V. Two More Laws (p. 322-325, 351-355) Read these pages first!

Ch. 10 & 11 - Ch. 10 & 11 - GasesGases

V. Two More Laws(p. 322-325, 351-355)Read these pages first!

V. Two More Laws(p. 322-325, 351-355)Read these pages first!

John A. Schreifels

Chemistry 211

2

The Behavior of Real The Behavior of Real GasesGasesThe Behavior of Real The Behavior of Real GasesGases

The molar volume is not constant as is expected for ideal gases.

These deviations due to an attraction between some molecules.

Finite molar molecular volume. For compounds that deviate from ideality the van der

Waals equation is used:

where a and b are constants that are characteristic of the gas.

Applicable at high pressures and low temperatures.

nRT=nb)-(VV

an+P2

2

John A. Schreifels

Chemistry 211

3

The Kinetic Theory – Molecular The Kinetic Theory – Molecular Theory of GasesTheory of GasesThe Kinetic Theory – Molecular The Kinetic Theory – Molecular Theory of GasesTheory of Gases

Microscopic view of gases is called the kinetic theory of gases and assumes that • Gas is collection of molecules (atoms) in

continuous random motion.• The molecules are infinitely small point-like

particles that move in straight lines until they collide with something.

• Gas molecules do not influence each other except during collision.

• All collisions are elastic; the total kinetic energy is constant at constant T.

• Average kinetic energy is proportional to T.

John A. Schreifels

Chemistry 211

4

Gases and Gas PressureGases and Gas PressureGases and Gas PressureGases and Gas Pressure

They form homogeneous solutions. All gases dissolve in each other. • Gases are compressible.• Large molar volume.

Barometer usually mercury column in tube; mm Hg is a measure of pressure.

Manometer tube of liquid connected to enclosed container makes it possible to measure pressure inside the container.

Pressure• One of the most important of the measured quantities for

gases• defined as the force/area P = f/area. • Pressure has traditionally been measured in units relating to

the height of the Hg and is thus expressed as mm Hg = 1 Torr.

John A. Schreifels

Chemistry 211

5

Gas PressureGas PressureGas PressureGas Pressure

Pressure is directly proportional to the height of the column in a barometer or manometer.

Mercury often used but other low density liquids are used for low pressure changes:

P = dHgghHg = doilghoil or dHghHg = doilhoil. E.g. Water is sometimes used to determine pressure; determine

the height of water if the barometer pressure was 750 mmHg. The density of Hg = 13.596 g/cm3 and 1.00 g/cm3 respectively.

Solution:

dghA

dVg

A

mg

A

FP

OmmH 10197

cm/g 00.1

cm/g 596.13mmHg 750

d

dhh

2

3

3

OH

HgHgOH

22

B. Dalton’s LawB. Dalton’s LawB. Dalton’s LawB. Dalton’s Law

The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases.

Ptotal = P1 + P2 + ...When a H2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H2 and water vapor.

GIVEN:

PH2 = ?

Ptotal = 94.4 kPa

PH2O = 2.72 kPa

WORK:

Ptotal = PH2 + PH2O

94.4 kPa = PH2 + 2.72 kPa

PH2 = 91.7 kPa


Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa.

Look up water-vapor pressure on p.899 for 22.5°C.

Sig Figs: Round to least number of decimal places.

The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H2 and water vapor.

GIVEN:

Pgas = ?

Ptotal = 742.0 torr

PH2O = 42.2 torr

WORK:

Ptotal = Pgas + PH2O

742.0 torr = PH2 + 42.2 torr

Pgas = 699.8 torr

A gas is collected over water at a temp of 35.0°C when the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas?

Look up water-vapor pressure on p.899 for 35.0°C.

Sig Figs: Round to least number of decimal places.


The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.

C. Graham’s LawC. Graham’s LawC. Graham’s LawC. Graham’s Law

DiffusionDiffusion• Spreading of gas molecules

throughout a container until evenly distributed.

EffusionEffusion

• Passing of gas molecules through a tiny opening in a container


KE = ½mv2

Speed of diffusion/effusionSpeed of diffusion/effusion

• Kinetic energy is determined by the temperature of the gas.

• At the same temp & KE, heavier molecules move more slowly.Larger m smaller v


Graham’s LawGraham’s Law• Rate of diffusion of a gas is inversely related

to the square root of its molar mass.• The equation shows the ratio of Gas A’s

speed to Gas B’s speed.

A

B

B

A

m

m

v

v

Determine the relative rate of diffusion for krypton and bromine.

1.381

Kr diffuses 1.381 times faster than Br2.

Kr

Br

Br

Kr

m

m

v

v2

2

A

B

B

A

m

m

v

v

g/mol83.80

g/mol159.80


The first gas is “Gas A” and the second gas is “Gas B”. Relative rate mean find the ratio “vA/vB”.

A molecule of oxygen gas has an average speed of 12.3 m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions?

A

B

B

A

m

m

v

v

2

2

2

2

H

O

O

H

m

m

v

v

g/mol 2.02

g/mol32.00

m/s 12.3

vH 2


3.980m/s 12.3

vH 2

m/s49.0 vH 2

Put the gas with the unknown

speed as “Gas A”.

An unknown gas diffuses 4.0 times faster than O2. Find its molar mass.

Am

g/mol32.00 16

A

B

B

A

m

m

v

v

A

O

O

A

m

m

v

v2

2

Am

g/mol32.00 4.0

16

g/mol32.00 mA

2

Am

g/mol32.00 4.0

g/mol2.0


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.

TEAM PRACTICE!TEAM PRACTICE!TEAM PRACTICE!TEAM PRACTICE!

Work the following problems in your book. Check your work using the answers provided in the margin.• p. 324

SAMPLE PROBLEM 10-6PRACTICE 1 & 2

• p. 355 SAMPLE PROBLEM 11-10PRACTICE 1, 2, & 3

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V. Two More Laws (p. 322-325, 351-355) Read these pages first!