1. Gases
Chapter 13

2. 13.1 The Gas Laws
The gas laws apply to ideal gases, which are described by the kinetic theory in the following five statements.
Gas particles do not attract or repel each other
Gas particles are much smaller than the spaces between them.
Gas particles are in constant, random motion.
No kinetic energy is lost when gas particles collide with each other or within the walls of their container.
All gases have the same kinetic energy at a given temperature.

4. Gases are made up of Two Types of Particles
Molecules (2 or more atoms bound together)
- Examples: CH4 , O2 , N2
2. Atoms (Noble gases: He, Ne, Ar)
Gas particles are widely spread out and moving around:

5. Measuring Gases
Four variables we use to measure a gas and talk about its properties
Amount
Volume
Temperature
Pressure (force exerted on the walls of its container)

6. Amount of Gas Quantity of gas is expressed in units of MOLES
Moles allow us to convert to grams of gas, liters of gas, or the number of gas particles we have
Don’t forget the three conversion factors…
grams L x 1023 items mole 1 mole mole

7. Volume Volume of a gas = volume of container
Measured in units of LITERS or unit of length3
1 L = 1000 cm3 = .001 m3

8. Temperature The temperature is often measured in degrees Celsius
ALWAYS CONVERT TO KELVIN when doing calculations
To Convert:
K = °C + 273

9. Pressure
Due to gas particles colliding w/ container (exert force on an area)
UNITS:
ATMOSPHERES (atm): close to the average atmospheric pressure at sea level
What’s atmospheric pressure?
The pressure on earth’s surface due to the mass of air in the atmosphere
Pascal (Pa) or Kilopascal (kPa)
1 atm = 101,325 Pa = kPa
mm Hg (millimeters of mercury)
1 atm = 760 mm Hg
Torr
1 atm = 760 torr

10. UNITS
In other words… 1 atm = kPa = Pa = 760 mm Hg = 760 torr

11. STP Stands for: Standard Temp. and Pressure
B/c gas behavior depends on Temperature and Pressure, we compare properties of different gases at a standard temperature and pressure
STP = 1 atm, 0 ° C

12. GAS LAWS
The Mathematical representations of relationships between the four variables used to describe a gas…

13. 1. Boyle’s Law (P-V relationship)
As pressure DECREASES, volume INCREASES
As pressure INCREASES, volume DECREASES
(inverse relationship)
Boyle's Law Video

14. Boyle’s Law (Equation)
AT CONSTANT TEMPERATURE
EQUATION: P1V1 = P2V2

15. Practice Problem (Boyle’s Law)
Suppose I have a 2.5 L balloon filled with He gas. The pressure in the balloon is 1.04 atm. What will the volume of the balloon be if I increase the pressure to 1.54 atm?
Boyle's Law DEMOS

16. Solution P1 = 1.04 atm P2 = 1.54 atm V1 = 2.5 L V2 = ? P1V1 = P2V2
(1.04 atm)(2.5 L) = (1.54 atm)(V2)
(1.04 atm)(2.5 L) = V2
(1.54 atm)
1.69 L = V2
* NOTE: It is important for V to be in LITERS. Convert to L if you are given mL or some other unit of volume.

17. 2. Charles’s Law (T-V Relationship)
Consider a gas in a cylinder w/ a moveable piston...
If we DECREASE the temperature, we DECREASE the volume
Heating a Balloon Video
HIGH TEMP 
 LOW TEMP

18. Charles’s Law AT CONSTANT PRESSURE…
As temperature increases, so does the volume of gas.
As temperature increases, so does the volume of gas when the amount of gas and pressure do not change.

19. Charles’s Law: Equation
AT CONSTANT PRESSURE…
Equation :
V1 = V2
T1 T2
As temperature increases, so does the volume of gas when the amount of gas and pressure do not change.

20. Practice Problem…(You try!)
Say I have a balloon that contains 5.1 L of gas at room temperature (25 ° C). What will be the new volume of the gas if I put it in the freezer (15° C)?
FIRST convert the temperature values to Kelvin!
K = ° C + 273

21. Solution
V1 = 5.1 L V2 = ?
T1 = 25°C K = 298 K T2 = 15°C K = 288 K
Use the equation V1 = V2
T T2
5.1 L = V2
298 K K
(288 K)(5.1 L) = V2
298 K
V2 = 4.93 L

22. Practice Problem…(You try!)
Say I have a balloon that contains 5.1 L of gas at room temperature (25 ° C). What will be the new volume of the gas if I put it in the freezer (15° C)?
FIRST convert the temperature values to Kelvin!
K = ° C + 273

23. 3. Gay-Lussac’s Law (P-T Relationship)
The pressure of a fixed amount of gas varies directly with temperature when the volume remains constant.
If we INCREASE the temperature, we INCREASE the pressure
Candle-Water Demo
Egg in a Bottle Demo
If volume is a constant, then there is a direct relationship between temp. and pressure

24. Gay-Lussac’s Law AT CONSTANT VOLUME…
As temperature increases, so does the pressure of gas.
As temperature increases, so does the volume of gas when the amount of gas and pressure do not change.

25. Gay-Lussac’s Law: Equation
AT CONSTANT VOLUME…
Equation :
P1 = P2
T1 T2
As temperature increases, so does the volume of gas when the amount of gas and pressure do not change.

26. Practice Problem…(You try!)
The pressure of oxygen gas inside a canister is 5.00 atm at 25.0°C. The canister is located at a camp high on Mount Everest. If the temperature there falls to -10.0°C, what is the new pressure inside the canister?
REMEMBER convert the temperature values to Kelvin!
K = ° C + 273

27. Solution T1 T2 P1 = P2 P1 = 5.00 atm, T1 = 25.0°C + 273 = 298 K
P2 = ????, T2 = -10.0°C = 263 K
5.00 atm = P2
298 K K
P2 = atm

28. 4. Avogadro’s Principle (V-n Relationship)
Equal volumes of gases at the same temperature and pressure contain equal numbers of particles.
If volume is a constant, then there is a direct relationship between temp. and pressure 28

29. Avogadro’s Law AT CONSTANT TEMP and PRESSURE…
The volume of a gas is completely dependent on how many moles of gas are in the container.
As temperature increases, so does the volume of gas when the amount of gas and pressure do not change. 29

30. Avogadro’s Law: Equation
AT CONSTANT TEMP and PRESSURE…
Equation :
V1 = V2
n1 n2
(n= number of moles)
Remember 1 mol = 22.4 L at STP
As temperature increases, so does the volume of gas when the amount of gas and pressure do not change. 30

31. Practice Problem…(You try!)
How many moles of acetylene (C2H2) gas occupy a volume of 3.25 L at STP?

32. Solution n1 n2 V1 = V2 V1 = 3.25 L, n1 = ???? mol
3.25 L = L
n mol
n1 = mol

33. 5. Dalton’s Law of Partial Pressures…
In a mixture of gases, each gas exerts a pressure as if it were on its own
The total pressure of a mixture of gases is the sum of the pressure due to each gas
PT = P1 + P2 + P3 + …
The total pressure (PT) is the sum of the pressures from each gas (P1 = pressure of gas 1, P2 = pressure of gas 2, etc)

34. Practice Problem
What is the atmospheric pressure if the partial pressures of nitrogen, oxygen, and argon (the components of air) are mm Hg, mm Hg, and 0.5 mm Hg, respectively?

35. Solution Use Dalton’s Law… PT = P1 + P2 + P3 + …
P = mm Hg

36. Gas Law Summary P1V1= P2V2 V1= V2 T1 T2 P1= P2 n1 n2 PT= P1 + P2 + P3
Equations
Constant
Boyle’s
P1V1= P2V2
Temperature & amount
Charles’s
V1= V2
T1 T2
Pressure & amount
Gay-Lussac’s
P1= P2
Volume & amount
Avogadro’s
n1 n2
Temperature & pressure
Dalton’s Partial Pressure
PT= P1 + P2 + P3

37. Putting the Laws Together…
Combined gas law:
P1V1 = P2V2
n1T1 n2T2

38. Combining the Laws into one equation…
The Ideal Gas Law
Combining the Laws into one equation…

39. THE IDEAL GAS LAW:
Describes the behavior of an ideal gas in terms of P, T, and n
Ideal Gas: gas described by kinetic molecular theory
Real gases behave like ideal gases under ordinary conditions (doesn’t apply to VERY LOW T and VERY HIGH P)

40. The Value of “R” Value of R Units 0.0821 atm-L mole-K 8.314 Pa-m3
R is called the “gas constant”
The value of R depends on the units you need to use to solve a problem
Value of R
Units
0.0821
atm-L
mole-K
8.314
Pa-m3
mole –K

41. Units: Which value of “R” do I use?? Depends on the units of P and V
P can be in atm or Pa
V can be in L or m3
T is ALWAYS in K

42. Practice Problem 1: PV = nRT
How many moles of gas are contained in a 2.0 L container with a pressure of 1.5 atm at 100°C?
Write out the variables given. Convert T to Kelvin if needed.
P =
V =
T =
What variable is missing?
Which value of R do you need to use?
Value of R
Units
0.0821
atm-L
mole-K
8.314
Pa-m3
mole –K
J____
mole- K

43. Practice Problem 1: PV = nRT
How many moles of gas are contained in a 2.0 L container with a pressure of 1.5 atm at 100°C?
Write out the variables given. Convert T to Kelvin if needed.
P = 1.5 atm
V = 2.0 L
T = 100°C = 373 K
What variable is missing? n
Which value of R do you need to use?
atm-L
mole-K
Value of R
Units
0.0821
atm-L
mole-K
8.314
Pa-m3
mole –K
J____
mole- K

44. Practice Problem 1:
Plug the values into the equation and solve for the unknown variable…
PV = nRT
(1.5 atm)(2.0L) = n (0.0821atm-L/mole-K)(373 K)
(1.5 atm)(2.0L)__________ = moles (0.0821atm-L/mole-K)(373 K)

45. If the gas is carbon dioxide, how many grams of gas are produced?
Carbon dioxide = CO2
0.098 moles x 44 grams = grams
1 mole