1. Chemistry AP/IB Dr. Cortes
Chapter 10: Gases
Chemistry AP/IB
Dr. Cortes

2. Elements that exist as gases at 250C and 1 atmosphere

3. homonuclear diatomic gases
monatomic noble gases

4. Physical Characteristics of Gases
Take on volume and shape of container
Most compressible state of matter
Flow
Form homogeneous mixtures with other gases
Example: air
N2, O2, Ar, CO2, trace gases (includes H2)
Lower densities vs. liquids and solids
Exert pressure

5. Pressure: force exerted by gas molecules striking a given area
(Force = mass x acceleration)
SI Unit of Pressure: pascal (Pa)
Conversion Factors:
1 Pa = 1 N/m2
1 atm = 760 mmHg = 760 torr = 101,325 Pa = kPa

6. Measuring Standard Atmospheric Pressure
Barometer: used to measure atmospheric pressure
Hg will rise 760 mm up the tube at standard atmospheric pressure
Standard Pressure:
1 atm
760 mmHg

7. Atmospheric Pressure and Altitude
10 miles
0.2 atm
4 miles
0.5 atm
Sea Level
1 atm
This bottle was closed at ~2,000 m altitude then brought back to sea level; it was crushed by air pressure

8. Manometers: used to measure gas pressure

9. Boyle studied the relationship between pressure and volume of a gas
As pressure (h) increases – volume decreases

10. Boyle’s Law: Pressure-Volume Relationship
For a fixed amount of gas at constant temperature, the volume of gas is inversely proportional to the pressure
If pressure goes up, volume goes down and vice-versa
P1 x V1 = P2 x V2

11. Sample Problem
A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas if the volume is reduced at constant temperature to 154 mL?
4460 mmHg

12. As temperature increases – volume increases
Charles studied the relationship between temperature and volume of a gas
As temperature increases – volume increases

13. Charles’ Law: Temperature-Volume Relationship
For a fixed amount of gas at constant pressure, the volume of gas is directly proportional to the Kelvin temperature
If temperature goes up, volume goes up and vice-versa
V V2
T T2 =

14. Kelvin = degrees celsius +273.15
-273 K, or absolute zero, is degrees celsius
All gases liquify or solidify before reaching absolute 0, so there are no gases that have a volume of 0: hypothetical situation that is never attained

15. Variation of gas volume with temperature at constant pressure:
Charles’ Law
V α T
Temperature must be
in Kelvin
V V2
T T2 =
T (K) = T (0C)

16. Sample Problem
A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?
192 K

17. Gay-Lussac’s Law: Temperature-Pressure Relationship
For a fixed amount of gas at constant volume, the pressure of gas is directly proportional to the Kelvin temperature
If temperature goes up, pressure goes up and vice-versa
P P2
T T2 =

18. Combined Gas Law
The other laws can be obtained from this law by holding one quantity (pressure, volume, or temp) constant
It also enables you to do calculations for situations in which none of the variables are constant!!

19. Sample Problem
The volume of a gas-filled balloon is 30.0L at 40.0 °C and 153 kPa. What volume will the balloon have at standard temperature and pressure?
39.5 L

20. Avogadro studied the relationship between number of molecules and volume of a gas
Avogadro’s Hypothesis: equal volumes of gases (at the same temperature and pressure) contain equal numbers of molecules. At STP, 1 mol = 22.4 L

21. Avogadro’s Law: Quantity-Volume Relationship
At constant temperature and pressure, the number of moles of gas is directly proportional to its volume
If number of moles goes up, volume goes up and vice-versa
V V2
n n2 =

22. The Ideal Gas Law
Ideal Gas Law: used to describe the behavior of an “ideal gas”
R: ideal gas constant with varying values (depending on required units)
Advantage of ideal gas law over combined gas law is it permits you to solve for the of a contained gas

24. Molar Volume ANSWER: Molar volume of any gas at STP is !
Molar volume: volume occupied by 1 mol of a gas ( )
SI units:
To solve for, rearrange ideal gas law:
PV = nRT
V/n =
QUESTION:
Find molar volume of a gas at STP (1 atm, and K)
ANSWER:
Molar volume of any gas at STP is !

25. Gas Densities and Molar Mass
Density = m/V
Units: g/L
Rearranging the ideal-gas equation with M as molar mass (g/mol) we get:
PV = nRT or n/V =
Multiply both sides by M
nM /V =
nM /V = (mol)(g/mol) / (L) = g/L = (density!)
relates density to the properties of gases

26. Sample Problem
A large natural gas storage tank is kept at 2.20 atm. On a cold day, when the temperature in -15°C, the volume of gas in the tank is 28,500 ft3. What is the volume of the same quantity of gas when the temperature is 31°C?

27. Sample Problems
Cyclopropane is used as a general anesthetic. It has a molar mass of g/mol. What is the density of cyclopropane gas at 25°C and 1.02 atm?
Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21°C and torr.

28. Sample Problem
A 5.00 L container is filled with nitrogen gas to a pressure of 3.00 atm at 523 K. What is the volume of a container that is used to store the same gas at STP?
Tennis balls are filled with air of nitrogen gas to a pressure above atmospheric pressure to increase their bounce. If a tennis ball has a volume of 144 cm3 and contains 0.33 g of nitrogen, what is the pressure inside the ball at 24°C?

29. Sample Problems
What volume of nitrogen gas at 720 torr and at 23°C is required to react with 7.35 L of hydrogen gas at the same temperature and pressure to yield ammonia gas?
4NH3(g) + 5O2(g)  4NO(g) + 6H2O(g)
How many liters of NH3(g) at 850°C and atm are required to react with 1.00 mol of O2(g) in this reaction?

30. Dalton’s Law of Partial Pressure
At constant volume and temperature, the total pressure exerted by a of the component gases
Ptotal = P1 + P2 + P3 +………..

31. Sample Problem
What is the total pressure exerted by a mixture of 2.00g of H2 and 8.00 g of N2 at 273 K in a 10.0 L vessel?

32. Kinetic Molecular Theory
KMT gives us an understanding of gas pressure at the molecular level:
Pressure results from the on the walls of container
As temperature increases, average …
…creating more chances for collisions with walls of container, so

33. Assumptions of Kinetic Molecular Theory
Gases consist of a large number of molecules in (n is high)
Volume of individual molecules is compared to volume of (V is high)
forces (forces between gas molecules) are
Energy can be transferred between molecules, but average KE is (at constant temperature)
Average KE of molecules is proportional to
At any given temperature, the molecules of any gas have the

34. Root-Mean-Squared Speed
Root-mean-square speed (rms): the sq root of the avg of the squared speeds of gas molecules in a sample
Symbol:
SI unit:
The higher the temp, the
The lower the molar mass, M, the

35. The higher the temp, the higher the rms…

36. The lower the molar mass the higher the rms…

37. Graham’s Law of Effusion
Effusion: the escape of a gas through
A balloon will deflate over time due to
Graham’s Law of Effusion: the rate of effusion of a gas (r) is inversely proportional to the square root of the gas’s molar mass

38. Diffusion and Mean Free Path
Diffusion: is the
Diffusion is faster for light gas molecules because

39. Behavior of Real Gases Real gases deviate from ideal gases!
Especially at:
Low
High
Small container
Because…
Gas molecules have “real” volume and take up space
Gas molecules interact with one another
We need to correct Ideal Gas Law for volume and intermolecular attractions…

40. The van der Waals Equation for Real Gases
a and b are empirically-determined constants for each gas
Corrects for
Corrects for

42. Sample Problems
What is the pressure exerted by one mole of argon at a volume of 2.00 L and at 300 K when it acts as an ideal gas and as a non-ideal gas?
a = 1.34 L2-atm/mol2 b = L/mol
Consider a sample of 1.00 mole of CO2 confined to a volume of 3.00 L at 0.0 °C. Calculate the pressure of gas when it acts as an ideal gas and a non-ideal gas?
a = 3.59 L2-atm/mol2 b = L/mol