1. Adds in the factor of number of moles of gas “n”.
The Ideal Gas Law
PV = nRT
Adds in the factor of number of moles of gas “n”.
P = Pressure (atm)
V = Volume (Liters)
T = Temperature (Kelvin)
n = number of moles
Remember when dealing with moles:
# moles (n) = grams of substance
Gram Formula Mass

2. What is “R”?
R is a constant, called the “Universal Gas Constant”
It is derived by plugging in the values for 1 mole of
gas at STP. (22.4 Liters, 273K, 1 atm)
R =
Instead of learning a different value for R for all the possible unit combinations, we can just memorize one value and convert the units to match R.
L • atm
Mol • K

3. Ideal Gas Law (Honors) IDEAL GAS LAW P = ? atm n = 0.412 mol
Calculate the pressure in atmospheres of mol of He at 16°C & occupying 3.25 L.
IDEAL GAS LAW
GIVEN:
P = ? atm
n = mol
T = 16°C = 289 K
V = 3.25 L
R = Latm/molK
WORK:
PV = nRT
P(3.25)=(0.412)(0.0821)(289)
L mol Latm/molK K
P = 3.01 atm

4. Example # 1 Honors Packet
A 9.81 L cylinder contains 23.5 moles of nitrogen at 23° C. What pressure is exerted by the gas?

5. Example # 2 Honors Packet
A pressure of 850 mmHg is exerted by 28.6 grams of sulfur dioxide at a temp of 40 °C. Calculate the volume of the vessel holding the gas.

6. Density is Hidden in this Formula
Density = Mass (g)
Volume
# moles = Mass (g)
Gram formula mass
Can you rework PV = nRT to solve for Density?

7. Example # 7 in Honors Packet
What is the density of neon at 40 °C and 1.23 atmospheres?

8. Dalton’s Law of Partial Pressures
Ptotal = P1+P2+….
Total pressure of a mixture of gases in a container is the sum of the individual pressures (partial pressures) of each gas, as if each took up the total space alone.
This is often useful when gases are collected “over water”

10. Collecting Gas over Water
Pressureatm = Pressure (O2) + Pressure (H2O vapor)
Crash Course: Partial Pressure and Vapor Pressure

11. Look up water-vapor pressure on for 22.5°C.
Dalton’s Law
H2 gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa.
GIVEN:
PH2 = ?
Ptotal = 94.4 kPa
PH2O = 2.72 kPa
WORK:
Ptotal = PH2 + PH2O
94.4 kPa = PH kPa
PH2 = 91.7 kPa
Look up water-vapor pressure on for 22.5°C.

12. Look up water-vapor pressure for 35.0°C.
Dalton’s Law
A gas is collected over water at a temp of 35.0°C when the barometric pressure is torr. What is the partial pressure of the dry gas?
DALTON’S LAW
GIVEN:
Pgas = ?
Ptotal = torr
PH2O = 42.2 torr
WORK:
Ptotal = Pgas + PH2O
742.0 torr = PH torr
Pgas = torr
Look up water-vapor pressure for 35.0°C.

13. Examples of Vapor Pressure Tables

14. You can even use Table H to find VP of Water

15. Using Mole Fraction (Honors)
Moles gas (X) x P (total) = P (X)
Total Moles Gas

16. Example # 4 Honors Packet
A mixture of 2.00 moles H2, 3.00 moles NH3, 4.00 moles CO2, and 5.00 moles N2 exert a total pressure of 800 mmHg. What is the partial pressure of each gas?

17. Graham’s Law Diffusion Effusion
Spreading of gas molecules throughout a container until evenly distributed.
Effusion
Passing of gas molecules through a tiny opening in a container
Smaller and lighter gas particles do this faster!
Crash Course: Grahams Law

18. Graham’s Law Speed of diffusion/effusion
At the same temp & KE, heavier molecules move more slowly.
Ex: Which of the following gases will diffuse most rapidly?
A.) N2 B.) CO2 C.) CH4

19. Graham’s Law Formula Graham’s Law
Rate of diffusion of a gas is inversely related to the square root of its molar mass.
Ratio of gas A’s speed to gas B’s speed

20. Graham’s Law Kr diffuses 1.381 times faster than Br2.
Determine the relative rate of diffusion for krypton and bromine.
The first gas is “Gas A” and the second gas is “Gas B”.
Relative rate mean find the ratio “vA/vB”.
Kr diffuses times faster than Br2.

21. Put the gas with the unknown speed as “Gas A”.
Graham’s Law
A molecule of oxygen gas has an average speed of m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions?
Put the gas with the unknown speed as “Gas A”.

22. Graham’s Law
An unknown gas diffuses 4.0 times faster than O2. Find its molar mass.
The first gas is “Gas A” and the second gas is “Gas B”.
The ratio “vA/vB” is 4.0.
Square both sides to get rid of the square root sign.

23. Example # 1 Honors Packet
Under the same conditions of temp and pressure, how many times faster will hydrogen effuse compared to carbon dioxide?

24. Example #7 Honors Packet
If CO2 diffuses from a flask in 30 seconds and an unknown gas diffuses from the same flask in 5 minutes, calculate the molecular weight of this unknown gas.

25. Avogadro’s Principle
Volume of a gas is directly proportional to the number of moles of gas particles present. V n

26. Equal volumes of gases contain equal numbers of moles of particles
at constant temp & pressure
true for any gas

27. Avogadros Law: https://www. youtube. com/watch
Molar Volume of a Gas:

28. Practice Questions
At the same temperature and pressure, 1.0 liter of CO(g) and 1.0 liter of CO2(g) have
equal masses and the same number of molecules
B. different masses and a different number of molecules
C. equal volumes and the same number of molecules
D. different volumes and a different number of molecules

29. Which rigid cylinder contains the same number of gas molecules at STP as a 2.0-liter rigid cylinder containing H2(g) at STP?
(1) 1.0-L cylinder of O2(g)
(2) 2.0-L cylinder of CH4(g)
(3) 1.5-L cylinder of NH3(g)
(4) 4.0-L cylinder of He(g

30. Which two samples of gas at STP contain the same total number of molecules?
(1) 1 L of CO(g) and 0.5 L of N2(g)
(2) 2 L of CO(g) and 0.5 L of NH3(g)
(3) 1 L of H2(g) and 2 L of Cl2(g)
(4) 2 L of H2(g) and 2 L of Cl2(g)

31. Gas Stoichiometry Moles  Liters of a Gas Non-STP Problems
STP - use 22.4 L/mol
Non-STP - use ideal gas law
Non-STP Problems
Given liters of gas?
start with ideal gas law
Looking for liters of gas?
start with stoichiometry conv.

32. Gas Stoichiometry Problem
What volume of CO2 forms from g of CaCO3 at 1.017atm & 25ºC?
CaCO3  CaO CO2
5.25 g
? L non-STP
Looking for liters: Start with stoich and calculate moles of CO2.
5.25 g
CaCO3
1 mol
CaCO3
100.09g
1 mol
CO2
CaCO3
= 1.26 mol CO2
Plug this into the Ideal Gas Law to find liters.

33. Gas Stoichiometry Problem
What volume of CO2 forms from g of CaCO3 at 1.017atm & 25ºC?
GIVEN:
P = 1.017atm
n = 1.26 mol
T = 25°C = 298 K
R = Latm/molK
WORK:
PV = nRT
(1.017atm)V =(1mol)(.0821 Latm/molK)(298K)
V = 1.26 L CO2

34. Gas Stoichiometry Problem
How many grams of Al2O3 are formed from 15.0 L of O2 at 0.96 atm & 21°C?
4 Al O2  2 Al2O3
15.0 L
non-STP
? g
GIVEN:
P = 0.96 atm
V = 15.0 L
n = ?
T = 21°C = 294 K
R = Latm/molK
WORK:
PV = nRT
(0.96 atm ) (15.0 L) = n (.0821 Latm/molK) (294K)
n = mol O2
Given liters: Start with Ideal Gas Law and calculate moles of O2.
NEXT 

35. Gas Stoichiometry Problem
How many grams of Al2O3 are formed from L of O2 at 0.96 atm & 21°C?
4 Al O2  2 Al2O3
15.0L
non-STP
? g
Use stoich to convert moles of O2 to grams Al2O3.
0.597
mol O2
2 mol Al2O3
3 mol O2
g Al2O3
1 mol
Al2O3
= 40.6 g Al2O3

36. Example # 10 Honors Multiple Choice Ni(CO)4 (l) → Ni (s) + 4CO (g)
What volume of CO is formed from the complete decomposition of 444g of Ni(CO)4 at 752 torr and 22.0 °C
Do stoich for 444g to find moles of CO.
Plug the moles into Ideal Gas Law to get V at non standard conditions.

37. Some Cool Videos Crash Course: Ideal Gas Laws
Crash Course: Ideal Gas Law Problems
Crash Course: Real Gases