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Chapter 9

- Gases Their Properties and Behavior

Properties of Gases

- There are 5 important properties of gases
- Confined gases exerts pressure on the wall of a

container uniformly - Gases have low densities
- Gases can be compressed
- Gases can expand to fill their contained

uniformly - Gases mix completely with other gases in the same

container

Kinetic Molecular Theory of Gases

- The Kinetic Molecular Theory of Gases is the

model used to explain the behavior of gases in

nature. - This theory presents physical properties of gases

in terms of the motion of individual molecules - Average Kinetic Energy ? Kelvin Temperature
- Gas molecules are points separated by a great

distance - Particle volume is negligible compared to gas

volume - Gas molecules are in rapid random motion
- Gas collisions are perfectly elastic
- Gas molecules experience no attraction or

repulsion

Properties that Describe a Gas

- These properties are all related to one another.
- When one variable changes, it causes the other

three to react in a predictable manner.

Gas Pressure (P)

- Gas pressure (P) is the result of constantly

moving gas molecules striking the inside surface

of their container.

Atmospheric Pressure

- Atmospheric pressure is the pressure exerted by

the air on the earth.

- Evangelista Torricelli invented the barometer in

1643 to measure atmospheric pressure. - Atmospheric pressure is 760 mm of mercury or 1

atmosphere (atm) at sea level.

What happens to the atmospheric pressure as you

go up in elevation?

Measurement of Gas Pressure

- Traditionally, the gas pressure inside of a

container is measured with a manometer

Units of Pressure

- Standard pressure is the atmospheric pressure at

sea level, 760 mm of mercury. - Here is standard pressure expressed in other

units

Gas Pressure Conversions

- The barometric pressure is 697.2 torr. What is

the barometric pressure in atmospheres? In mm Hg?

In Pascals (Pa)?

Gas Law Problems

Boyles Law (V and P)

- Boyles Law states that the volume of a gas is

inversely proportional to the pressure at

constant temperature.

- Mathematically, we write
- For a before and after situation

P1V1 P2V2

Boyles Law Problem

- A 1.50 L sample of methane gas exerts a pressure

of 1650 mm Hg. What is the final pressure if the

volume changes to 7.00 L?

(1650 mm Hg )(1.50 L)

354 mm Hg

7.00 L

Charles Law (V and T)

- In 1783, Jacques Charles discovered (while hot

air ballooning) that the volume of a gas is

directly proportional to the temperature in

Kelvin.

- Mathematically, we write
- For a before and after situation

T ? V

Charles Law Problem

- A 275 L helium balloon is heated from 20?C to

40?C. What is the final volume at constant P?

V1 T2

V2

rearranges to

T1

Gay-Lussacs Law (P and T)

- In 1802, Joseph Gay-Lussac discovered that the

pressure of a gas is directly proportional to the

temperature in Kelvin.

- Mathematically, we write
- For a before and after situation

T ? P

Gay-Lussacs Law Problem

- A steel container of nitrous oxide at 15.0 atm is

cooled from 25?C to 40?C. What is the final

volume at constant V?

P1 T2

P2

rearranges to

T1

(15.0 atm)(298 K)

11.7 atm

233 K

Avogadros Law (n and V)

- In the previous laws, the amount of gas was

always constant. - However, the amount of a gas (n) is directly

proportional to the volume of the gas, meaning

that as the amount of gas increases, so does the

volume.

- Mathematically, we write
- For a before and after situation

n ? V

Avogadros Law Problem

- A steel container contains 2.6 mol of nitrous

oxide with a volume 15.0 L. If the amount of

nitrous oxide is increased to 8.4 mol, what is

the final volume at constant T and P?

V1 n2

rearranges to

V2

n1

(15.0 L)(8.4 mol)

48.5 L

2.6 mol

Combined Gas Law

- When we introduced Boyles, Charles, and

Gay-Lussacs Laws, we assumed that one of the

variables remained constant. - Experimentally, all three (temperature, pressure,

and volume) usually change. - By combining all three laws, we obtain the

combined gas law

Combined Gas Law Problem

- Oxygen gas is normally sold in 49.0 L steel

containers at a pressure of 150.0 atm. What

volume would the gas occupy if the pressure was

reduced to 1.02 atm and the temperature raised

from 20oC to 35oC?

Molar Volume and STP

- Standard temperature and pressure (STP) are

defined as 0?C and 1 atm. - At standard temperature and pressure, one mole of

any gas occupies 22.4 L. - The volume occupied by one mole of gas (22.4 L)

is called the molar volume.

1 mole Gas 22.4 L

Molar Volume Calculation Volume to Moles

- A sample of methane, CH4, occupies 4.50 L at STP.

How many moles of methane are present?

Mole Unit Factors

- We now have three interpretations for the mole
- 1 mol 6.02 1023 particles
- 1 mol molar mass
- 1 mol 22.4 L (at STP for a gas)
- This gives us 3 unit factors to use to convert

between moles, particles, mass, and volume.

Mole Calculation - Grams to Volume

- What is the mass of 3.36 L of ozone gas, O3, at

STP?

Mole Calculation Molecules to Volume

- How many molecules of hydrogen gas, H2, occupy

0.500 L at STP?

1.34 1022 molecules H2

Gas Density and Molar Mass

- The density of a gas is much less than that of a

liquid. - We can calculate the density of any gas at STP

easily. - You can rearrange this equation to find the Molar

mass of an unknown gas too!

molar mass in grams (MM)

density, g/L

molar volume in liters (MV)

Calculating Gas Density

- What is the density of ammonia gas, NH3, at STP?
- 1.96 g of an unknown gas occupies 1.00 L at STP.

What is the molar mass?

The Ideal Gas Law

- When working in the lab, you will not always be

at STP. - The four properties used in the measurement of a

gas (Pressure, Volume, Temperature and moles) can

be combined into a single gas law - Here, R is the ideal gas constant and has a value

of - Note the units of R. When working problems with

the Ideal Gas Law, your units of P, V, T and n

must match those in the constant!

PV nRT

0.0821 atm?L/mol?K

Ideal Gas Law Problem

- Sulfur hexafluoride (SF6) is a colorless,

odorless, very unreactive gas. Calculate the

pressure (in atm) exerted by 1.82 moles of the

gas in a steel vessel of volume 5.43 L at 69.5C.

Ideal Gas Law and Molar Mass

- Density and Molar Mass Calculations
- You can calculate the density or molar mass (M)

of a gas. - The density of a gas is usually very low under

atmospheric conditions.

Ideal Gas Law and Molar Mass

- What is the molar mass of a gas with a density of

1.342 g/L1 at STP? - What is the density of uranium hexafluoride, UF6,

(MM 352 g/mol) under conditions of STP? - The density of a gaseous compound is 3.38 g/L1

at 40C and 1.97 atm. What is its molar mass?

Gases in Chemical Reactions

- Gases are involved as reactants and/or products

in numerous chemical reactions. - Typically, the information given for a gas in a

reaction is its Pressure (P), volume (V) (or

amount of the gas (n)) and temperature (T). - We use this information and the Ideal Gas Law to

determine the moles of the gas (n) or the volume

of the gas (V). - Once we have this information, we can proceed

with the problem as we would any other

stoichiometry problem.

A (g) X (s) ? B (s) Y (l)

Reaction with a Gas

- Hydrogen gas is formed when zinc metal reacts

with hydrochloric acid. How many liters of

hydrogen gas at STP are produced when 15.8 g of

zinc reacts? - Zn (s) 2HCl (aq) ? H2 (g) ZnCl2 (aq)

Can use because at STP!

Reaction with a Gas

- Hydrogen gas is formed when zinc metal reacts

with hydrochloric acid. How many liters of

hydrogen gas at a pressure of 755 atm and 35C

are produced when 15.8 g of zinc reacts? - Zn (s) 2HCl (aq) ? H2 (g) ZnCl2 (aq)

Use because not at STP!

Daltons Law of Partial Pressures

- In a mixture of gases the total pressure, Ptot,

is the sum of the partial pressures of the gases - Daltons law allows us to work with mixtures of

gases.

Ptot P1 P2 P3 etc.

Daltons Law of Partial Pressures

- For a two-component system, the moles of

components A and B can be represented by the mole

fractions (XA and XB). - What is the mole fraction of each component in a

mixture of 12.45 g of H2, 60.67 g of N2, and 2.38

g of NH3?

n

n

1

B

A

X

X

X

X

B

A

B

A

n

n

n

n

B

A

B

A

Daltons Law of Partial Pressures

- Mole fraction is related to the total pressure

by - On a humid day in summer, the mole fraction of

gaseous H2O (water vapor) in the air at 25C can

be as high as 0.0287. Assuming a total pressure

of 0.977 atm, what is the partial pressure (in

atm) of H2O in the air?

Daltons Law of Partial Pressures

- Exactly 2.0 moles of Ne and 3.0 moles of Ar were

placed in a 40.0 L container at 25C. What are

the partial pressures of each gas and the total

pressure? - A sample of natural gas contains 6.25 moles of

methane (CH4), 0.500 moles of ethane (C2H6), and

0.100 moles of propane (C3H8). If the total

pressure of the gas is 1.50 atm, what are the

partial pressures of the gases?

Kinetic Molecular Theory of Gases

- The Kinetic Molecular Theory of Gases is the

model used to explain the behavior of gases in

nature. - This theory presents physical properties of gases

in terms of the motion of individual molecules. - Average Kinetic Energy ? Kelvin Temperature
- Gas molecules are points separated by a great

distance - Particle volume is negligible compared to gas

volume - Gas molecules are in rapid random motion
- Gas collisions are perfectly elastic
- Gas molecules experience no attraction or

repulsion

Kinetic Molecular Theory of Gases

Kinetic Molecular Theory of Gases

- Average Kinetic Energy (KE) is given by

Kinetic Molecular Theory of Gases

- The RootMeanSquare Speed (uRMS) is a measure

of the average molecular speed of a particle of

gas.

Taking square root of both sides gives the

equation

R 8.314 J/mol K

Kinetic Molecular Theory of Gases

- Calculate the rootmeansquare speeds (uRMS) of

helium atoms and nitrogen molecules in m/s at

25C.

Grahams Law Diffusion and Effusion

- Diffusion is the mixing of different gases by

random molecular motion and collision.

- Effusion is when gas molecules escape without

collision, through a tiny hole into a vacuum.

Grahams Law Diffusion and Effusion

- Grahams Law The rate of effusion is

proportional to its RMS speed (uRMS). - For two gases at same temperature and pressure

Rate ?

Grahams Law Diffusion and Effusion

- Under the same conditions, an unknown gas

diffuses 0.644 times as fast as sulfur

hexafluoride, SF6 (MM 146 g/mol). What is the

identity of the unknown gas if it is also a

hexafluoride? - What are the relative rates of diffusion of the

three naturally occurring isotopes of neon 20Ne,

21Ne, and 22Ne?

Behavior of Real Gases

- Deviations from Ideal behavior result from two

key assumptions about ideal gases. - Molecules in gaseous state do not exert any

force, either attractive or repulsive, on one

another. - Volume of the molecules is negligibly small

compared with that of the container. - These assumptions breakdown at high pressures,

low volumes and low temperatures.

Behavior of Real Gases

- At STP, the volume occupied by a single molecule

is very small relative to its share of the total

volume - For example, a He atom (radius 31 pm) has

roughly the same space to move about as a pea in

a basketball - Lets say we increase the pressure of the system

to 1000 atm, this will cause a decrease in the

volume the gas has to move about in - Now our He atom is like a pea in a ping pong ball
- Therefore, at high pressures, the volume occupied

by the gaseous molecules is NOT negligible and

must be considered. - So the space the gas has to move around in is

less than under Ideal conditions!

VReal gt VIdeal

Behavior of Real Gases

- At low volumes, particles are much closer

together and attractive forces become more

important than at high volumes. - This increase in intermolecular attractions pulls

the molecules away from the walls of the

containers, meaning that they do not hit the wall

with as great a force, so the pressure is lower

than under ideal conditions.

PReal lt PIdeal

Behavior of Real Gases

- A similar phenomenon is seen at low temperatures

(aka. The Flirting Effect) - As molecules slow down, they have more time to

interact therefore increasing the effect of

intermolecular forces. - Again, this increase in intermolecular

attractions pulls the molecules away from the

walls of the containers, meaning that they do not

hit the wall with as great a force, so the

pressure is lower than under ideal conditions.

PReal lt PIdeal

Behavior of Real Gases

Behavior of Real Gases

- Corrections for non-ideality require the van der

Waals equation.

Correction for Intermolecular Attractions

Correction for Molecular Volume

VReal gt VIdeal

PReal lt PIdeal

n moles of gas a and b are constants given in

the problem

Behavior of Real Gases

- Given that 3.50 moles of NH3 occupy 5.20 L at

47C, calculate the pressure of the gas (in atm)

using - (a) the ideal gas equation
- (b) the van der Waals equation. (a 4.17, b

0.0371) - Calculate the pressure exerted by 4.37 moles of

molecular chlorine confined in a volume of 2.45 L

at 38C. Compare the pressure with that

calculated using the ideal gas equation. (a

6.49 and b 0.0562)