1. To understand the Ideal Gas Law and use it in calculations
Objectives
To understand the Ideal Gas Law and use it in calculations
To understand the relationship between the partial and total pressure of a gas mixture
To do calculations involving Dalton’s Law of partial pressures
To prepare for the Universal Gas Constant lab

2. So far we have considered “what happens,” but not “why.”
In science, “what” always comes before “why.”

3. Postulates of the Kinetic Molecular Theory
1) The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero).

4. Postulates of the Kinetic Molecular Theory
2) The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.

5. Kinetic Molecular Theory

6. Postulates of the Kinetic Molecular Theory
3) The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other.

7. Postulates of the Kinetic Molecular Theory
The average internal kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.
PHet gas behavior

8. A. The Kinetic Molecular Theory of Gases (IDEAL)

9. P1V1 = P2V2 n1T1 n2T2 Boyle’s Law V = k (at constant T and n) P
A. The Ideal Gas Law
Boyle’s Law V = k (at constant T and n) P
Charles’s Law V = bT (at constant P and n)
Avogadro’s Law V = an (at constant T and P)
We can combine these equations to get the Combined Gas Law
P1V1 = P2V2
n1T1 n2T2

10. PV = R (a constant) nT R = 0.08206 L atm **Found mol K Experimentally
A. The Ideal Gas Law
PV = R (a constant) nT
Rearranging the equation gives the Ideal Gas Law
PV = nRT
R = L atm **Found mol K Experimentally

11. A sample of hydrogen gas, H2, has a volume of 8
A sample of hydrogen gas, H2, has a volume of 8.56 L at a temperature of 0 oC and a pressure of 1.5 atm. Calculate the number of moles of H2 present in this gas sample. Assume that the gas behaves ideally.
PV=nRT P= V= n= R= T=

12. PV=nRT
P= 1.5 atm **UNITS**
V= 8.56 L
n= ?
R= Latm/molK
T= 0 oC = 273 K
n = PV RT
n = (1.5 atm)(8.56 L) = 0.57 mol
( Latm/molK)(273 K)

13. What volume is occupied by 0.250 mol of CO2 gas at 25 oC and 371 torr?
PV=nRT P= V= n= R= T=

14. What volume is occupied by 0. 250 mol of CO2 gas at 25 oC and 371 torr
What volume is occupied by mol of CO2 gas at 25 oC and 371 torr? *(1 atm = 760 torr)
PV=nRT
P= 371 torr
V= ?
n= mol
R= Latm/molK
T= 25 oC = 298 K
V = nRT P

15. What volume is occupied by 0. 250 mol of CO2 gas at 25 oC and 371 torr
What volume is occupied by mol of CO2 gas at 25 oC and 371 torr? *(1 atm = 760 torr)
V = nRT = mol)( Latm/molK)(298K)
P torr
V = L ??
371 torr 1 atm = atm
760 torr
V = nRT =(0.250 mol)( Latm/molK)(298K)
P atm
V = 12.5 L ****Watch the units!!!****

16. n1T1 n2T2 Derive Boyle’s Law (P1V1 = P2V2) from IGL
PV=nRT PV = R = constant (LAB) nT
P1V1 = P2V2
n1T1 n2T2
IGL Video, fire syringe

17. B. Dalton’s Law of Partial Pressures
What happens to the pressure of a gas as we mix different gases in the container?
Dalton’s Law of Partial Pressures
For a mixtures of gases in a container, the total pressure exerted is the sum of the partial pressures of the gases present.
Ptotal = P1 + P2 + P3

18. B. Dalton’s Law of Partial Pressures
The pressure of the gas is affected by the number of particles but not the type of particles.

19. B. Dalton’s Law of Partial Pressures
Two crucial things we learn from this are:
The volume of the individual particles is not very important.
The forces among the particles must not be very important.

20. B. Dalton’s Law of Partial Pressures
A container holds a mixture of three gases that exhibit a total pressure of 1.8 atm. If gas A exerts 0.9 atm and gas B exerts 0.4 atm, what is the partial pressure of gas C?
Ptotal = P1 + P2 + P3
Ptotal =
P1 =
P2 =
P3 = ?

21. B. Dalton’s Law of Partial Pressures
Ptotal = P1 + P2 + P3
Ptotal = 1.8 atm
P1 = 0.9 atm
P2 = 0.4 atm
P3 = ?
P3 = Ptotal - P1 - P2
P3 = 1.8 atm – 0.9 atm – 0.4 atm = 0.5 atm

22. P He = P O2 = V = V = n = n = R = R = T = T =
Mixtures of helium and oxygen can be used in scuba tanks to prevent “the bends.” For a particular dive, 46 L He at 25 oC and 1.0 atm and 12 L of O2 at 25oC and 1 atm were pumped into a tank with a volume of 5.0 L Calculate the partial pressure of each gas and the total pressure in the tank at 25 oC For each gas…
P He = P O2 =
V = V =
n = n =
R = R =
T = T =
For oxygen:
P1V1=P2V2
(1.30 atm)(27.4 L) = (P2)(5.81 L)
P2 = 6.13 atm
For helium:
(2.00 atm)(8.50 L) = (P2)(5.81 L)
P2 = 2.93 atm
The total pressure is therefore = 9.06 atm.

23. P He = 1 atm P O2 = 1 atm V = 46 L V = 12 L n = ? n = ?
R = Latm/mol K R =
T = 25 oC T = 25 oC
n = PV/RT n = PV/RT
1.9 mol He mol O2
This quantifies how many moles of each gas is contained in the sample…pressure for each gas in the 5 L tank? PV = nRT…
For oxygen:
P1V1=P2V2
(1.30 atm)(27.4 L) = (P2)(5.81 L)
P2 = 6.13 atm
For helium:
(2.00 atm)(8.50 L) = (P2)(5.81 L)
P2 = 2.93 atm
The total pressure is therefore = 9.06 atm.

24. Pt =9.3 atm + 2.4 atm = 11.7 atm total pressure
P He = ? P O2 = ?
V = 5 L V = 5 L
n = 1.9 mol n = 0.49 mol
R = Latm/mol K R =
T = 25 oC T = 25 oC
P = nRT/V P = nRT/V
9.3 atm atm
Pt = P1 + P2
Pt =9.3 atm atm = 11.7 atm total pressure
For oxygen:
P1V1=P2V2
(1.30 atm)(27.4 L) = (P2)(5.81 L)
P2 = 6.13 atm
For helium:
(2.00 atm)(8.50 L) = (P2)(5.81 L)
P2 = 2.93 atm
The total pressure is therefore = 9.06 atm.

25. Exercise
27.4 L of oxygen gas at 25.0°C and 1.30 atm, and 8.50 L of helium gas at 25.0°C and 2.00 atm were pumped into a tank with a volume of 5.81 L at 25°C.
Calculate the new partial pressure of oxygen.
6.13 atm
Calculate the new partial pressure of helium.
2.93 atm
Calculate the new total pressure of both gases.
9.06 atm
For oxygen:
P1V1=P2V2
(1.30 atm)(27.4 L) = (P2)(5.81 L)
P2 = 6.13 atm
For helium:
(2.00 atm)(8.50 L) = (P2)(5.81 L)
P2 = 2.93 atm
The total pressure is therefore = 9.06 atm.

26. B. Dalton’s Law of Partial Pressures
Collecting a gas over water
Total pressure is the pressure of the gas + the vapor pressure of the water.

27. B. Dalton’s Law of Partial Pressures
Collecting a gas over water
How can we find the pressure of the gas collected alone?
Ptotal = P1 + P2
Ptotal = atmospheric
P1 = PH2O (from chart)
P2 = P (gas collected)

28. To understand the ideal gas law and use it in calculations
Objectives Review
To understand the ideal gas law and use it in calculations
To understand the relationship between the partial and total pressure of a gas mixture
To do calculations involving Dalton’s law of partial pressures
To prepare for the Universal Gas Constant lab
Work Session:
459 Practice Problem 13.8
460 Practice Problem 13.9
469 Practice Problem – PH2O ONLY
481 # 35, 36 PO2 ONLY
Review # 3

29. To convert between pressure units using the unit analysis approach
Objectives
To double check for unit agreement when working the 5-Step Problem Solving Method
To convert between pressure units using the unit analysis approach
To remember how to convert from gmol!!

30. Convert 5.2 atmospheres to mm Hg. 5.2 atm =
Pressure Unit Conversions, Unit Analysis Approach
1 atm = 760 mm Hg
760 mm Hg = 760 torr
1 atm = 101, 325 Pa
Convert 5.2 atmospheres to mm Hg.
5.2 atm =
Convert 5.2 atmospheres to torrs.

31. Convert 5.2 atmospheres to Pa. 5.2 atm = Convert 748 torrs to Pa
Pressure Unit Conversions, Unit Analysis Approach
1 atm = 760 mm Hg
760 mm Hg = 760 torr
1 atm = 101, 325 Pa
Convert 5.2 atmospheres to Pa.
5.2 atm =
Convert 748 torrs to Pa
748 torr =

32. Convert 7.48 g nitrogen gas to mol 7.48 g =
g  mol Conversions, Unit Analysis Approach
Convert 5.2 g CH4 to mol CH4
5.2 g CH =
Convert 7.48 g nitrogen gas to mol
7.48 g =

33. A sample of hydrogen gas, H2, has a volume of 9
A sample of hydrogen gas, H2, has a volume of 9.46 L at a temperature of 0 oC and a pressure of 988 torr. Calculate the number of grams of H2 present in this gas sample.
PV=nRT P= V= n= R= T=

34. A sample of hydrogen gas, H2, has a volume of 9
A sample of hydrogen gas, H2, has a volume of 9.46 L at a temperature of 0 oC and a pressure of 988 torr. Calculate the number of grams of H2 present in this gas sample.
PV=nRT
P= 988 torr
V= 9.46 L
n= ?
R= Latm/molK
T= 0 oC = 273 K

35. A sample of hydrogen gas, H2, has a volume of 9
A sample of hydrogen gas, H2, has a volume of 9.46 L at a temperature of 0 oC and a pressure of 988 torr. Calculate the number of grams of H2 present in this gas sample.
n = PV RT
n = PV = (1.3 atm)(9.46 L) = 0.55mol
RT ( Latm/molK) (273 K)
n = 0.55 mol H2

36. To convert between pressure units using the unit analysis approach
Objectives Review
To double check for unit agreement when working the 5-Step Problem Solving Method
To convert between pressure units using the unit analysis approach
To remember how to convert from gmol!!
Work Session: Page 480 # Review # 2 (g mol)

37. To understand the molar volume of an ideal gas
Objectives
To understand the molar volume of an ideal gas
To learn the definition of STP
To understand the relationship between laws and models (theories)
To understand the postulates of the kinetic molecular theory
To understand temperature
To learn how the kinetic molecular theory explains the gas laws
To describe the properties of real gases

38. Standard temperature and pressure (STP) 0oC and 1 atm
A1. Gas Stoichiometry
Molar Volume
Standard temperature and pressure (STP)
0oC and 1 atm
For one mole of a gas at STP
Molar volume of an ideal gas at STP L

39. PV=nRT P= V= n= R= T= 0.078 moles N2
A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N2 are present?
PV=nRT P= V= n= R= T=
0.078 moles N2

40. Exercise
A sample of oxygen gas has a volume of 2.50 L at STP. How many grams of O2 are present?
3.57 g
3.57 g of O2 are present.
(1.00 atm)(2.50 L) = n( )(273)
n = mol O2 × g/mol = 3.57 g O2

41. A. Laws and Models (Theories) : A Review
A model (theory) is an approximation and is destined to be modified as we understand more or are able to better measure phenomena occurring around us.
A model (theory) can never be proved absolutely true.

42. B. The Kinetic Molecular Theory of Gases

43. C. The Implications of the Kinetic Molecular Theory
Meaning of temperature – Kelvin temperature is directly proportional to the average kinetic energy of the gas particles
Relationship between Pressure and Temperature – gas pressure increases as the temperature increases because the particles speed up
Relationship between Volume and Temperature – volume of a gas increases with temperature because the particles speed up

44. D. Real Gases
Gases do not behave ideally under conditions of high pressure and low temperature.
Why?

45. The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero).
The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.
3) The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other.
The average internal kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

46. B. The Kinetic Molecular Theory of Gases

47. At high pressure the volume is decreased
D. Real Gases
At high pressure the volume is decreased
Molecule volumes become important
Attractions become important

48. Math Laws are still approximations….. PV = nRT ……. …..or does it?
D. Real Gases
Math Laws are still approximations…..
PV = nRT …….
…..or does it?

49. Calculate the pressure exerted by 0. 75 mol of He in a 1
Calculate the pressure exerted by 0.75 mol of He in a 1.0 L container at standard temperature. Use vdW…
P= nRT – a(n/V)2
(V-nb)
P = atm vs atm

50. To understand the molar volume of an ideal gas
Objectives Review
To understand the molar volume of an ideal gas
To learn the definition of STP
To understand the relationship between laws and models (theories)
To understand the postulates of the kinetic molecular theory
To understand temperature
To learn how the kinetic molecular theory explains the gas laws
To describe the properties of real gases (PHet)
Work session: Page Review # 1 - 5