The Gas Laws Learning about the special behavior of gases Intro. to Objective # 4 Section 21.5, Note pack pg. 8

The Gas LawsThe Gas LawsThe Gas LawsThe Gas LawsLearning about the special behavior of Learning about the special behavior of

gasesgases

Intro. to Objective # Intro. to Objective # 44

Section 21.5, Note pack pg. 8Section 21.5, Note pack pg. 8

Avogardro’s Hypothesis

• Although gas molecules of different gases are different sizes, equal volumes of gases at the same temperature and pressure contain equal number of particles.

In other words…• Even though Chlorine gas

molecules are 35 times bigger than hydrogen gas molecules, equal numbers of the two gases would occupy the same volume at the same temperature and pressure.

Example 1Determine the volume occupied

by .202 mole of a gas at STP



.202 mol x 22.4 L 1 1 mol



.202 mol x 22.4 L = 4.52 L 1 1 mol

Example 2

What is the volume occupied by .742 mol of Argon at STP?

Example 2


.742 mol Ar x 22.4L Ar 1 1 mol Ar

Example 2


.742 mol Ar x 22.4L Ar = 16.62 L Ar

1 1 mol Ar

Example 3

• Determine the volume occupied by 14 grams of nitrogen gas at STP?

Example 3

• Determine the volume occupied by 14 grams of nitrogen gas at STP?14g N2 x 1 mol N2

1 28g N2

Example 3

• Determine the volume occupied by 14 grams of nitrogen gas at STP?14g N2 x 1 mol N2 = 0.5 mol N2

1 28g N2

Example 3


1 28g N2

0.5 mol N2 x 22.4 L N2

1 1 mol N2

Example 3


1 28g N2

0.5 mol N2 x 22.4 L N2 = 11.2 L N2

1 1 mol N2

Dalton’s Law of Partial Pressures

• Many gases, including air, are mixtures. Remember, the particles in a gas at the same temperature have the same average kinetic energy.

• Gas pressure depends only on the number of gas particles in a given volume and their average kinetic energy. The kind of particle is not important.

Dalton’s Law of Partial Pressures

• Define Partial Pressure -– “The contribution each gas in a mixture

makes to the total pressure” is the partial pressure exerted by that gas…

• Dalton’s Law - At constant volume and temp, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures.

•

• the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures.

For the examples shown, we will follow this

progression:Mass ofThe gas

# of Moles

Ideal GasLaw

Daltons Law of Partial

Pressures

Example 1 Air contains oxygen, nitrogen, carbon dioxide,

and trace amounts of other gases. What is the partial pressure of oxygen (PO2) at 101.3 kPa if the partial pressure of nitrogen, carbon dioxide, and other gases are 79.1 kPa, 0.04 kPa, and 0.94 kPa, respectively.



If Ptotal = PO2 + PN2 + PCO2 + Pother and




101.3 kPa = ? + 79.1 kPa + 0.04 kPa + 0.94 kPa




101.3 kPa = ? + 79.1 kPa + 0.04 kPa + 0.94 kPa

Then PO2 = Ptotal – (PN2 + PCO2 + Pothers) …or…




101.3 kPa = ? + 79.1 kPa + 0.04 kPa + 0.94 kPa

Then PO2 = Ptotal – (PN2 + PCO2 + Pothers) …or…

PO2 = 101.3 kPa – (79.1 + 0.04 + 0.94)

Example 1 Air contains oxygen, nitrogen, carbon dioxide, and

trace amounts of other gases. What is the partial pressure of oxygen (PO2) at 101.3 kPa if the partial pressure of nitrogen, carbon dioxide, and other gases are 79.1 kPa, 0.04 kPa, and 0.94 kPa, respectively.


101.3 kPa = ? + 79.1 kPa + 0.04 kPa + 0.94 kPa

Then PO2 = Ptotal – (PN2 + PCO2 + Pothers) …or… PO2 = 101.3 kPa – (79.1 + 0.04 + 0.94)

PO2 = 21.22 kPa



# of

Moles

Ideal Gas

Law

Daltons

Law of Partial Pressures

Example 2Determine the total pressure of a gas mixture that

contains oxygen, nitrogen, and helium if the partial pressure of the gases are as follows:

• Oxygen = 20 kPa• Nitrogen = 46.7 kPa• Helium = 26.7 kPa



• Oxygen = 20 kPa• Nitrogen = 46.7 kPa• Helium = 26.7 kPaIf Ptotal = PO2 + PN2 + PHe and



• Oxygen = 20 kPa• Nitrogen = 46.7 kPa• Helium = 26.7 kPaIf Ptotal = PO2 + PN2 + PHe and __?__ kPa = 20 kPa + 46.7 kPa + 26.7 kPa



• Oxygen = 20 kPa• Nitrogen = 46.7 kPa• Helium = 26.7 kPaIf Ptotal = PO2 + PN2 + PHe and

__?__ kPa = 20 kPa + 46.7 kPa + 26.7 kPa

Then the total pressure is 93.4 kPa



# of Moles

Ideal Gas

Law

Daltons

Law of Partial Pressures

Example 3A mixture containing 0.538 mole of He (g), 0.315 mol Ne (g),

and 0.103 mole Ar (g) is confided in a 7 Liter vessel at 25 Celsus.

• A. Calculate the partial pressure of each of the gases in the mixture




We will need to re-arrange the Ideal Gas Law for each of these:





PHe = nRT

V PNe = nRT

V PAr = nRT

V





PHe = nRT = (0.538 mol)x(8.31 kPaL/ molK )x(298K) = 190.3 kPa

V (7 Liters)PNe = nRT

VPAr = nRT

V





PHe = nRT = (0.538 mol)x(8.31 kPaL/ molK )x(298K) = 190.3 kPa

V (7 Liters)PNe = nRT = (0.315 mol)x(8.31 kPaL/ molK )x(298K) = 111.4

kPa V (7 Liters)PAr = nRT

V

Example 3A mixture containing 0.538 mole of He (g), 0.315 mol

Ne (g), and 0.103 mole Ar (g) is confided in a 7 Liter vessel at 25 Celsus.


We will need to re-arrange the Ideal Gas Law for each of these:PHe = nRT = (0.538 mol)x(8.31 kPaL/ molK )x(298K) = 190.3 kPa V (7 Liters)PNe = nRT = (0.315 mol)x(8.31 kPaL/ molK )x(298K) = 111.4 kPa V (7 Liters)PAr = nRT = (0.103 mol)x(8.31 kPaL/ molK )x(298K) = 36.4 kPa V (7 Liters)

Now we know how much pressure each gas is contributing to the mixture.

Example 3A mixture containing 0.538 mole of He (g), 0.315

mol Ne (g), and 0.103 mole Ar (g) is confided in a 7 Liter vessel at 25 Celsus.


PHe = 190.3 kPa

PNe = 111.4 kPa

PAr = 36.4 kPa

• B. Calculate the total pressure of the mixture




PHe = 190.3 kPa

PNe = 111.4 kPa

PAr = 36.4 kPa

• B. Calculate the total pressure of the mixtureP total = PHe + PNe + PAr




PHe = 190.3 kPa

PNe = 111.4 kPa

PAr = 36.4 kPa


P total = 190.3 kPa + 111.4 kPa + 36.4 kPa




PHe = 190.3 kPa

PNe = 111.4 kPa

PAr = 36.4 kPa


P total = 190.3 kPa + 111.4 kPa + 36.4 kPa

= 338.1 kPa



# of Moles

Ideal GasLaw

Daltons Law of Partial

Pressures

Example 4:A mixture of 2.5 grams of each of CH4, C2H4, and C4H10 is

contained in a 2 liter flask as a temperature of 15o Celsius.• Calculate the partial pressure of each of the gases in the

mixture.

• Calculate the total pressure of the mixture.



mixture.Before we can find the pressure, we first need to convert the

masses into moles of each gas.





masses into moles of each gas.2.5g CH4 1 2.5g C2H4 1 2.5g C4H10 1





masses into moles of each gas.2.5g CH4 x 1 mol CH4 = 1 16g CH4

2.5g C2H4 x 1 mol C2H4 = 1 28g C2H4

2.5g C4H10 x 1 mol C4H10 = 1 58g C4H10





masses into moles of each gas.2.5g CH4 x 1 mol CH4 = 0.156 mol CH4

1 16g CH4

2.5g C2H4 x 1 mol C2H4 = 0.089 mol C2H4

1 28g C2H4

2.5g C4H10 x 1 mol C4H10 = 0.043 mol C4H10

1 58g C4H10

Now we will use the number of moles to help us find the partial pressure of each gas.




mixture. Now we can find the partial pressure for each gas.PCH4 = nRT V PC2H4 = nRT V PC4H10 = nRT V




mixture. We’ll use the # of moles we found as “n”.PCH4 = nRT = (0.156 mol)__________________ V PC2H4 = nRT = (0.089 mol)_________________ V PC4H10 = nRT = (0.043 mol)_________________ V




mixture. Now we can find the partial pressure for each gas.PCH4 = nRT = (0.156 mol)x(8.31 kPaL/molK)x(288K) = V (2 Liters)PC2H4 = nRT = (0.089 mol)x(8.31 kPaL/molK)x(288K) = V (2 Liters)PC4H10 = nRT = (0.043 mol)x(8.31 kPaL/molK)x(288K) = V (2 Liters)




mixture. Now we can find the partial pressure for each gas.PCH4 = nRT = (0.156 mol)x(8.31 kPaL/molK)x(288K) = 186.7 kPa V (2 Liters)PC2H4 = nRT = (0.089 mol)x(8.31 kPaL/molK)x(288K) = 106.5

kPa V (2 Liters)PC4H10 = nRT = (0.043 mol)x(8.31 kPaL/molK)x(288K) = 51.5 kPa V (2 Liters)




mixture. Now we can find the partial pressure for each gas.PCH4 = nRT = (0.156 mol)x(8.31 kPaL/molK)x(288K) = 186.7 kPa V (2 Liters)PC2H4 = nRT = (0.089 mol)x(8.31 kPaL/molK)x(288K) = 106.5 kPa V (2 Liters)PC4H10 = nRT = (0.043 mol)x(8.31 kPaL/molK)x(288K) = 51.5 kPa V (2 Liters)

• Calculate the total pressure of the mixture.Ptotal = PCH4 + PC2H4 + PC4H10





= (186.7 kPa) + (106.5 kPa) + (51.5 kPa)





344.7 kPa = (186.7 kPa) + (106.5 kPa) + (51.5 kPa)

Page 10It would be good to review the

section. Collecting Gas over Water

The Gas LawsThe Gas LawsThe Gas LawsThe Gas Laws

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The Gas Laws Learning about the special behavior of gases Intro. to Objective # 4 Section 21.5, Note pack pg. 8