1. Gas Laws 1

2. Section 13.1 The Gas Laws Objectives:
State the relationships among pressure, temperature, and volume of a constant amount of gas.
Apply the gas laws to problems involving the pressure, temperature, and volume of a constant amount of gas.
For a fixed amount of gas, a change in one variable—pressure, temperature, or volume—affects the other two.

3. Gases Variable volume and shape Expand to occupy volume available
Volume, Pressure, Temperature, and the number of moles present are interrelated
Can be easily compressed
Exert pressure on whatever surrounds them
Easily diffuse into one another 3

4. Mercury Barometer Used to define and measure atmospheric pressure
On the average at sea level the column of mercury rises to a height of about 760 mm.
This quantity is equal to 1 atmosphere
It is also known as standard atmospheric pressure 4

5. Pressure Units & Conversions
The above represent some of the more common units for measuring pressure. The standard SI unit is the Pascal or kilopascal.
The US Weather Bureaus commonly report atmospheric pressures in inches of mercury.
Pounds per square inch or PSI is widely used in the United States.
Most other countries use only the metric system. 5

6. Gas Pressure (cont.)

7. Boyle’s Law
According to Boyle’s Law the pressure and volume of a gas are inversely proportional at constant temperature.
As pressure increases, volume decreases.
P1V1 = P2V2 7

8. Boyle’s Law
A graph of pressure and volume gives an inverse function 8

9. Sample Problem 1: = 336 kPa = 340 kPa
If the pressure of helium gas in a balloon has a volume of 4.00 dm3 at 210 kPa, what will the pressure be at 2.50 dm3?
P1 V1 = P2 V2
(210 kPa) (4.00 dm3) = P2(2.50 dm3)
P2 = (210 kPa) (4.00 dm3)
(2.50 dm3)
= 336 kPa
= 340 kPa 9

10. Charles’ Law According to Charles’ Law the volume of a gas is
proportional to the Kelvin temperature as long as
the pressure is constant
Absolute zero is zero on the Kelvin scale.
Note: The temperature for gas laws must always be expressed in Kelvin where
Kelvin = oC
(or 273 to 3 significant digits) 10

11. Charles’ Law A graph of temperature and volume yields a straight line.
Where this line crosses the x axis (x intercept) is defined as absolute zero 11

12. Sample Problem 2
A gas sample at 40 oC occupies a volume of 2.32 dm3. If the temperature is increased to 75 oC, what will be the final volume?
V1 = V2
T T2
Convert temperatures to Kelvin. 40oC = 313K
75oC = 348K
2.32 dm3 = V2
313 K K
(313K)( V2) = (2.32 dm3)(348K)
V2 =
2.58 dm3 12

13. Gay-Lussac’s Law P1 = P2 T2 T1
Gay-Lussac’s Law defines the relationship between pressure and temperature of a gas.
The pressure and temperature of a gas are directly proportional
P = P2 T2 T1 13

14. Sample Problem 3:
The pressure of a gas in a tank is 3.20 atm at 22 oC. If the temperature rises to 60oC, what will be the pressure in the tank?
P1 = P2
T T2
Convert temperatures to Kelvin:
22oC = 295K
60oC = 333K
3.20 atm = P2
295 K K
(295K)( P2) = (3.20 atm)(333K)
P2 =
3.61 atm 14

15. The Combined Gas Law
1. If the amount of the gas is constant, then Boyle’s, Charles’ and Gay-Lussac’s Laws can be combined into one relationship 2. 15

16. Sample Problem 4:
A gas at 110 kPa and 30 oC fills a container at 2.0 dm3. If the temperature rises to 80oC and the pressure increases to 440 kPa, what is the new volume?
Convert temperatures to Kelvin.
30oC = 303K
80oC = 353K
P1V1 = P2V2
T T2
V2 = V1 P1 T2
P2 T1
= (2.0 dm3) (110 kPa ) (353K)
(440 kPa ) (303 K)
V2 = 0.58 dm3 16

17. STOP here for today.

18. A B C D Section 13.1 Assessment
Boyle’s Law explains which relationship of properties in gases?
A. pressure and volume
B. amount and pressure
C. temperature and volume
D. volume and temperature A B C D
Section 13-1

19. A B C D Section 13.1 Assessment
Atoms are in their lowest energy state at what temperature?
A. 0° Celsius
B. 0° Fahrenheit
C. –100° Celsius
D. 0 kelvin A B C D
Section 13-1

20. Section 13.2 The Ideal Gas Law
Relate number of particles and volume using Avogadro’s principle.
Relate the amount of gas present to its pressure, temperature, and volume using the ideal gas law.
Compare the properties of real and ideal gases.
mole: an SI base unit used to measure the amount of a substance; the amount of a pure substance that contains 6.02 × 1023 representative particles
Section 13-2

21. Avogadro's Principle Avogadro’s principle
states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.
Section 13-2

22. Avogadro's Principle (cont.)
The molar volume of a gas
the volume 1 mol occupies at 0.00°C and 1.00 atm of pressure.
0.00°C and 1.00 atm are called standard temperature and pressure (STP).
At STP, 1 mol of gas occupies 22.4 L.
Section 13-2

23. Combined gas law to ideal gas law
The Ideal Gas Law
Ideal gas particles occupy a negligible volume and are far enough apart to exert minimal attractive or repulsive forces on each other.
Combined gas law to ideal gas law
Section 13-2

24. The Ideal Gas Law (cont.) ideal gas constant represented by R
Section 13-2

25. ideal gas law describes the physical behavior of an ideal gas in terms of pressure, volume, temperature, and amount.
(R)

26. Example: What volume will 25.0 g O2 occupy
at 20oC and a pressure of atmospheres? :
PV = nRT so V = nRT/P 26

27. The Ideal Gas Law—Molar Mass and Density
Molar mass and the ideal gas law
Section 13-2

28. The Ideal Gas Law—Molar Mass and Density (cont.)
Density and the ideal gas law
Section 13-2

29. A 2. 10 L vessel contains 4. 65 g of a gas at 1. 00 atmospheres and 27
A 2.10 L vessel contains 4.65 g of a gas at 1.00 atmospheres and 27.0oC. What is the molar mass of the gas?
mRT PV
M =
M =
54.6 g/mol
Scheffler 29

30. Real Versus Ideal Gases
Ideal gases follow the assumptions of the kinetic-molecular theory.
Ideal gases experience:
There are no intermolecular attractive or repulsive forces between particles or with their containers.
The particles are in constant random motion.
Collisions are perfectly elastic.
No gas is truly ideal, but most behave as ideal gases at a wide range of temperatures and pressures.
Section 13-2

31. Real Versus Ideal Gases (cont.)
Real gases deviate most from ideal gases at high pressures and low temperatures.
Polar molecules have larger attractive forces between particles.
Polar gases do not behave as ideal gases.
Section 13-2

32. A B C D Section 13.2 Assessment
Which of the following is NOT one of the related physical properties described in the ideal gas law?
A. pressure
B. volume
C. density
D. temperature A B C D
Section 13-2

33. A B C D Section 13.2 Assessment
3.00 mol of O2 at STP occupies how much volume?
A L
B L
C L
D L A B C D
Section 13-2