CHEMICAL PROCESS PRINCIPLES


ADVISORY

BOARD

For Books in Chemical
T . H . C H I L T O N , Chem.

Engineering

E.

Engineering Department, Experimental Station,
E. I. du Pont de Nemours and Company
T.

B. D R E W ,

SM.

Professor of Chemical Engineering, Columbia
University
O . A . HouGEN, Ph.D.
Professor of Chemical Engineering, University of
Wisconsin
D . B . :g^YEs;
A.D.
Vice President, Heyden Chemical Corporatioti
i

K.

M.

WATSON,

Ph.D.

Professor of Chemical Engineering, University of
Wisconsin
HAROLD C . WEBER,

D.SC.

Professor of Chemical Engineering, Massachusetts
Institute of Technology


CHEMICAL PROCESS
PRINCIPLES
A COMBINED VOLUME CONSISTING OF

Part One • MATERIAL AND ENERGY BALANCES
Part Two • THERMODYNAMICS
Part Three • KINETICS AND CATALYSIS

OLAF A. HOUGEN
AND


KENNETH M. WATSON
PROFESSORS OP CHEMICAL ENGINEERINC
UNIVERSITY OF WISCONSIN

NEV YORK
J O H N WILEY & SONS, INC.
CHAPMAN AND HALL, LIMITED
LONDON


e

M
}o&i'^
PART I

COPYRIGHT, 1943
BY
OLAF A . HODGEN
AND
KENNETH M . WATSON

PART II
COPYBIGHT, 1947
BY
OLAF A . HOTJGEN
AND
KENNETH M . WATSON

PART III

COPTBIGHT, 1947
BY

OLAF A . HonoEN
AND
KENNETH M . WATSON

All Rights Reserved
Thin hook or any 'part thereof must not
he reproduced in any form without
the written permission- of the publisher.

P R I N T E D If* T H E U N I T E D STATES OF AMERICA


PREFACE
" In the following pages certain industrially important principles of chemistry and physics have been selected for detailed study. The significance
of each principle is intensively developed and its applicability and limitations
scrutinized." Thus reads the preface to the first edition of Industrial Chemical
Calculations, the precursor of this book. The present book continues to give
intensive quantitative training in the practical applications of the principles
of physical chemistry to the solution of complicated industrial problems and
in methods of predicting missing physicochemical data from generalized
principles. In addition, through recent developments in thermodynamics
and kinetics, these principles have been integrated into procedures for process
design and analysis with the objective of arriving at optimum economic
results from a minimum of pilot-plant or test data. The title Chemical Process
Principles has been selected to emphasize the importance of this approach to
process design and operation.
The design of a chemical process involves three types of problems, which

although closely interrelated depend on quite different technical principles.
The first group of problems is encountered in the preparation of the material
and energy balances of the process and the establishment of the duties to be
performed by the various items of equipment. The second type of problem
is the determination of the process specifications of the equipment necessary
to perform these duties. Under the third classification are the problems of
equipment and materials selection, mechanical design, and the integration
of the various units into a coordinated plot plan.
These three types may be designated as process, unit-operation, and plant. design problems, respectively. In the design of a plant these problems cannot
be segregated and each treated individually without consideration of the
others. However, in spite of this interdependence in application the three
types may advantageously be segregated for study and development because
of the different principles involved. Process problems are primarily chemical
and physicochemical in nature; unit-operation problems are for the most
part physical; the plant-design problems are to a large extent mechanical.
In this book only process problems of a chemical and physicochemical
nature are treated, and it has been attempted to avoid overlapping into the
fields of unit operations and plant design. The first part deals primarily
with the applications of general physical chemistry, thermophysics, thermochemistry, and the first law of thermodynamics. Generalized procedures
for estimating vapor pressures, critical constants, and heats of vaporization
have been elaborated. New methods are presented for dealing with equilibrium problems in extraction, adsorption, dissolution, and crystallization.
The construction and use of enthalpy-concentration charts have been extended
to complex systems. The treatment of material balances has been elaborated
to include the effects of recycling, by-passing, changes of inventory, and
accumulation of inerts.


vi

PREFACE


In the second part the fundamental principles of thermodynamics are presented with particular attention to generalized methods. The applications
of these principles to problems in the compression and expansion of fluids,
power generation, and refrigeration are discussed. However, it is not attempted to treat the mechanical or equipment problems of such operations.
Considerable attention is devoted to the thermodynamics of solutions
with particular emphasis on generalized methods for dealing with deviations
from ideal behavior. These principles are applied to the calculation of equilibrium compositions in both physical and chemical processes.
Because of the general absence of complete data for the solution of process
problems a chapter is devoted to the new methods of estimating thermodynamic properties by statistical calculations. This treatment is restricted to
simple methods of practical value.
All these principles are combined in the solution of the ultimate problem
of the kinetics of industrial reactions. Quantitative treatment of these
problems is difficult, and designs generally have been based on extensive
pilot-plant operations carried out by a trial-and-error procedure on successively larger scales. However, recent developments of the theory of absolute
reaction rates have led to a thermodynamic approach to kinetic problems
which is of considerable value in clarifying the subject and reducing it to the
point of practical applicability. These principles are developed and their
apphcation discussed for homogeneous, heterogeneous, and catalytic systems.
Particular attention is given to the interpretation of pilot-plant data. Economic considerations are emphasized and problems are included in estabhshing
optimum conditions of operation.
In covering so broad a range of subjects, widely varying comprehensibility
is encountered. It has been attempted to arrange the material in the order
of progressive difficulty. Where the book is used for college instruction in
chemical engineering the material of the first part is suitable for second- and
third-year undergraduate work. A portion of the second part is suitable
for third- or fourth-year undergraduate work; the remainder is of graduate
level. To assist in using the book for undergraduate courses in thermodynamics and kinetics those sections of Part II which are recommended for such
survey courses are marked. This material has been selected and arranged
to give continuity in a preliminary treatment which can serve as a foundation
for advanced studies, either by the individual or in courses of graduate level.

The authors wish to acknowledge gratefully the assistance of Professor
R. A. Ragatz in the revision of Chapters I and VI, and the suggestions of Professors Joseph Hirschfelder, R. J. Altpeter, K. A. Kobe, and Dr. Paul Bender.
OLAF A. HOUQEN
KENNETH M . WATSON
MADISON, WISCONSIN

August, 194s


CONTENTS
Page

PREFACE .

v

TABLE OF SYMBOLS

ix

PART
MATERIAL

AND

I

ENERGY

BALANCES


Chapter

I

STOICHIOMETRIC PRINCIPLES

II

BEHAVIOR OF IDEAL GASES

27

III

VAPOR PRESSURES

53

IV/

HUMIDITY AND SATURATION

89

SOLUBILITY AND SORPTION

Ill

V

Vr/

MATERIAL BALANCES

167

THERMOPHYSICS

201

THERMOCHEMISTRY

249

I X y FUELS AND COMBUSTION

323

YJy
viy/
•

1

X

CHEMICAL, METALLURGICAL, AND PETROLEUM PROCESSES

383


PART

II

THERMODYNAMICS
XI

.

.

THERMODYNAMIC PROPERTIES OF FLUIDS

.

.

479

XIII

EXPANSION AND COMPRESSION OF FLUIDS

. . . .

538

XIV

THERMODYNAMICS OF SOLUTIONS


XII

XV
XVI

XVII

THERMODYNAMIC PRINCIPLES .

.

.

.
.

.
.

. '

437

595

PHYSICAL EQUILIBRIUM

644


CHEMICAL EQUILIBRIUM

691

THERMODYNAMIC PROPERTIES FROM MOLECULAR STRUCTURE

vii

756


viii

CONTENTS
PART
KINETICS

AND

III
CATALYSIS

Chapter

XVIII
XIX
XX
XXI
XII


Page

805

HOMOGENEOUS REACTIONS
CATALYTIC REACTIONS

902

MASS AND HEAT TRANSFER IN CATALYTIC BEDS .

.

973

CATALYTIC REACTOR DESIGN

.

1007

.

1049

UNCATALYZED HETEROGENEOUS REACTIONS

.

.


APPENDIX

jcvii

AUTHOR INDEX

xxiii

SUBJECT INDEX

xxvii


TABLE OF SYMBOLS
A
A
A
A
a
Om
ttp

ttv

B
B
B
C
C


c
c
c
c.
c.
c.
c
c
c
Cp
Cv

d
D
DAB

Dp

D',
,

d
E
E
E^

area
atomic weight
component A

total work function
activity
external surface per unit mass
external surface per particle
external surface per unit volume
component B
constant of Calingaert-Davis equation
thickness of effective^ film
component C
concentration per unit volume
degrees centigrade
number of components
over-all rate constant
heat capacity at constant pressure
heat capacity at constant volume
Sutherland constant
concentration of adsorbed molecules per unit mass of
catalyst
specific heat
velocity of light
molal heat capacity at constant pressure
molal heat capacity at constant volume
surface concentration of adsorbed molecules per unit
catalyst area
diameter
diffusivity of A and B
effective particle diameter equal to diameter of sphere
having the same external surface area as particle
effective diameter equal to diameter of sphere having
same area per unit volume as particle

differential operator
energy in general
energy of activation, Arrhenius equation
effectiveness factor of catalysis


TABLE OF SYMBOLS

c
F
F
F
F,
Fi

S
/
/
Q
6
0

o
5
LQ
(g)
9
ffo
H
H

H
He
Hi
HH

Fp
H,
HH
Hr

Ht
AH
AHc
AHf
AHr
A/^»
H
H

AH

ft
h
I
I
I

Ti(i

base of natural logarithms

degrees of freedom
feed rate
force
external void fraction
internal void fraction
friction factor
_
|^
fugacity
,,
j^
weight fraction
, '
-^^
free energy
_
^\
mass velocity per unit area
„
specific gravity
< ~- ,
^^.
free energy per mole
,, '.
^Y
partial molal free energy
,^^.,_
^
change in free energy "
j -'6

gaseous state
. >., ,,,',
,.- v^
degeneracy
•
-^ • - n^i •
standard gravitational constant, 32.174 (ft/sec)/sec
enthalpy
Henry's constant
• ..
/ v-*!
humidity
.
•<
height of catalytic unit
#
y
height of mass-transfer unit
•
-i
height of heat-transfer unit
^'
height equivalent to a theoretical plate
percentage humidity
height of reactor unit
,<
relative humidity
; »
height of transfer unit
change in enthalpy

,,;. - /
,,
heat of combustion
.
/
heat of formation
, :>•,
/
|i|
heat of reaction
' ,»
standard enthalpy of activation
'\..(\
enthalpy per mole
rpartial molal enthalpy
partial molal enthalpy change
Planck's constant
heat-transmission coefficient
inert component
integration constant
moment of inertia


TABLE OF SYMBOLS
J
/
jt
i.-jis^ii . , , t . '
'•' K ' " ' "
K

^•^'' '• ;*; '
:
K
K
Ka
Ke
Kg
Kj,
Kp
K'
It
k
ft
kj^
k'ji
kg
kj^
k'
L
L
Lfi
L'
I
Ip
l„
(1)
]n
1(^
M
Mm

m
m
m
N
N
Nt

xi

Jacobian function
mechanical equivalent of heat
mass-transfer factor in
fluid
film
n
heat-transfer factor in fluid
film
"-l
characterization factor
degrees Kelvin
«'
distribution coefficient
'•••'- xtl-nH
,«j
equifibrium constant
;i
y
vaporization equilibrium constant '
^ •
equilibrium constant for adsorption

^
equilibrium constant, concentration units
over-all mass-transfer coefficient, pressure units
over-all mass-transfer coefficient, fiquid concentration
units
equilibrium constant, pressure units
irt?
surface equilibrium constant
i
M,^'
forward-reaction velocity constant ^
tj,"'
thermal conductivity
"'
?>
Boltzmann constant
r ,•!•',-• .s
?,
adsorption velocity constant
•' •
?•*
desorption velocity constant
'S^
?*
mass-transfer coeflScient, gas film ' 'p\.
mass-transfer coefficient, liquid film
^^
reverse-reaction velocity constant
ai*
mass velocity of fiquid per unit area

'?*A
total molal adsorption sites per unit mass
molal mass velocity of liquid per unit area
active centers per unit area of catalyst
length
heat of pressure change at constant pressure
heat of expansion at constant temperature
liquid state
natural logarithm
''•'
"' ^3
logarithm to base 10
"•
''•'
it
molecular weight
' >'
M
mean molecular weight
>M '
"i
mass
>'
^
slope of equilibrium curve dy*/dx
^J
Thiele modulus
Avogadro number 6.023(1023)
-'^
mole fraction

number of transfer units


ai

TABLE OP SYMBOLS

No
Nj^
n
P
Pf
Q
Q
q
g,
R
R
r
r,^
r,nA
r^
S
8
S
8
Sp
Sr
(S«
AiS*

8
8
(B)
T
t
V
U
V
u
V
V
Vf
V
w
w
We

number of transfer units, gas film '
number of transfer units, liquid film
number of moles
pressure (used only in exceptional cases to distinguish
pressure of pure components from partial pressures
of some component in solution
factor for unequal molal diffusion in gas film
heating value of fuel ; .
'0,
;\
partition function
,,;i
heat added to a system

,V
rate of heat
flow
.>\
component R
,
,;A
gas constant
,
»
radius
rate of reaction or transfer of A per unit area
rate of reaction or transfer of A per unit mass
rate of reaction or transfer of A per unit volume
component S
cross section
entropy
humid heat
percentage saturation
relative saturation
* .•
i
space velocity
entropy of activation
molal entropy
number of equidistant active sites adjacent to each
other
solid state ,
absolute temperature, degrees Rankine or Kelvin
temperature, °F or °C

internal energy
,
; ;;;
over-all heat-transfer coefficient
/
^j
internal energy per mole
,;;
velocity
molecular volume in Gilliland equation
volume
volume of reactor
volume per mole
ri
weight
work done by system
work of expansion done by system


TABLE OF SYMBOLS
to/
w.
X^
X
X
.

X

y

y*

z
zz
z

xiil

electrical work dme by system
shaft work
*
activated complex
mole fraction in liquid phase
' mole fraction of reactant converted in feed
qualitymole fraction in vapor
mole fraction in vapor, equilibrium value
elevation above datum plane =' v
height or thickness of reactor
'
compressibility factor
mole fraction in total system
!'>'4
DiMENSIONLESS NuMBEHS

., '
Nj,,

Beynold's number

DQ

—

iVp,

Prandtl number

—r- '

Nst

Stanton number

7777

Nsc,

Schmidt number

•*=?-

k

«•

•rS

•

A
a

B
b

C
c

D
D
e

f
f
f

G
H
L
L

,

SUBSCEIPTS

' component A
air

•> 1
_

•


•

'••"

' component B
'
• >-i' , .\
normal boiling point '
. . * , .;,-:
component C
. 1 • • • ..1
critical state
< ' ~^
component D
>'
dense arrangement '
expansion
" "
electrical and radiant
, • x.-, (
formation
fusion
• ' •'' ' "
•=
gas or vapor
" ''.• . •- ' '•••' •
isenthalpic
hquid
• '^

loose arrangement
'jv-x. *?f i. j .


xiv

TABLE OF SYMBOLS
p
R
r
r
S
S
s
s
T
t
t
V
V

w

constant pressure rcomponent R
reduced conditions
relative
component S >
isentropic
normal boiling point
saturation

isothermal
i;?,;
temperature .
transition
constant volume <
vapor
water vapor
''^''

(a)
a
a
a
a
(/3)
(3
7
(7)
A
S
S
d
c >.
T)
0
K
A
X
X
X/

H
11
V
V

: •'

G E E B K SYMBOLS

crystal form
coefficient of compressibility
proportionality factor for diffusioA
relative volatility
thermal diffusivity
=.'.-.••...,-'.
crystal form
^
coefficient of volumetric expansioA ;
activity coefficient
crystal form
finite change of a property; positive value indicates an
increase
- .
change in moles per mole of r e a c t ^ t
deformation vibration
partial differential operator
' .~ i
,{
energy per molecule
,

*efficiency
fraction of total sites covered
ratio of heat capacities
heat of vaporization
heat of vaporization per mole
wave length
heat of fusion per mole
chemical potential
viscosity
frequency
fugacity coefficient of gas


TABLE OF SYMBOLS
V
V
V

a
a
V

P
PB

Pp

Pc

S

a
T

4>
<f>
t

n u m b e r of ions
„^
n u m b e r of molecules
valence or stretching vibration
expansion factor of liquid
wave number
"total pressure of mixture, used where necessary to
distinguish from p
„ ,.
density
%,
•
bulk density
4"
particle density
t r u e solid density
:, „summation
surface tension
symmetry number
>
. :
time

activity coefficient
n u m b e r of phases
SUPERSCRIPTS

*,
*

ideal behavior
equilibrium state

o
A,

standard state
pseudo state
leverse rate
standard state of activation

/

t

XV

-



CHAPTER I
STOICHIOMETRIC PRINCIPLES

The principal objective to be gained in the study of this book is the
ability to reason accurately and concisely in the application of the
principles of physics and chemistry to the solution of industrial problems.
It is necessary that each fundamental principle be thoroughly understood, not superficially memorized. However, even though a knowledge
of scientific principles is possessed, special training is required to solve
the more complex industrial problems. There is a great difference
between the mere possession of tools and the ability to handle them
skilfully.
• Direct and logical methods for the combination and application of
certain principles of chemistry and physics are described in the text and
indicated by the solution of illustrative problems. These illustrations
should be carefully, studied and each individual operation justified.
However, it is not intended that these illustrations should serve as forms
for the solution of other problems by mere substitution of data. Their
function is to indicate the organized type of reasoning which will lead to
the most direct and clear solutions. In order to test the understanding
of principles and to develop the ability of organized, analytical reasoning, practice in the actual solution of typical problems is indispensable. The problems selected represent, wherever possible, reasonable
conditions of actual industrial practice.
Conservation of Mass. A system refers to a substance or a group of
substances under consideration and a process to the changes taking
place within that system. Thus, hydrogen, oxygen, and water may
constitute a system, and the combustion of hydrogen to form water,
the process. A system may be a mass of material contained within
a single vessel and completely isolated from the surroundings, it may
include the mass of material in this vessel and its association with the
surroundings, or it may include all the mass and energy included in a
complex chemical process contained in many vessels and connecting lines
and in association with the surroundings. In an isolated system the
boundaries of the system are limited by a mass of material and its
energy content is completely detached from all other matter and

energy. Within e given isolated system the mass of the system remains
constant regardless of the changes taking place within the system.
This statement is known as the law of conservation of mxiss and is the
basis of the so-called material balance of a process.
I


2

STOICHIOMETRIC PRINCIPLES

[CHAP. I

The state of a system is defined by numerous properties which are
classified as extensive if they are dependent on the mass under consideration and intensive if they are independent of mass. For example,
volume is an extensive property, whereas density and temperature are
intensive properties.
In the system of hydrogen, oxygen, and water undergoing the process
of combustion the total mass in the isolated system remains the same.
If the reaction takes place in a vessel and hydrogen and oxygen are
fed to the vessel and products are withdrawn then the incoming and
outgoing streams must be included as part of the system in applying
the law of conservation of mass or in estabhshing a material- balance.
The law of conservation of mass may be extended and appUed to the
mass of each element in a system. Thus, in the isolated system of
hydrogen, oxygen, and water undergoing the process of combustion the
inass of hydrogen in its molecular, atomic, and combined forms remains
constant. The same is true for oxygen.
In a strict sense the conservation law should be applied to the combined energy and mass of the system and not to the mass alone. By
the emission of radiant energy mass is converted into energy and also

in the transmutation of the elements the mass of one element must
change; however, such transfon;\ations never fall within the range of
experience and detection in industrial processes so that for all practical
purposes the law of conservation of mass is accepted as rigorous and
valid.
Since the word weight is entrenched in engineering hterature as synonomous with moss, the common practice will be followed in frequently
referring to weights of material instead of using the more exact term
mass as a measure of quantity. Weights and masses are equal only at
sea level but the variation of weight on the earth's surface is negligible
in ordinary engineering work.
STOICHIOMETRIC RELATIONS

Nature of Chemical Compounds. According to generally accepted
theory, the chemical elements are composed of submicroscopic particles
which are known as atoms. Further, it is postulated that all of the
atoms of a given element have the same weight,' but that the atoms of
different elements have characteristically different weights.
^ Since the discovery of isotopes, it is commonly recognized, that the individual
atoms of certain elements vary in weight, and that the so-called atomic weight of an
element is, in reality, the weighted average of the atomic weights of the isotopes.
In nature the various isotopes of a given element are always found in the same proportions; hence in computational work it is permissible to use the weighted average
atomic weight as though all atoms actually possessed this average atomic weight. ^


CHAP." I]

NATURE OF CHEMICAL COMPOUNDS

3

When the atoms of the elements unite to form a particular compound, it is observed that the compound, when carefully purified, has a
fixed and definite composition rather than a variable and indefinite
composition. For example, when various samples of carefully purified
sodium chloride are analyzed, they all are found to contain 60.6 per
cent chlorine and 39.4 per cent sodium. Since the sodium chloride is
composed of sodium atoms, each of which has the same mass, and of
chlorine atoms, each of which has the same mass (but a mass that is
different from the mass of the sodium atoms), it is concluded that in
the compound sodium chloride the atoms of sodium and chlorine have
combined according to some fixed and definite integral ratio.
By making a careful study of the relative weights by which the
chemical elements unite to form various compounds, it has been possible to compute the relative weights of the atoms. Work of this type
occupied the attention of many of the early leaders in chemical research
and has continued to the present day. This work has resulted in the
famihar table of international atomic weights, which is still subject to
periodic revision and refinement. In this table, the numbers, which
are known as atomic weights, give the relative weights of the atoms of
the various chemical elements, all referred to the arbitrarily assigned
value of exactly 16 for the oxygen f tom.
A large amount of work has been done to determine the composition
of chemical compounds. As a result of this work, the composition of a
great variety of chemical compounds can now be expressed by formulas
which indicate the elements that comprise the compound and the
relative number of the atoms of the various elements present.
It should be pointed out that the formula of the compound as ordinarily written does not necessarily indicate the exact nature of the
atomic aggregates that comprise the compound. For example, the
formula for water is written as H2O, which indicates that when hydrogen
and oxygen unite to form water, the union of the atoms is in the ratio
of 2 atoms of hydrogen to 1 atom of oxygen. If this compound exists
as steam, there are two atoms of hydrogen permanently united to one

atom of oxygen, forming a simple aggregate termed a molecule. Each
molecule is in a st^te of random motion and has no permanent association with other similar molecules to form aggregates of larger size.
However, when this same substance is condensed to the liquid state,
there is good evidence to indicate that the individual molecules become
associated, to form aggregates of larger size, (Il20)j:, x being a
variable quantity. With respect to solid substances, it may be said
that the formula as written merely indicates the relative number of
atoms present in the compound and has no further significance. For
example, the formula for cellulose is written CeHioOe, but it should not


4

STOICHIOMETRIC PRINCIPLES

[CHAP.

I

be concluded that individual molecules, each of which contains only
6 atoms of carbon, 10 atoms of hydrogen and, 5 atoms of oxygen exist.
There is much evidence to indicate that aggregates of the nature of
(CeHioOs)! are formed, with x a large number.
It is general practice where possible to write the formula of a chemical compound to correspond to the number of atoms making up one
molecule in the gaseous state. If the degree of association in the
gaseous state is unknown the formula is written to correspond to the
lowest possible number of integral atoms which might make up the
molecule. However, where the actual size of the molecule is important
care must be exercised in determining the degree of association of a
compound even in the gaseous state. For example, hydrogen fluoride

is commonly designated by the formula H F and at high temperatures
and low pressures exists in the gaseous state in molecules each comprising one atom of fluorine and one atom of hydrogen. However, at
high pressures and low temperatures even the gaseous molecules undergo association and the compound behaves in accordance with the
formula (HF)i, with x a function of the conditions of temperature and
pressure. Fortunately behavior of this type is not common.
Mass Relations in Chemical Reactions. In stoichiometric calculations, the mass relations existing between the reactants and products
of a chemical reaction are of primary interest. Such information may
be deduced from a correctly written reaction equation, used in conjunction with atomic weight values selected from a table of atomic
weights. As a typical example of the procedures followed, the reaction
between iron and steam, resulting in the production of hydrogen and the
magnetic oxide of iron, Fe304, may be considered. The first requisite
is a correctly written reaction equation. The formulas of the various
reactants are set down on the left side of the equation, and the formulas
of the products are set down on the right side of the equation, taking
care to indicate correctly the formula of each substance involved in the
reaction. Next, the equation must be balanced by inserting before
each formula coefficients such that for each element present the total
number of atoms originally present will exactly equal the total number
of atoms present after the reaction has occurred. For the' reaction
under consideration the following equation may be written:
3Fe + 4H2O -> Fe304 + 4H2
The next step is to ascertain the atomic weight of each element involved
in the reaction, by consulting a table of atomic weights. From these
atomic weights the respective molecular weights of the various compounds may be calculated.


CHAP. I]

!/

VOLUME RELATIONS IN CHEMICAL REACTIONS

Atomic Weights: <•
Iron
Hydrogen
Oxygen

-

Molecular Weights:
H2O
FeaOi
H2

'..•...,11.,, ..
55.84
1.008
16.00

•

• i ' i'• '•
• 1
(2 X 1.008) + 16.00 = 18.02
(3 X 55.84) + (4 X 16.00) = 231.5
(2 X 1.008) = 2.016
. , ;

The respective relative weights of the reactants and products maybe determined by multiplying the respective atomic or molecular
weights by the coefficients that precede the formulas of the reaction

equation. These figures may conveniently be inserted directly below
the reaction equation, thus:
3Fe
' *:-' -(i .;

(3X55.84)
167.52

+

4H2O

-* FesOi +

(4X18.02)
72.08

231.5
231.5

4H2
(4X2.016)
8.064

Thus, 167.52 parts by weight of iron react with 72.08 parts by weight
of steam, to form 231.5 parts by weight of the magnetic oxide of iron
and 8.064 parts by weight of hydrogen. By the use of these relative
weights it is possible to work out the particular weights desired in a
given problem. For example, if it is required to compute the weight
of iron and of steam required to produce 100 pounds of hydrogen, and

the weight of the resulting oxide of iron formed, the procedure would
be as follows:
Reactants:
Weight of iron = 100 X (167.52/8.064)
Weight of steam = 100 X (72.08/8.064)
Total
Products:
Weight of iron oxide = 100 X (231.5/8.064)
Weight of hydrogen
Total

2075 lb
894 Jb
2969 lb
'.

2869 lb
100 lb
2969 lb

Volume Relations in Chemical Reactions. A correctly written reaction equation will indicate not only the relative weights involved in a
chemical reaction, but also the relative volumes of those reactants and
products which are in the gaseous state. The coefficients preceding
the molecular formulas of the gaseous reactants and products indicate
the relative volumes of the different substances. Thus, for the reaction
under consideration, for every 4 volumes of steam, 4 volumes of hy-


6

STOICHIOMETRIC PRINCIPLES

[CHAP.

I

drogen are produced, when both materials are reduced to the same
temperature and pressure. This volumetric relation follows from
Avogadro's law, which states that equal volumes of gas at the same
conditions of temperature and pressure contain the same number of
molecules, regardless of the nature of the gas. That being the case,
and since 4 molecules of steam produce 4 molecules of hydrogen, it maybe concluded that 4 volumes of steam will produce 4 volumes of hydrogen. It cannot be emphasized too strongly that this volumetric
relation holds only for ideally gaseous substances, and must never be
applied to liquid or to solid substances.
The Gram-Atom and the Pound-Atom. The numbers appearing in
a table of atomic weights give the relative weights of the atoms of the
various elements. It therefore follows that if masses of different elements are taken in such proportion that they bear the same ratio to one
another as do the respective atomic weight numbers, these masses will
contain the same number of atoms. For example, if 35.46 grams of
chlonae, which has sa atomic wei^t oi 35.46, are. takea, and if 55.84
grams of iron, which has an atomic weight of 55.84, are taken, there
will be exactly the same number of chlorine atoms as of iron atoms in
these respective masses of material.
'
The mass in grams of a given element which is equal numerically to its
atomic weight is termed a gram-atom. Similarly, the mass in pounds of
a given element that is numerically equal to its atoinic weight is termed
a pound-atom. From these definitions, the following equations may be
written:
Gram-atoms of an elementary substance = -—:—rAtomic weight

Grams of an elementary substance = Gram-atoms X Atomic weight
Pound-atoms of an elementary substance = —
r^
:
Atomic weight
Pounds of an elementary substance = Polind-atoins X Atomic weight
The actual number of atoms in one gram-atom' of an elementary substance has been determined by several methods, the average result being
6.023 X 10^1 This numbel^ known as the Avogadi-o number, is of considerable theoretical importance.
The Gram-Mole and the Pound-Mole. It has been pointed out that
the formula of a chemical compound indicates the relative numbers and
the kinds of atoms that unite to form a compound. For example, the
formula NaCl indicates that sodium and chlorine atoms are present in


CHAP. I]

RELATION BETWEEN MASS AND VOLUME

7

the compound in a 1 : 1 ratio. Since the gram-atom as above defined
contains a definite number of atoms, which is the same for all elementarysubstances, it follows that gram atoms will unite to form a compound in
exactly the same ratio as do the atoms themselves, forming what may be
termed a gram-mole of the compound. For the case under consideration,
it may be said that one gram-atom of sodium unites with one gram-atom
of chlorine to form one gram-mole of sodium chloride.
One gram-mole represents the weight in grams of all the gram-atoms
which, in the formation of the compound, combine in the same ratio as
do the atoms themselves. Similarly, one pound-mole represents the
weight in pounds of all of the pound-atoms which, in the formation of

the compound, combine in the same ratio as do the atoms themselves.
From these definitions, the following equations may be written:
^
,
.
,
Gram-moles oi a substance

Mass in grams
Molecular weight

Grams of a substance = Gram-moles X Molecular weight
„
,
,
,
, ,
Pound-moles oi a substance =

Mass in pounds
^
—
Molecular weight
Pounds of a substance = Pound-moles X Molecular weight

The value of these concepts may be demonstrated by consideration of
the reaction equation for the production of hydrogen by passing steam
over iron. The reaction equation as written indicates that 3 atoms of
iron unite with 4 molecules of steam, to form 1 molecule of magnetic
oxide of iron and 4 molecules of hydrogen. It may also be interpreted

as saying that 3 gram-atoms of iron unite with 4 gram-moles of steam,
to form 1 gram-mole of Fe304 and 4 gram-moles of Ha. In other words,
the coefficients preceding the chemical symbols represent not only the
relative number of molecules (and atoms for elementary substances that
are not in the gaseous state) but also the relative number of gram-moles
(and of gram-atoms for elementary substances not in the gaseous state).
Relation Between Mass and Volume for Gaseous Substances. Laboratory measurements have shown that for all substances in the ideal
gaseous state, 1.0 gram-mole of material at standard conditions {0°C, 760
mm Hg) occupies 22.4 liters.^ Likewise, if 1.0-pound-mole of the gaseous
material is at standard conditions, it will occupy a volume of 359 cu ft.
2 The actual volume corresponding to 1 gram-mole of gas at standard conditions
will show some variation from gas to gas owing to various degrees of departure from
ideal behavior. However, in ordinary work the ideal values given above may be
used without serious error.
•


8

STOICHIOMETRIC PRINCIPLES

[CHAP.

I

Accordingly, with respect to the reaction equation previously discussed, it may be said that 167.52 grams of iron (3 gram-atoms) will
form 4 gram-moles of hydrogen, which will, when brought to standard
conditions, occupy a volume of 4 X 22.4 Uters, or 89.6 liters. Or, if
Enghsh units are to be used, it may be said that 167.52 pounds of iron
(3 pound-atoms) will form 4 pound-moles of hydrogen, which will

occupy a volume of 4 X 359 cubic feet (1436 cubic feet) at standard
conditions.
. . ? T. .,^^r,';•.!•••• iY>'/';.r^-'''«>
Illustration 1. A cylinder contains 25 lb of liquid chlorine. What volume in
cubic feet will the chlorine occupy if it is released and brought to standard conditions?
Basis of Calculation: 25 lb of chlorine.
Liquid chlorine, when vaporized, forma a gas composed of diatomic molecules, CI2.
Molecular weight of chlorine gas = (2 X 35.46)
Lb-moles of chlorine gas = (25/70.92)

70.92
0.3525

Volume at standard conditions = (0.3525 X 359).... 126.7 cu ft
Illustration 2. Gaseous propane, CsHg, is to be Uquefied for storage in steel
cylinders. How many grams of liquid propane will be formed by the liquefaction of
500 liters of the gas, the volume being measured at standard conditions?
Basis of Calculation: 500 liters of propane at standard conditions.

••'

Molecular weight of propane

44.06

Gram-moles of propane = (500/22.4);

22.32

Weight of propane = 22.32 X 44.06

,

985 grams

The Use of Molal Units in Computations. The great desirability of
the use of molal units for the expression of quantities of chemical compounds cannot be overemphasized. Since one molal unit of one compound will always react with a simple multiple number of molal units of
another, calculations of weight relationships in chemical reactions are
greatly simplified if the quantities of the reacting compounds and products are expressed throughout in molal units. This simphfication is not
important in very simple calculations, centered about a single compound
or element. Such problems are readily solved by the means of the combining weight ratios, which are commonly used as the desirable means
for making such calculations as may arise-in quantitative analyses.
However, in an industrial process successive reactions may take place
with varying degrees of completion, and it may be desired to calculate
the weight relationships of all the materials present at the various stages
of the process. In such problems the use of ordinary weight units with
combining weight ratios will lead to great confusion and opportunity for
arithmetical error. The use of molal units, on the other hand, will give
a more direct and simple solution in a form which may be easily verified.


'CHAP.

I]

THE USE OF MOLAL UNITS IN COMPUTATIONS

9

It is urged as highly advisable that familiarity with molal units be gained

through their use in all calculations of weight relationships in chemical
compounds and reactions.
A still more important argument for the use of molal units lies in the
fact that many of the physicochemical properties of materials are
expressed by simple laws when these properties are on the basis of a molal
unit quantity.
The molal method of computation is shown by the following illustrative problem which deals with the reaction considered earlier in this
section, namely, the reaction between iron and steam to form hydrogen
and the magnetic oxide of iron:
v i< •• •
. i •
Illustration 3. (o) Calculate the weight of iron and of steam required to produce
100 lb of hydrogen, and the weight of the Fe304 formed. (6) What volume will the
hydrogen occupy at standard conditions?
Reaction
,.:

Equation:

B<, .1.

Basis of Calculation:

3Fe + 4H2O —>FesOs + 4Hj
100 lb of hydrogen.

• ~,-.--i

Molecular and atomic weights:
i'

Fe

!'':'

H20

''""'"'"'*'"
. ,

FesOi
Hj

' '55.84
18.02

•

fX

»

or
or
or

'•• •

231.5
2.016

Hydrogen produced = 100/2.016
Iron required = 49.6 X 3/4
37.2 X 55.84
Steam required = 49.6 X 4 / 4
49.6X18.02
FeaOi formed = 49.6 X 1/4
12.4X231.6
Total input = 2075 -|- 894

49.6
37.2
2075
49.6
894
12.4
2870
2969

lb-moles
lb-atoms
lb
lb-moles
1b
lb-moles
1b
lb

Total output = 2870 4-100

2970 1b

,;,,,

- M ».»

Volume of hydrogen at standard conditions =
49.6X359

17,820 cu ft

In this simple problem the full value of the molal method of calculation is not apparent; as a matter of fact, the method seems somewhat
more involved than the solution which was presented earUer in this
section, and which was based on the simple rules of ratio and proportion.
It is in the more complex problems pertaining to industrial operations
that the full benefits of the molal method of calculation are realized.