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- Lecture 06 (Chapter 6)
- The Gaseous State

Physical States of Matter

- Matter can exist as
- Solid
- Liquid
- Gas

Temperature Dependent States

http//www.uni.edu/iowawet/H2OProperties.html

http//en.wikipedia.org/

Solid Phase

- A solid has fixed shape and volume.

Solid Br2 at low temperature

Liquid Phase

- A liquid has fixed volume but no definite shape.
- The density of a solid or a liquid is given in

g/mL.

Liquid Br2

Gas Phase

- A gas has no fixed volume or definite shape.
- The density of a gas is given in g/L whereas

liquids and solids are in g/mL.

Gaseous Br2

Summary of Gas Phase Characteristics

- Characteristics of gases
- Particles in constant random motion
- Particles far apart, travel in straight lines,

collide frequently - Low Density (particles widely separated)
- Indefinite Shape (little cohesion, particles

expand to shape of container) - Large Compressibility (gas is mostly empty space)
- Moderate Thermal Expansion (increase in

temperature causes particles to collide with more

energy, increases volume)

Seager SL, Slabaugh MR, Chemistry for Today

General, Organic and Biochemistry, 7th Edition,

2011 http//www.chemistry.wustl.edu/edudev/LabTu

torials/Airbags/airbags.html

Pressure of a Gas

- Pressure is the force per unit area exerted on a

surface. - The pressure of the atmosphere is measured with a

barometer.

Manometers

- Both open and closed end manometers measure

pressure differences. - In Figs. A and B (open manometers), h represents

difference in P between a gas and the atmosphere. - In Fig. C (closed manometer), h represents P of

the gas.

A

B

C

Units of Pressure

- One atmosphere of pressure (1 atm) is the normal

pressure at sea level. The SI unit of pressure

is the pascal (Pa), but is a very small unit and

is not used frequently by chemists.

1 atm 760 mm Hg 1 atm 101.3 kPa 1 atm 760

torr 1 atm 1.01 bar 1 torr 133.3 Pa

1 atm 29.9 in Hg 1 atm 14.7 psi

Gas Laws

- Describe behavior of gases when mixed, subjected

to pressure or temperature changes, or allowed to

diffuse - Laws describes relationships between temperature

(T), volume (V), pressure (P) and moles (n) - The physical properties of all gases behave in

the same manner, regardless of the identity of

the gas

- Boyles law
- Charless law

- Combined gas law
- Avogadros law

- Ideal gas law

Boyles Law

- A constant relationship exists between pressure

(P) and volume (V) at constant temperature (T) - If pressure increases, volume occupied by the gas

decreases - If volume increases, pressure created by the gas

decreases

Boyles Law

- A plot of volume versus 1/P is a straight line.

Formula for straight line

Example Boyles Law

- A sample of a gas occupies 5.00 L at 0.974 atm.

Calculate the volume of the gas at 1.00 atm, when

the temperature held is constant.

How do you solve this problem? What do you

know? If P1V1 k1, and k1 is constant (at

constant T), then P1V1 P2V2 Check P1V1

(5.00L)(0.974 atm) 4.87 Latm k1 V (k1 /P)

(4.87 Latm)/(1.00 atm) 4.87 L Or P1V1

P2V2 rearranges to V2 (P1V1)/P2 (0.974 atm

5.00 L)/1.00 atm 4.87 L

Charless Law

- At constant pressure, the volume of a gas sample

is directly proportional to the temperature

(expressed in kelvins) - If temperature increases, volume increases at

constant pressure

Seager SL, Slabaugh MR, Chemistry for Today

General, Organic and Biochemistry, 7th Edition,

2011

Charless Law

- A plot of volume versus temperature is a straight

line. - Extrapolation to zero volume yields absolute zero

in temperature (which isnt going to happen!!) - -273o C.
- V k2 x T, where T is given in units of kelvin.

Example Charless Law

- A balloon filled with oxygen gas at 25C occupies

2.1 L. At constant pressure, what is the volume

at 100C?

How do you solve this problem? What do you

know? First, convert T value(s) from C to

K. Ti in K 25 273 298 K Tf in K 100

273 373 K If then

P, V, T Relationships Combined Gas Law

- Boyles law and Charless law can be combined to

relate P, V and T, when mass of gas remains

constant.

- Because k is a constant, we can use this

equation to evaluate changes in these variables

over time (between some initial state and a final

state). - Any problem that can be solved with either

Boyles law or Charless law, can also be solved

using the Combined Gas Law.

Combined Gas Law Examples

- 2500 liters of oxygen gas is produced at 1.00 atm

of pressure. It is to be compressed and stored in

a 20.0 liter cylinder. If temperature is

constant, calculate the pressure of the oxygen in

the cylinder. - A 3.2 liter sample of gas is at 40C and 1.0

atmosphere of pressure. If the temperature

decreases to 20C and the pressure decreases to

0.60 atmospheres, what is the new volume in

liters?

Combined Gas Law Examples

- A sample of a gas occupies 4.0 L at 25o C and

2.0 atm of pressure. Calculate the volume at STP

(T 0 oC, P 1 atm). - A sample of a gas occupies 200 mL at 100oC. If

the pressure is held constant, calculate the

volume of the gas at 0oC.

Avogadros Hypothesis

- Two different gases of equal volume measured at

same T and P contain equal numbers of molecules - Mass would not be identical due to different MWs

Avogadros Law

- A plot of the volume of all gas samples, at

constant T and P, vs. the number of moles (n) of

gas is a straight line. - V k3 x n

Ideal Gas Law

P Pressure

V Volume

n number of moles

T Temperature

R Universal Gas Constant

m mass

Also, because

MW molecular weight

STP (Standard Temperature and Pressure) T 0

C P 1.0 atm V of 1 mol ideal gas (any gas)

22.4 L at STP

We can also express the ideal gas law as

Ideal Gas Law Calculation

- Calculate the number of moles of argon gas in a

30 L container at a pressure of 10 atm and

temperature of 298 K. - How do we solve this problem?

Ideal Gas Law Calculation

- Calculate the number of moles of argon gas in a

30 L container at a pressure of 10 atm and

temperature of 298 K. - PV nRT
- n
- n 12 mol

Molar Mass and Density

- The ideal gas law can be used to calculate

density (mass/volume) and molar mass (mass/moles)

of a gas. - At constant pressure and temperature the density

of a gas is proportional to its molar mass, so

the higher the molar mass, the greater the

density of the gas.

Example Molar Mass

- Calculate the molar mass of a gas if a 1.02 g

sample occupies 220 mL at 95o C and a pressure of

750 torr.

Example Molar Mass

- Calculate the molar mass of a gas if a 1.02 g

sample occupies 220 mL at 95o C and a pressure of

750 torr.

Gases and Chemical Equations

- The ideal gas law can be used to determine the

number of moles, n, for use in problems involving

reactions. - The ideal gas law relates n to the volume of gas

just as molar mass is used with masses of solids

and molarity is used with volumes of solutions.

Example Gases with Equations

- Calculate the volume of O2 gas formed in the

decomposition of 2.21 g of KClO3 at STP.

2KClO3(s) 2KCl(s) 3O2(g)

Gas Volumes in Reactions

- Equal volumes of gases at same P and T contain

same number of moles. - In chemical rxns under same conditions, gas

volumes combine in same proportions as

coefficients of equation. - Therefore, 3 L of hydrogen gas, combined with 2 L

of nitrogen gas, forms 2 L of ammonia.

Example Gas Volumes in Reactions

- Calculate the volume of NH3 gas produced in the

reaction of 4.23 L of H2 with excess N2 gas.

Assume the volumes are measured at the same

temperature and pressure.

Daltons Law of Partial Pressure

- The pressure exerted by each gas in a mixture is

called its partial pressure. - For a mixture of two gases A and B, the total

pressure, PT, is - PT PA PB

Example Partial Pressures

- Calculate the pressure in a container that

contains O2 gas at a pressure of 3.22 atm and N2

gas at a pressure of 1.29 atm.

PT PA PB 3.22 atm 1.29 atm 4.51 atm

Example Partial Pressures

- A gas sample in a 1.2 L container holds 0.22 mol

N2 and 0.13 mol O2. Calculate the partial

pressure of each gas, and the total pressure at

50C.

We will use Ideal Gas law to calculate P for each

of the 2 gases.

Mole Fraction

Mole Fraction

- Mole fraction of the yellow gas is 3/12 0.25

and the mole fraction of the red gas is 9/12

0.75

Example Partial Pressure

- Calculate the partial pressure of Ar gas in a

container that contains 2.3 mol of Ar and 1.1 mol

of Ne and is at a total pressure of 1.4 atm.

Collecting Gases over Water

- The volume of gas generated in a rxn can be

determined by water displacement. - The collected gas contains both O2 gas from the

rxn and water vapor, and each contribute to total

P.

Example Collecting Gases

- Sodium metal is added to excess water, and H2 gas

produced in the reaction is collected over water

with the gas volume of 1.2 L. If the pressure is

745 torr and the temperature 26o C, what was the

mass of the sodium? The vapor pressure of water

at 26o C is 25 torr. 2Na(s) 2H2O(l) H2(g)

2NaOH(aq)

Kinetic Molecular Theory of Gases

- Describes the behavior of (ideal) gas particles

at molecular level, based on 4 postulates. - 1. Gases consist of small particles that are in

constant and random motion. - 2. Gas particles are very small compared to the

average distance that separates them. - 3. Collisions of gas particles with each other

and the walls of the container are elastic (i.e.,

no loss of kinetic energy). - 4. The average kinetic energy of gas particles

is proportional to the temperature on the Kelvin

scale.

Kinetic Molecular Theory of Gases

- How does this theory explain the observed

behavior of gases? - Because gases consist of small particles that are

in constant and random motion and they are

constantly colliding with each other and with the

walls of the container, and because these

collisions involve no loss of average KE, the

result is increased pressure. - 2. Because gas particles are very small compared

to the average distance that separates them, at

constant T, they can be compressed into a smaller

volume (P increases), or they can expand to fill

a larger volume (P decreases). - 3. Because the average kinetic energy of gas

particles is proportional to the temperature (on

the Kelvin scale), KE of the molecules increases

with increasing T resulting in more collisions

over time involving greater force thus, at

constant P, V would have to increase (Charless

law).

Average Speed of a Gas

Maxwell-Boltzmann distribution curves

- Although gas particles move at different

velocities, we can calculate an average velocity

(see previous slide), which is also called the

root mean square (rms) speed, urms, and is the

square root of the average squared speed. - This number can be derived mathematically and

represented by the associated curve.

R 8.314 J/mol.K molar mass in kilograms per

mole

Average Speed of a Gas

- From this plot and the equation, you can see

that velocity, or root mean square speed, of

molecules decreases with increasing molar mass

(at constant T).

Effusion (Grahams law) and Diffusion

- The Kinetic Molecular Theory also correctly

described both effusion and diffusion - Effusion - the passage of a gas through a small

hole into an evacuated space. - Gases with low molar masses effuse more rapidly

(e.g., heavier gases move more slowly). - Diffusion is the mixing of particles due to

motion.

Effusion (Grahams law)

- Grahams Law is frequently used to compare rates

of effusion of 2 gases.

Effusion (Grahams law) Example

Calculate the molar mass of a gas if equal

volumes of nitrogen and the unknown gas take 2.2

and 4.1 minutes, respectively, to effuse through

the same small hole (at constant T and P).

Deviations from Ideal Behavior

- Gases deviate from the ideal gas law at high

pressures in 2 ways.

Deviations from Ideal Behavior

- The assumption that gas particles are small

compared to the distances separating them fails

at high pressures. - The observed value of PV/nRT will be greater than

1 under these conditions.

Forces of Attraction in Gases

- The forces of attraction between closely spaced

gas molecules reduce the impact of wall

collisions. - These attractive forces cause the observed value

of PV/nRT to decrease below the expected value of

1 at moderate pressures.

Ideal Gases

- A gas (O2 below) deviates from ideal gas behavior

at low temperatures (near the condensation point

) and high pressures. - In other words, removing heat removes energy

applied to molecules, so they slow down, and in

doing so, are more susceptible to effects caused

by force of attraction.

van der Waals Equation

- The van der Waals equation corrects for

attractive forces and the volume occupied by the

gas molecules. - a is a constant related to the strength of the

attractive forces. - b is a constant that depends on the size of the

gas particles. - a and b are determined experimentally for each

gas. - (Review Example 6.17 on your own)