Study Guide GASES - docfish.com · The kinetic-molecular theory helps to explain the physical behavior of gases, as well as solids and liquids. For example, why do gases take on both

D:\sg\sg_Gases.docx

Study Guide

GASES

N.B. This document is intended as a supplement to the textbook – not a replacement. You

still have to read the book. There is no replacement, substitute, or shortcut for

reading the textbook. These are only my notes. Add your own notes.

Chemistry Study Guide: GASES P.1

N.B.

(1) ALWAYS USE KELVIN TEMPERATURE (K = oC + 273).

(2) 0 K is absolute zero. (No translational movement of particles; can’t get any colder than this.)

(3) Temperature is abbreviated as upper case “T”. Lower case ‘t’ is generally reserved for time.


TABLE OF CONTENTS

OVERVIEW OF GAS LAWS ...................................................................................................................... 3

I. KINETIC-MOLECULAR THEORY OF MATTER .......................................................................... 4

A. Review and Overview .................................................................................................................. 4 B. The Concept of an Ideal Gas and the Kinetic-Molecular Theory of Matter ................................. 4

II. PRESSURE ......................................................................................................................................... 6

A. Overview ...................................................................................................................................... 6 B. Units of Pressure ........................................................................................................................... 6 C. Standard Temperature and Pressure ............................................................................................. 7

III. GAS LAWS (BOYLE’S, CHARLES’S, GAY-LUSSAC’S = COMBINED GAS LAWS) ............... 7

A. Boyle’s Law – Pressure & Volume .............................................................................................. 7 B. Charles’s Law – Volume & Temperature ..................................................................................... 8 C. Gay-Lussac’s Law – Pressure & Temperature ............................................................................. 8 D. Combined Gas Law ...................................................................................................................... 9

IV. DALTON’S LAW OF PARTIAL PRESSURES .............................................................................. 10

V. AVOGADRO’S LAW & MOLAR VOLUME ................................................................................. 11

VI. IDEAL GAS LAW ............................................................................................................................ 12

VII. GAS STOICHIOMETRY ................................................................................................................. 13

VIII. GRAHAM’S LAW ........................................................................................................................... 14

A. Effusion and Diffusion ............................................................................................................... 14

IX. SPEED OF GAS PARTICLES ......................................................................................................... 16

A. Distribution of Molecular Speeds ............................................................................................... 16

X. DEVIATION FROM IDEAL BEHAVIOR ...................................................................................... 17

A. van der Waals Equation .............................................................................................................. 17 B. Summary of Conditions Where Gases Deviate from Ideal Behavior ......................................... 17

XI. APPENDIX ....................................................................................................................................... 18

A. Water-Vapor Pressure at Selected Temperatures ....................................................................... 18 B. van der Waals Constants for Some Common Gases* ................................................................. 18


OVERVIEW OF GAS LAWS

There are essentially four important gas laws. Each is used in a different circumstance and for a different

purpose (Table ).

Table 1. Overview of Gas Laws

Law Equation Comments

Combined Gas Law

22

22

11

11

Tn

VP

Tn

VP

· changes in pressure (P), volume (V),

temperature (T; use kelvin), and/or number of

moles

Dalton’s Law of Partial

Pressures PT = P1 + P2 + P3 + … · collected over water (or by water

displacement)

· heterogeneous mixture of gases

Ideal Gas Law PV = nRT

P

dRTM

· static conditions of a gas to determine pressure,

volume, number of moles, or temperature

· ideal gas constant (R = 0.0821 L-atm/K-mol)

· d = density; M = molar mass

Graham’s Law

A

B

B

A

m

m

v

v

· rate of effusion (v) is related to molar mass (m)


I. KINETIC-MOLECULAR THEORY OF MATTER

A. Review and Overview

The three common states of matter are gases, liquids and solids.

Liquids assume the shape of their containers but possess a definite volume.

Solids possess their own shape and volume.

Gases assume the shape and volume of their containers.

o Gases are the most compressible and expandable of the states of matter

o Gases mix evenly and completely when confined in the same container

o Gases have much lower density than liquids or solids.

Several elements exist as gases at room temperature, including the ‘magnificent

seven’ diatomic molecules (HONClBrIF). Many molecules exist as gases at

room temperature (e.g., methane, CH4, and hydrogen disulfide, H2S – the smell

of rotten eggs).

B. The Concept of an Ideal Gas and the Kinetic-Molecular Theory of Matter

The kinetic-molecular theory helps to explain the physical behavior of gases, as well as solids and liquids.

For example, why do gases take on both the shape and volume of their containers; liquids, the shape but

not the volume; solids, neither shape nor volume? To understand the physical behavior of these three

common states of matteri, we first need to understand the kinetic-molecular of gases. Then we can apply

it to all matter.

The basis for the kinetic-molecular theory of gas is that the gas is made of only particles of an ideal gas.

Most real gases can be modeled as an ideal gas at room temperature and pressure. An ideal gas is an

imaginary gas that fits the five assumptions of the kinetic-molecular theory (Table 1).

Table 1. Assumptions of an Ideal Gas

Assumption Comments

1. Gases consist of a large number of very tiny

particles that are far apart relative to their size.

These particles are generally atoms or

molecules (on the order of 10–12 meters in

radius) – and are very small compared to the

volume of the container holding them.

Particles in the gaseous phase are generally a

thousand times further apart than they are in

the liquid or solid phases. This means that the

gas has a volume approximately 1000 times

larger than the corresponding liquid.

Most of the volume occupied by a gas is empty

space. This accounts for:

the density of gases being far less than that of

liquids or solids,

gases are easily compressed; liquids and solids

are not.


2. Collisions between gas particles (or particles

and container walls) are completely elastic. Elastic there is no net loss of kinetic energy.

(Think of billiard balls not slowing down due

to friction but continuously and completely

bouncing off each other forever.)

Total kinetic energy remains the same as long

as temperature is constant.

3. Gas particles are in constant, rapid and random

motion.

Gases: constant motion (indefinite volume and

take on shape of container); liquids: a little

slip-and-slide motion (definite volume but take

on shape of container); solids: stuck in place

4. There are no forces of attraction or repulsion

between particles or walls of container

Example: compare the intermolecular bonding

of CH4, NH3, H2O, and Ne – more lone pairs

result in more intermolecular bonding result in

more interaction result in gas, liquid, solid and

gas, respectively (at room temperature).

5. Average kinetic energy of gas particles depends

on temperature of gas.

Kinetic energy vs. potential energy

All gas particles, at same temperature and

pressure, have same kinetic energy

KE = ½ mv2 (v = speed)

¿Which has more impact in a crash: a VW

Jetta (~2,000 lb @ 60 mph) or H3 (~4,000 lb

@ 30 mph)?

Gases have several characteristic properties, such as the ability to expand to fill the container and low

density. The kinetic-molecular theory can be used to explain these properties (Table 2).

Table 2. Properties of Gases.

Term Explanation

Expansion Gases do not have definite shape/volume. The particles move in rapid, random and

continuous motion all directions stopping only when hitting another particle or the

walls of the container. This results in the gas filling space available to it, having no

definite shape or volume.

Fluidity Because attractive forces between particles are insignificant, gas particles glide

easily past one another.

Low Density Density of gases is about 1/1000 the density of liquid or solid. Results from gas

particles are very far apart relative to their size

Compressibility Particles, initially far apart, are crowded together. Results from decreasing space

between particles.

Diffusion /

Effusion

Depends on particle speed, diameter and attractive forces between them. Particles

are in random and constant motion. Lack of attractive forces between particles

allows them to travel until struck by another particle or their forward motion is

stopped by a container wall. If no wall, the gas particles will eventually fill the

entire space available to them.


II. PRESSURE

A. Overview

Pressure is defined as the force per unit area exerted against a surface. area

force Pressure

What we consider to be pressure (e.g., inside a soda bottle or a balloon) results from the

force of the molecules hitting against the inside of the container walls compared with

the force of the molecules hitting against the outside of the container. Gas molecules

are in constant, rapid and random motion. They continue in straight lines until hit by

another gas particle or hit the surface of the container, much like moving billiard balls.

The force exerted by the particles is determined by the number of hits and the amount

of energy (e.g., mass and velocity of the moving particles) of each hit against the wall. For example,

blowing up a balloon introduces more gas molecules; this increases the number of hits against the wall

thereby increasing the pressure inside the balloon.

The SI unit for force is the newton (N) which is defined as the force that will increase the speed of one

kilogram mass by one meter per second each second. At the Earth’s surface, due to gravity, each

kilogram exerts 9.8 N of force.

Position: Flat-Foot En-Point

Force: 500 N 500 N

Area of Contact: 325 cm2 13 cm2

area

force Pressure

2

2N/cm 1.5

cm 325

N 500 2

2N/cm 38.5

cm 13

N 500

Figure 1. Comparison of the pressure exerted by a ballet dancer with flat foot and en-point on the floor.

The en-point dancer exerts approximately 25 times more pressure.

B. Units of Pressure

The air in the atmosphere above the earth produces a pressure, at sea level, of 1

atmosphere.

1 atm = 760 mm Hg = 760 torr = 14.7 psi = 101.325 kPa

In the early 1600’s, Evangelista Torricelli created the barometer – an

instrument used to measure the atmospheric pressure. Placing an inverted

glass tube (one hole located at the bottom of the tube; the top is sealed) in a

bath of liquid mercury. The pressure on the bath pushed the mercury up

the glass tube to a height of 760 mm above the surface of the

mercury. This pressure, 760 mm Hg, is also referred to as 760 torr,

in his honor. Several other units are used to measure pressure:

atmospheres (atm), pounds per square inch (psi; the inside of an

automobile tire is approximately 2 atm, or 28 psi above atmospheric pressure)

and kilopascals (kPa).


C. Standard Temperature and Pressure

The important parameters to consider when dealing with gases are pressure (P), volume (V), moles (m)

(number of gas particles), and temperature (T). To standardize conditions, scientists have chosen 1 atm of

pressure and 0oC temperature as standard temperature and pressure (STP). Helpful to remember this

is if you were stranded on a deserted island, how would you make standard conditions? A nice day at the

beach has a pressure of 1 atm. It’s more difficult to standardize temperature. Fresh water freezes at 0oC

(water doesn’t always boil at 100oC – e.g., consider Denver, although it doesn’t have an ocean front

beach). So you make an ice-water bath (0oC). Thus:

Standard Temperature and Pressure (STP) = 1 atm & 0oC.

III. GAS LAWS (BOYLE’S, CHARLES’S, GAY-LUSSAC’S = COMBINED GAS LAWS)

A. Boyle’s Law – Pressure & Volume

In 1662, Robert Boyle discovered that gas pressure and volume are mathematically related.

How are volume and pressure related?

Inversely or directly? If P*V = constant, they

are inversely related (one increases, the other

decreases, keeping the product constant). If

P/V = constant, they are directly related (one

increases, the other increases accordingly,

keeping the dividend constant). Fill in the

table and determine the relationship.

Mathematically, Boyle’s law is express as:

PV = k (Eq. 1a)

Boyle’s law is frequently used to determine the related changes in pressure

and volume of a gas in a closed container:

P1V1 = P2V2 (Eq. 1b)

where P1 and V1 are the pressure and volume, respectively, at the initial

conditions and P2 and V2 are the pressure and volume, respectively, at the

final conditions.

Example 1. A sample of gas has a volume of 144 mL at 0.987 atm. What will the volume be if the pressure is

decreased to 0.947 atm?

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 500 1000 1500

Pressure (atm)

Vo

lum

e (

mL

)

Volume (mL) Pressure (atm) P * V P / V

1200 0.5

600 1.0

300 2.0

200 3.0

150 4.0

120 5.0

100 6.0


B. Charles’s Law – Volume & Temperature

In 1783, Jacques Alexandre César Charles, a French scientist, inventor, balloonist and

mathematician, made the first flight of a hydrogen balloon. In 1787, he discovered that

gas volume and temperature are mathematically related.

Temp (K) Vol (mL) V * T V / T

546 1092

373 746

283 566

274 548

273 546

272 544

200 400

100 200

0 100

How are volume and temperature

related? Inversely or directly? Fill in

the table and determine the relationship.

Mathematically, Charles’s law is express as:

kT

VkTV (Eq. 2a)

Charles’s law is frequently used to determine the related changes in volume

and temperature of a gas in a closed container. It is more commonly

expressed as follows:

2

2

1

1

T

V

T

V (Eq. 2b)

Where V1 and T1 are the volume and temperature, respectively, at the

initial conditions and V2 and T2 are the volume and pressure, respectively,

at the final conditions.

C. Gay-Lussac’s Law – Pressure & Temperature

In 1802, the French scientist Joseph Louis Gay-Lussac determined the relationship between temperature

and pressure of a gas in a closed container. As a side note, he was also an avid balloonist and, in 1808

with Sir Humphry Davy, Joseph Louis Gay-Lussac, and Louis Jacques Thénard,, discovered the element

boron.

Temp

(K) Pressure

(atm) P * T P / T

100 0.168

273 0.458

298 0.500

398 0.667

523 0.877

595 1.000

How are pressure and temperature

related? Inversely or directly? Fill in the

table and determine the relationship.

0

100

200

300

400

500

600

0 500 1000 1500

Temp (K)

Vo

l (m

L)


Mathematically, Gay-Lussac’s law is express as:

kT

PkTP (Eq. 3a)

Gay-Lussac’s law is frequently used to determine the related changes in

pressure and temperature of a gas in a closed container. It is more commonly

expressed as follows:

2

2

1

1

T

P

T

P (Eq.

3b)

Where P1 and T1 are the pressure and temperature, respectively, at the initial

conditions and P2 and T2 are the volume and pressure, respectively, at the final

conditions.

D. Combined Gas Law

If it seems that Boyle’s, Charles’s and Gay-Lussac’s laws are related, they are. These three laws are

combined into a single gas law, the Combined Gas Law.

Combined Gas Law 22

22

11

11

Tn

VP

Tn

VP (Eq. 4)

This equation includes Avogadro’s law and molar volume (below). Notably, it can be used for any of the

above gas laws (i.e., Boyle’s, Charles’, and Gay-Lussac’s). Where there is no change (e.g., no change in

the number of moles of gas), those values for the initial and final conditions are the same and, thus, cancel

out.

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0 200 400 600 800

Temp (K)

Pre

ssu

re (

atm

)


IV. DALTON’S LAW OF PARTIAL PRESSURES

The partial pressure of a gas is pressure of each gas in a mixture. For example, dry air is

approximately 78% nitrogen, 21% oxygen, 0.93% argon, 0.04% carbon dioxide, and a

mixture of other gases in trace amounts. John Dalton (yes, the same one delineated the five

postulates of the modern atomic theory) discovered that the sum of the partial pressures of

mixture of gases is equal to the sum of total pressure of the mixture of gases (Eq. 5).

PT = P1 + P2 + P3 + … (Eq. 5)

Where PT is the total pressure of the mixture, P1 is the partial pressure of gas 1, P2 is the pressure of gas 2,

etc.

Application # 1: To determine the partial pressure(s) of component gas(s) or the total pressure of a gas

mixture.

Example 2.

What is the partial pressure of oxygen and carbon dioxide in dry air? Assume a total pressure of

0.987 atm.

Application # 2: To determine the partial pressure of gas produced by a chemical reaction. This can be

used to determine the amount of gas produced and, hence, is

useful for stoichometric calculations. Frequently, the gas

produced from a chemical reaction is collected by water

displacement (or ‘over water’) (Figure 2).

Example 3.

Oxygen gas is produced by the decomposition of potassium chlorate:

2KClO3(s)

2KCl(s) + 3O2(g). What is the partial pressure of the

oxygen gas produced by this reaction if it is collected over water at 731.0

torr and 20.0oC?

ANS:

1. Volume of oxygen gas.

The total pressure (731.0 torr) is given in the problem. The partial pressure of water at this

temperature (17.5 torr) is given in the Water-Vapor Pressure at Selected Temperatures table in the

appendix.

PT = P1 + P2 + P3 + …

PT = PO2 + PH2O

PO2 = PT – PH2O

PO2 = 731.0 torr – 17.5 torr = 713.5 torr

Figure 2. Gas product

of a chemical reaction

collected by water

displacement.


V. AVOGADRO’S LAW & MOLAR VOLUME Avogadro’s Law = equal volumes of gases at the same temperature and pressure

contain equal numbers of molecules.

This means that gas volumes are directly related to the number of moles of gases. A

corollary of this law is that, providing the gases to not chemically combine, there is conservation of

volume of gases.

2H2(g) + 1O2(g) 2H2O(g)

2 molecules 1 molecule 2 molecules

2 moles 1 mole 1 mole

2 volumes (e.g., L) 1 volume (e.g., L) 2 volumes (e.g., L)

Recall, there is a conservation of mass/energy but there is no conservation of volumes where liquids and

solids are concerned.

Avogadro’s number, the number of ‘things’ (6.022 x 1023

) in one mole, was named in honor of

Avogadro. Also, the volume occupied by one mole of gas at STP is called the molar volume of a gas is

22.414 10 L. For most calculations, 22.4 L / mol is adequate.


VI. IDEAL GAS LAW

This law is not called the Ideal Gas Law because it is perfect but rather because it is the mathematical

relationship of pressure, volume, temperature, and the number of moles of an ideal gas. (It is, however, a

darn good law!)

In its fundamental form, the Ideal Gas Law is given below:

PV = nRT (Eq. 6)

Where P is pressure (atm), V is volume (L), n is the number of moles and T is the temperature (K). The

ideal gas constant, R, is 0.0821 L-atm/K-mol.

Corollaries of the Ideal Gas Law are used to determine molar mass or density of a gas, and mass of a gas

sample.

a. Using the Ideal Gas Law to find Molar Mass:

n (number of moles) = (g/mol) massmolar

(g) mass=

M

m

Substituting m/M for n in the Ideal Gas Law gives: M

mRTPV

This can be rearranged to solve for molar mass: PV

mRTM (Eq. 6b)

b. Using the Ideal Gas Law to find Gas Density:

d (density) = V

m

(L) volume

(g) mass (d)density

Substituting the equation for density into Eq. 6 yields P

dRTM

Rearranging for density: RT

MPd (Eq. 6c)

If you forget the value for R, you can calculate it from the standard values for P (1 atm), V (22.4 L), n

(1 mol), and T (273 K). Calculate R from these values using the Ideal Gas Law:


VII. GAS STOICHIOMETRY

Based on our previous work, we can now expand our stoichometric calculations to include gases.

Example 4.

Decomposition of a specific quantity of potassium chlorate produces 0.050 L of oxygen gas at

STP (see Example_03). What is the mass of the potassium chlorate?

ANS:

First, convert the volume of oxygen gas into moles of oxygen gas. Then we can perform a moles-to-

mass stoichometric calculation.

PV = nRT n = PV / RT

Next, perform the standard stoichometric calculation to determine the mass of KClO3 needed to make

0.0223 mol of oxygen gas:


VIII. GRAHAM’S LAW

A. Effusion and Diffusion

Diffusion is the gradual mixing of two gases due to their spontaneous, random motion. An

example of diffusion is the smell of coffee (or perfume) as it wafts across the room.

Effusion is similar to diffusion but the molecules of one of the gases are confined to a container and pass

through a tiny opening in the container.

In the 1831, the Scottish chemist Thomas Graham discovered the mathematical

relationship between the rate of effusion (or diffusion) and the molar mass of a chemical.

Graham’s law of effusion states the rates of effusion of gases (at the same temperature

and pressure) are inversely proportional to the square roots of their molar masses. The

derivation and expression of Graham’s law is given below.

The equation for the kinetic energy of particles in a gas is KE = 2½Mv (assumption #5 of the Kinetic-

Molecular Theory). In addition, also based on this assumption is that all gases, at the same temperature

and pressure, have the same kinetic energy. Therefore, for two gases, A and B, and the same conditions:

2

B

2

A ½M½M BA vv (Eq. 7a)

Simplified this can be expressed as follows:

2

B

2

A MM BA vv (Eq. 7b)

Place similar units on the same sides of the equation give us Graham’s law of effusion:

A

B

2

2

M

M

B

A

v

v OR

A

B

M

M

B

A

v

v (Eq. 7c)

N.B. Caution: The molar masses and rates of effusion are placed diagonally (A

B

B

A ).

(continued on next page)


(Graham’s law continued)

Example 5.

A sample of hydrogen gas effuses through a porous container 8.05 times faster than an unknown gas.

Estimate the molar mass of the unknown gas.

MH2 = 2.02 g vH2 = 8.05

MX = ? g vX = 1

𝑣𝐻22

𝑣𝑋2 =

𝑀𝑋

𝑀𝐻2

𝑀𝑥 =(𝑣𝐻2

2 )(𝑀𝐻2)

𝑣𝑋2

𝑀𝑥 =(8.052)(2.02)

1

𝑀𝑥 = 131 𝑔/𝑚𝑜𝑙 (close to xenon, 131.3 g/mol)


IX. SPEED OF GAS PARTICLES

A. Distribution of Molecular Speeds

According to the kinetic-molecular theory, gases

at the same conditions have the same kinetic

energy. But the particles move in random and

predictable motion. So, how fast does a gas

particle move at any give temperature? The

answer is a probability distribution curve (Figure

3). The peak for any given curve represents the

most probable speed – the speed at which the

largest number of gas particles is traveling.

Figure 3. Distribution of speeds for four gases

(He-4, Ne-20, Ar-40 and Xe-132).

One way to estimate the particle speed is with the root-mean-square (rms) speed (urms). From the

kinetic-molecular theory, the total kinetic energy of a mole of gas equals 3/2 RT. The average kinetic

energy of one particle is 2

2

1um . The average speed for the particles in one mole becomes

RTumN A2

3)

2

1( 2 , where NA is Avogadro’s number. (Eq. 8a)

Avogadro’s number (NA) times the mass of each particle equals the molar mass of the gas, or

(NA)(m) = M. (Eq. 8b)

Therefore:

Substituting 8b into 8a yields: RTuN

MN

A

A2

3)

2

1( 2 (Eq. 8c)

Cancellation and rearrangement yields: M

RTu

32 (Ea. 8d)

Taking the square root of both sides yields: M

RTurns

3 (Ea. 8e)

This equation (Eq. 8e) shows that the (root-mean-square) speed of the gas particles is directly

proportional to the temperature (in kelvin) and inversely proportional to its molar mass.


X. DEVIATION FROM IDEAL BEHAVIOR

A. van der Waals Equation

Although real gases don’t always act ideally in terms of pressure, volume, etc., the ideal gas equation can

be modified to fit. The Dutch physicist J.D. van der Waals (1873) provided us with a way to interpret real

gases at the molecular level. Based on experimental evidence, he proposed that the pressure exerted by a

real gas can be applied to that of an ideal gas using a correction term:

2

2

V

anPP obsideal (Eq. 9a)

where Pideal = pressure of an ideal gas; Pobs = observed pressure exerted by a real gas; a = a constant; n =

number of moles, and; V = volume of the gas. Taking into account corrections for pressure and volume,

the ideal gas law can be rewritten using a correction for the real gas pressure (Eq. 9a) and volume (not

shown) below. (Correction values for some selected gases are given in the Appendix.)

nRTnbVV

anP ))((

2

2

(Eq. 9b)

B. Summary of Conditions Where Gases Deviate from Ideal Behavior Among the assumptions of the Kinetic-Molecular Theory is that gas particles do not repel or attract each other; that collisions are completely elastic. Another assumption is that gas particles are negligibly small relative to the distance between them and the size of the container. What happens if either of these assumptions is not present? For example, without intermolecular forces, gases would condense to liquids (or deposit as solids). Or if the container is so small that we can’t assume the gas particles are negligibly small. As particles slow down, or are pressed closer to each other, there is more chance that they will interact (e.g., van der Waals forces) with each other. For example, if you reduce the temperature, the gas will condense into liquid and, eventually, deposit as a solid.

Deviations from ideal behavior is large at high pressures and low temperatures.

Pressure Temperature

Note: For an ideal gas, 1 mole = PV/RT. Various deviations occur from this at high pressures and low

temperatures where the gas particles have a better change in interacting with each other and the walls of

the container.

corrected

pressure

corrected

volume


XI. APPENDIX

A. Water-Vapor Pressure at Selected Temperatures

Temperature Pressure Temperature Pressure

(oC) (mm Hg) (kPa) (oC) (mm Hg) (kPa)

0.0 4.6 0.61 23.0 21.1 2.81

5.0 6.5 0.87 23.5 21.7 2.90

10.0 9.2 1.23 24.0 22.4 2.98

15.0 12.8 1.71 24.5 23.1 3.10

15.5 13.2 1.76 25.0 23.8 3.17

16.0 13.6 1.82 26.0 25.2 3.36

16.5 14.1 1.88 27.0 26.7 3.57

17.0 14.5 1.94 28.0 28.3 3.78

17.5 15.0 2.00 29.0 30.0 4.01

18.0 15.5 2.06 30.0 31.8 4.25

18.5 16.0 2.13 35.0 42.2 5.63

19.0 16.5 2.19 40.0 55.3 7.38

19.5 17.0 2.27 50.0 92.5 12.34

20.0 17.5 2.34 60.0 149.4 19.93

20.5 18.1 2.41 70.0 233.7 31.18

21.0 18.6 2.49 80.0 355.1 47.37

21.5 19.2 2.57 90.0 525.8 70.12

22.0 19.8 2.64 95.0 634.0 84.53

22.5 20.4 2.72 100.0 760.0 101.32

B. van der Waals Constants for Some Common Gases*

Gas a )(

2

2

mol

Latm b )(mol

L

He 0.034 0.0237

Ne 0.211 0.0171

Ar 1.34 0.0322

Kr 2.32 0.0398

Xe 4.19 0.0266

H2 0.244 0.0266

N2 1.39 0.0391

O2 1.36 0.0318

Cl2 6.49 0.0562

CO2 3.59 0.0427

H4C 2.25 0.0428

H3N 4.17 0.0371

H2O 5.46 0.0305

* source: Chang, Raymond (2006). General Chemistry: The Essential Concepts, 4th Ed. McGraw-Hill. New York. p.159.


ENDNOTES i There are five states of matter: solid, liquid, gas, plasma and Bose-Einstein condensate. Only the first three are

present in significant amounts on earth. The fourth, plasma, is “a collection of charged particles (as in the

atmospheres of stars or in a metal) containing about equal numbers of positive ions and electrons and exhibiting

some properties of a gas but differing from a gas in being a good conductor of electricity and in being affected by

a magnetic field” (http://www.m-w.com Feb. 2007). The Bose-Einstein condensate (BEC) “is a state where all

the particles participating in a BEC have overlapping quantum states and are attractively interactive. This

condition appears when the relative motion of individual particles approaches zero or when their common de

Broglie wavelengths are greater than the interparticle distances” (www.singtech.com/definitions.html; Feb. 2007).

It is very rarely encountered – principally only under laboratory conditions.

http://www.m-w.com/

http://www.singtech.com/definitions.html

Documents

Study Guide GASES - docfish.com · The kinetic-molecular theory helps to explain the physical behavior of gases, as well as solids and liquids. For example, why do gases take on both