
repel each other.
2. Ideal gas molecules themselves take up
no volume.
Constant Gas = 0.082 L.atm
K.mol

14. Combined Gas Law
 It is a law that combines the previous laws into
one.
P1V1
T1
=
P2V2
T2
P1V1T2 = P2V2T1

15. DERIVATIONS

18. Combined Gas Law
 Example 1:
A sample of N2 gas was placed in a
flexible 9.0L container at 300K at a
pressure of 1.5 atm. The container was
compressed to a volume of 3.0L and
heat was added until the temperature
reached 600K. What is the new
pressure inside the container?

19. Combined Gas Law
 Example 2:
A 20.0L container holds 0.650 mol of
He gas at 37.0C at a pressure of 628.3
torr. What will be the new pressure
inside the container if the volume is
reduced to 12.0L, the temperature is
increased to 177C, and 1.25 mol of
additional He gas was added to it?

20. Combined Gas Law
 Example 3: A gas sample exerts
a pressure of 12 atm, a volume of
23 L and a temperature of 200 K.
Suddenly, the pressure becomes
14 atm and increased the
temperature to 300 K, what is the
new volume of the gas?

21. Combined Gas Law
 Begin by converting to Kelvin. It is
not necessary in this problem.

22. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 =
 V1 =
 T1 =
 P2 =
 V2 =
 T2 =

23. Combined Gas Laws
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 =
 T1 =
 P2 =
 V2 =
 T2 =

24. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 =
 P2 =
 V2 =
 T2 =

25. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 = 200K
 P2 =
 V2 =
 T2 =

26. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 = 200K
 P2 = 14 atm
 V2 =
 T2 =

27. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 = 200K
 P2 = 14 atm
 V2 = x
 T2 =

28. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 = 200 K
 P2 = 14 atm
 V2 = x
 T2 = 300 K

29. Combined Gas Law
 Now plug in the information you have .
. .
P1V1
=
P2V2
T1 T2
12atm(23L)
=
14 atm (x)
200K 300K

30. Combined Gas Law
 Cross multiply to solve for x
12atm(23 L)(300K) = 200 K (14L)(x)
82800 = 2800x
x = 29.57 Liters

31. Solve:
A 50-ml bubble is released from a diver’s
air tank at a pressure of 3.5 atm and a
temperature of 25 degree Celsius. What
is the volume of the bubble when it
reaches the ocean surface, where the
pressure is 1.0 atm and a temperature of
20 degree Celsius?

32. DERIVATIONS:

33. Example:

34. What does it mean?
 For a gas at constant temperature and
pressure, the volume is directly
proportional to the number of moles of
gas. volume
pressure

35. Ideal Gas Law
 UNIVERSAL GAS CONSTANT
 R=0.08206 Latm/molK
 R=8.315 dm3kPa/molK
PV = nRT

37.  EXAMPLE
 What is the density of oxygen at
 a)STP?
 b) 25 degree Celsius and 790mmHg?

40. SOLVE

41.  1. A 1.5-g sample of KClO3 was heated. The
liberated oxygen was collected over water at
23 degree Celsius and 750torr. What was
the volume of the gas collected? (water
vapor pressure = 21.2 torr)
 2. A 50-ml bubble is released from a diver’s
air tank at a pressure of 3.5 atm and a
temperature of 25 degree Celsius. What is
the volume of the bubble when it reaches
the ocean surface, where the pressure is 1.0
atm and a temperature of 20 degree
Celsius?

42.  3. A gas has a volume of 800.0 mL at
−23.0 °C and 300.0 torr. What would
the volume of the gas be at 227.0 °C
and 600.0 torr of pressure?

43.  4. 500.0 liters of a gas in a flexible-
walled container are prepared at 700.0
mmHg and 200.0 °C. The gas is
placed into a tank under high pressure.
When the tank cools to 20.0 °C, the
pressure of the gas is 30.0 atm. What
is the volume of the gas?