Chapter 10: Properties of Gases: The Air We Breathe · Chapter 10: Properties of Gases: The Air We...

2/20/2017

1

Chapter 10: Properties of Gases:

The Air We Breathe

http://ozonewatch.gsfc.nasa.gov

South Pole Sept 24, 2006

15 February 2017

2/20/2017

2

Chapter Outline

10.1 The Properties of Gases

10.2 Effusion and the Kinetic Molecular Theory of Gases

10.3 Atmospheric Pressure

10.4 Relating P,T, and V: The Gas Laws

10.5 The Combined Gas Law

10.6 Ideal Gases and the Ideal Gas Law

10.7 Densities of Gases

10.8 Gases in Chemical Reactions

10.9 Mixtures of Gases

10.10 Solubilities of Gases and Henry’s Law

10.11 Gas Diffusion: Molecules Moving Rapidly

10.12 Real Gases

2/20/2017

3

The Properties of Gases

Neither definite shape nor definite volume


Gases can be compressed.

2/20/2017

4


All gases are miscible with all other gases.

http://catalog.flatworldknowledge.com/bookhub/4309?e=averill_1.0-ch13_s01

Chapter Outline












10.12 Real Gases

2/20/2017

5

1. Gas particles have tiny volumes compared with their container’s volume

Kinetic Molecular Theory of Gases

2. They don’t interact with other gas molecules, e.g. no intermolecular forces.


X

2/20/2017

6

3. They move randomly and constantly


4. Elastic collisions with walls of container and other gas molecules


2/20/2017

7

5. Have average kinetic energy that is proportional to absolute Kelvin temperature:


KEavg = ½ mu2rms

rms velocity 1/M

= 32 g/mol

= 28

= 18

= 4

2/20/2017

8

Graham’s Law of Effusion, p. 415

Effusion is the process

where a gas escapes

through a small pore in the

container wall into a region

of lower pressure.

Sample Exercise 10.1: Calculating

Relative Rates of Effusion

An odorous gas emitted by a hot spring was found to effuse

at 0.342 times the rate at which helium effuses. What is the

molar mass of the emitted gas?

2/20/2017

9

Chapter Outline












10.12 Real Gases

Pressure = force/unit area

Molecules collide with the inside surface of the container.

The force of the collision is measured as pressure.

Pounds/in2 (psi)

Atmospheres (atm)

Pascals (N/m2)

Torr (mmHg)

14.7 psi

1 atm

101.325 X 103 Pa

760 mmHg

Pressure at Sea Level

2/20/2017

10

Torricelli’s Barometer

vacuum

Column of

mercury

760 mm Hg

Atmospheric

pressure

The pressure of the

atmosphere on the surface

of the mercury in the dish

is balanced by the

downward pressure

exerted by the mercury in

the column.

Elevation and Atmospheric

Pressure

0.83 atm

0.62 atm

0.35 atm

Sea level

2/20/2017

11

Chapter Outline












10.12 Real Gases

State Variables for a Gas

P = pressure V = volume

T = temperature n = number of

moles

2/20/2017

12

Boyle’s Law: P and V

(n and T held constant)

Gases are compressible

• Pressure ↑ as Volume ↓

Boyle’s Law:

• P 1/V (T and n fixed)

• or, P × V = constant

• or, P1V1 = P2V2

• Decreasing volume increases

number of collisions/area; P↑

(KMT Postulates #3 & 4)

Boyle’s Law and Respiration

2/20/2017

13

Applying Boyle’s Law Example

A bubble of oxygen at the bottom of a lake floats up to the surface. The pressure at the bottom of the lake is 4.75 atm and the volume is 5.65 mL. At the surface, the new volume is 5.65 mL. Assuming that the temperature and number of moles remained constant, what is the final volume of the bubble?

Explaining Boyle’s Law Using Kinetic

Molecular Theory

2/20/2017

14

Charles’s Law: V and T

(n and P held constant)

Charles’s Law:

• V T (P, n constant)

Volume of a gas extrapolates

to zero at absolute zero (0 K

= −273°C).

Kinetic energy ↑ as T ↑; force of

collisions increases and gas

expands to maintain constant

P (KMT Post. #3, 4 & 5).

or,V1

T1

=V2

T2

Jacques Alexandre Charles (1796-1823)

The French chemist Charles was most famous in his lifetime for his experiments in

ballooning. The first such flights were made by the Montgollier brothers in June 1783,

using a large spherical balloon made of linen and paper and filled with hot air. In

August 1783, however, a different group. supervised by Jacques Charles, tried a

different approach. Exploiting his recent discoveries in the study of gases, Charles

decided to inflate the balloon with hydrogen gas. Because hydrogen would escape

easily from a paper bag, Charles made a bag of silk coaled with a rubber solution.

Inflating the bag to its final diameter took several days and required nearly 500

pounds of acid and 1000 pounds of iron to generate the hydrogen gas. A huge crowd

watched the ascent on August 27, 1783. The balloon stayed aloft for almost 45

minutes and travelled about 15 miles. When it landed in a village, however, the

people were so terrified they tore if to shreds.

2/20/2017

15

Sample Exercise 10.4:

Applying Charles’ Law

Several students at a northern New England campus are hosting a party celebrating the mid-January start of “spring” semester classes. They decide to decorate the front door of their apartment building with party balloons. The air in the inflated balloons is initially 70 oF. After an hour outside, the temperature of the balloons is -12 oF. Assuming no air leaks from the balloons and the pressure in them does not change significantly, how much does their volume change? Express your answer as a percentage of the initial volume.

Explaining Charles’ Law Using Kinetic

Molecular Theory

2/20/2017

16

Avogadro’s Law: V and n

(T and P held constant)

Volume is directly proportional to the number

of moles of gas, V n (T, P constant)

constant

n

V

2

2

1

1,n

V

n

Vor

Increasing n increases the

number of collisions, gas

expands to keep pressure

constant (KMT Post. #3 & 4).

Explaining Avogadro’s Law Using

Kinetic Molecular Theory

2/20/2017

17

Amonton’s Law: P and T

(n and V held constant)

P T (n, V constant)

or,P1

T1

=P2

T2

Increasing T will increase force

of collisions if volume is kept

constant; P will increase (KMT

Post. #3, 4 & 5).

P

T= constant


Applying Amonton’s Law

Labels on aerosol cans caution against their incineration because the cans may explode when the pressure inside them exceeds 3.00 atm. At what temperature in degrees Celcius might an aerosol can burst if its internal pressure is 2.00 atm at 25 oC?

2/20/2017

18

Explaining Amonton’s Law Using

Kinetic Molecular Theory

Chapter Outline












10.12 Real Gases

2/20/2017

19

Combining Boyle’s and Charles’ Law (where n is held constant)

The Combined Gas Law


Applying the Combined Gas Law

The pressure inside a weather balloon as it is released is 798 mmHg. If the volume and temperature of the balloon are 131 L and 20 oC, what is the volume of the balloon when it reaches an altitude where its internal pressure is 235 mmHg and T = -52 oC?

2/20/2017

20

Chapter Outline












10.12 Real Gases

Ideal Gas Equation

Charles’ law: V T (at constant n and P)

Avogadro’s law: V n (at constant P and T)

Boyle’s law: V (at constant n and T) 1 P

2/20/2017

21

Standard Temperature and Pressure (STP).

PV = nRT

Experiments show that at STP,

1 mole of an ideal gas

occupies 22.414 L.


Applying the Ideal Gas Law

Bottles of compressed O2 carried by climbers ascending Mt. Everest are

designed to hold one kilogram of the gas. What volume of O2 can one

bottle deliver to a climber at an altitude where the temperature is -38 oC

and the atmospheric pressure is 0.35 atm? Assume that each bottle

contains 1.00 kg of O2.

2/20/2017

22

Chapter Outline




10.4 The Gas Laws






10.10 Solubility of Gases and Henry’s Law


10.12 Real Gases

Densities and Molecular Weights of

Gases Using PV = nRT

PV = nRT

2/20/2017

23


Calculating the Density of a Gas

According to the U.S National Weather Service, the air temperature in Phoenix, AZ

reached 78 oF on January 1, 2012, when the atmospheric pressure was 1024 millibars.

What is the density of the air? Assume the average molar mass of air is 28.8 g/mol,

which is the weighted average of the molar masses of the various gases in dry air.

Example: Calculating the Molecular

Weight from PV = nRT

1.018 g of Freon-113 gas is trapped in a 145 mL container at

760 mmHg and 50.0°C. What is the molar mass of Freon-113?

2/20/2017

24

Chapter Outline




10.4 The Gas Laws








10.12 Real Gases

Gas Laws & Stoichiometry

2/20/2017

25

Example: Combining Stoichiometry and

the Ideal Gas Law

Chlorine gas can be prepared in the laboratory by the reaction of

manganese dioxide with hydrochloric acid:

MnO2(s) + 4 HCl(aq) MnCl2(aq) + 2 H2O(l) + Cl2(g)

How many grams of MnO2 should be added to excess HCl to obtain 275

mL of chlorine gas at 5.0°C and 650 mmHg?

Chapter Outline












10.12 Real Gases

2/20/2017

26

Dalton’s Law of Partial Pressures

For a mixture of gases in a container:

• Ptotal = P1 + P2 + P3 + . . .

Total pressure depends only on total number moles

of gas, not on their identities

Mole Fraction & Partial Pressure

Mole Fraction:

• Ratio of the # of moles of a given component

in a mixture to the total # of moles in a

mixture:

Mole Fraction in Terms of Pressure:

• When V and T are constant, P n

1 11

total 1 2 3

n nx

n n n n ...

2/20/2017

27

Since P n

And:

Then…

1 11

total total

n Px

n P

1 1 totalP x P

11

total

Px

P

Mole Fraction & Partial Pressure


Mole Fractions and Partial Pressures

Scuba divers who dive to depths below 50 meters may breathe a gas mixture called Trimix during the deepest parts of their dives. One formulation of the mixture, called Trimix 10/70, is 10% oxygen, 70% helium, and 20% nitrogen by volume. What is the mole fraction of each gas in this mixture, and what is the partial pressure of oxygen in the lungs of a diver at a depth of 60 meters (where the ambient pressure is 7.0 atm)?

2/20/2017

28

Collecting a Gas over Water

2 KClO3(s) → 2 KCl(s) + 3 O2(g)

Gases collected:

O2(g) and H2O(g)

2 2total O H OP P P

During the decomposition of KClO3, 92.0 mL of gas is collected by the displacement of water at 25.0 oC. If atmospheric pressure is 756 mmHg, what mass of O2 is collected?

Sample Exercise 10.12: Calculating the Quantity

of a Gas Collected by Water Displacement

2/20/2017

29

Chapter Outline




10.4 The Gas Laws








10.12 Real Gases

Solubility of Gases

Solubility of gases

depends on T and P

Solubility ↑ as Pressure ↑

Solubility ↓ as Temperature ↑

2/20/2017

30

Henry’s Law

Henry’s Law:

• The higher the partial

pressure of the gas

above a liquid, the

more soluble

• Cgas Pgas

• Cgas kH Pgas

Solubility of Oxygen in Water

2/20/2017

31


Gas Solubility Using Henry’s Law

Lake Titicaca is located high in the Andes Mountains between Peru and Bolivia. Its surface is 3811 m above sea level, where the average atmospheric pressure is 0.636 atm. During the summer, the average temperature of the water’s surface rarely exceeds 15 oC. What is the solubility of oxygen in Lake Titicaca at that temperature? Express your answer in molarity and in mg/L.

2/20/2017

32

Chapter Outline












10.12 Real Gases

Gas Diffusion: Molecules Moving Rapidly

𝑢𝑟𝑚𝑠 =3𝑅𝑇

𝑀

R = 8.314 J/mol K

2/20/2017

33

Practice Exercise 10:14

Calculating Root-Mean-Square Speeds

Calculate the root-mean-squared speed of nitrogen molecules at 25 oC.

𝑈𝑟𝑚𝑠,𝐴

𝑈𝑟𝑚𝑠,𝐵=

𝑒𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝐴

𝑒𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝐵=

𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝐴

𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝐵=

𝑀𝐵

𝑀𝐴

Graham’s Law of Effusion:

Same for Diffusion!

Problem 10.121

A flask of ammonia is connected to a flask of an unknown acid HX by a 1.00 m

glass tube. As the two gases diffuse down the tube, a white ring of NH4X forms

68.5 cm from the ammonia flask. Identify element X.

Chapter 10: Properties of Gases: The Air We Breathe · Chapter 10: Properties of Gases: The Air We...

Documents

Transcript of Chapter 10: Properties of Gases: The Air We Breathe · Chapter 10: Properties of Gases: The Air We...