
There’s no need to memorize cubed or
squared conversion factors

gc =
Notes on CheCal 1 with input
Collab on 08/12/21










Difference of Units and Dimensions:
o Units:
standard
way
of
describing physical quantity
o Dimensions: physical quantity
Conversion Factor: gives the relationship
of the two units involved; in fraction
form
SI Units:
o Greek prefixes
o In powers of 10
o Base unit + Greek prefix (also
called multiplier)
Format for solution:
o Given,
required,
solution:
conversion factors then solution
For answers:
o Usually 5% difference or
deviation
from
calculated
answer for engineering students
but only 0.1% for sir
“No particular rule for rounding off”, as
long as it is reasonable and not too long
**use exponential form if possible to be
safe
Exponential and logarithmic shouldn’t
have units
gc is a conversion factor to relate mass
and force
**it’s referred to as the “C” in
Himmelblau’s where it is defined as a
constant with a value of one to balance
the units and is dependent on the units
of the dimensions used in the equation
Dyne: is force used for small objects
In writing exponential form: x 10n as en
1 𝑔∙𝑐𝑚/𝑠2
𝑑𝑦𝑛𝑒
32.174 𝑙𝑏𝑚 ∙𝑓𝑡/𝑠2
=
𝑙𝑏𝑓
1 𝑘𝑔∙𝑚/𝑠2
𝑁
=
Not on collab notes:

1 Btu = 3.93 x 10-4 hp-hr
Collab on 08/17/20



Density as conversion factor
o 1 g/cm3 = 62.4 lb/ft3
o 1 cP = 0.01 g/cm•s
For dimensional analysis/consistency;
changing the units of the components:
o Do it reverse, use the goal units
then convert back to the original
unit –new units back to original
units
o Work only on one side of the
equation
o The resulting unit of the
equation is added at the end and
will be converted to the
desired/goal unit
Try checking the method in SIM, the one
that tackles temperature etc.
Collab on 08/19/21

Mole unit
o Amount of particles (molecules,
atoms, electrons)
o 0.012 kg of C-12


o
o
o
o
o
o








𝑛=
𝑚
𝐹𝑊
=
12 𝑔
12 𝑔/𝑚𝑜𝑙
1000𝑔
1 𝑘𝑔
= 12 𝑔
𝑚 𝑖𝑛 𝑙𝑏
𝑀𝑊 𝑖𝑛 𝑙𝑏/𝑙𝑏𝑚𝑜𝑙
𝑚 𝑖𝑛 𝑔
1 𝑔𝑚𝑜𝑙 =
𝑀𝑊 𝑖𝑛 𝑔/𝑔𝑚𝑜𝑙
𝑚 𝑖𝑛 𝑘𝑔
1 𝑘𝑔𝑚𝑜𝑙 = 𝑀𝑊 𝑖𝑛 𝑘𝑔/𝑘𝑚𝑜𝑙
1 𝑙𝑏𝑚𝑜𝑙 =
Also kgmol
Density
o Mass of substance per unit
volume
o Kg/m3, lb/ft3, g/mL, g/cm3
Specific volume is reciprocal of density
Density
of
water,
at
80-100
temperature, density changes (it goes
down)
Relative density = specific gravity
SG
o A universal reference scale
o Has two major drawbacks:
 Laboratory precision
 Limited range of scale
o Often expressed to an accuracy
of 2 or 3 decimal places
Reference density for SG:
o For liquids and solids, water
o For gases, air
Comparing the density-temperature
graph of NH3 and water, the former has
apparent changes in density depending
on the temperature
Solutions assume no changes in density
as temperature changes
𝑆𝐺 =
𝜌𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒
𝜌𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒

Usual density used as reference for
solids and liquids is density of water at
4˚C >> 1.00 g/cm3

𝑆𝐺 = 0.72
= 1𝑚𝑜𝑙𝐶
Etymology > mole > Latin > heap
Amount of substance
1
mole
=
6.022x1023
atoms/molecules/ions
 Avogadro’s number of
elementary
units/entities


𝑚𝑐 = 0.012 𝑘𝑔 ×
o
o

˚API
o
20°
4°
Numerator: temperature of
substance when measured
Denominator: temperature of
reference when measured
American Petroleum Institute
141.5
o
°𝐴𝑃𝐼 =
o
Hydrometric scale based on
petroleum products
Measure of the density of
petroleum liquid in relation to
density of water
Gravity or density of crude oil
and liquid petroleum products
Devised by American Petroleum
Institute and NIST – National
Institute of Standards and
Technology
Oil with the least specific gravity
has the highest API gravity
API
gravity
is
directly
proportional with temperature
(SG is inversely proportional to
T)
 Volume of petroleum
liquid
is
directly
proportional
to
temperature
Crude oil quality standard
adopted worldwide
Indicate oil quality
One of the important factors in
deciding the price of various
varieties of crude oil
˚API > 45, extra light crude oil
˚API (33,45), light crude oil
o
o
o
o
o
o
o
o
o
o
𝑆𝐺
60℉
60℉
− 131.5
o
o
o
o

˚API (22, 33), medium crude oil
˚API (10, 22), heavy crude oil
˚API ≤ 10, extra heavy crude oil
Light crude oil is more expensive
than heavy crude oil
 Higher percentage of
gasoline and diesel fuel
Baumé scale
o ˚Be
o
°𝐵𝑒 = 145 −

o
°𝐵𝑒 =



°𝑇𝑊 =
o
Scale for SG of solutions, first
two digits to the right of the
decimal point multiplied by 2
Reports the measured SG of a
liquid relative to water
Only used for liquids with SG
greater than that of water
 Usually ranges between
1.00 and 1.85
Used in the British dye and
bleach manufacturing industries
W. Twaddell Glasgow/ Thomas
Twaddell > coined after
Charles Macintosh > person
behind
Used philosophical bubbles or
SG beads
Used in heavy industries to
determine strength of solution
of various substances such as
brine, sugar solutions (syrup,
juice, honey, brewers, must) and
acids
Scale little known outside of UK,
mainly in England and Scotland
Used for acids in tanning
industry and alkaline lye in
papermaking
Uses:
 Tanning industry
 Determine
strength
of
synthetic
tanning agents
 Easier
to
determine the
extra
water
needed
to
dilute mixture
to
desired
o
o
145
𝑆𝐺
Heavier than water
145
𝑆𝐺
o
− 130
Lighter than water
Some sources say it’s
140/SG
o Antoine Baumé
o Devised
for
making
hydrometers
o Used to determine the sugar
content of must
o Used to calculate what the
wine’s alcohol content will be
after fermentation
o Used as a measure of density or
concentration
o SG of a sugar solution has a good
correlation
to
sugar
concentration
 In brewing >> wine
making and sugar beet
processing
o A traditional description of a
solutions concentration
o A number of acids has its
concentration measured in
˚Baume >> also called heaviness
scale
o Strength of acids is expressed by
their relative weight
Twaddell scale
o ˚TW
𝑆𝐺−1
0.0005
o
o
o
o
o
o
o
o
strength
Twaddells
popular

𝐸𝑥𝑡𝑟𝑎 𝑤𝑎𝑡𝑒𝑟 𝑛𝑒𝑒𝑑𝑒𝑑 =
𝑉


in
>
𝑇𝑤 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
Pottery industry
 Calculating the
volume to add
given
the
concentration
of
sodium
silicate
(deflocculant)
1𝑔 𝑠𝑢𝑔𝑎𝑟
o
1°𝐵𝑥 =
o
Uses refracometer
 Light bends more in a
substance with higher
sugar content
Interchanged with degrees Plato
(˚P) and degrees Balling
Expresses the weight percentage of
sugar solutions and relate it to SG
Measure of sugar content
Measure of all solutes in a beverage
or preparation
o
o
o


𝑇𝑤 𝑜𝑟𝑖𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ−𝑇𝑤 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
Brix Scale
o ˚Bx
o °𝐵𝑥 = 231.61(𝑆𝐺 − 0.9977)
o Measurement in percentage by
weight of sucrose in pure water
solution
 Only valid for pure
sucrose solutions >
extracted from sugarcone or sugar-beet
o Measures the sugar content in a
solution
 Allows to estimate
alcohol content of
product (wine making)
o

100𝑔 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
= 1% 𝑠𝑢𝑔𝑎𝑟
Other scales: Oechsle or ˚Oe (wine
making) and Plato or ˚P (brewing
industry)
Above are SG-based scales
Mass flow rate is ṁ
Collab on 08/24/21








Unless stated, always use reference
density (density of water) at 4˚C
Make calculations as simple as possible
Solve problems more easily
Empirical formula
o Formula that doesn’t make
sense dimensionally
o Used/based on experiments/
empirical data
Do not overthink solutions
Mole and mass fractions are mostly used
in CHE calculations
Concentrations such as molality,
molarity, and normality are rarely used
in CHE and are for smaller amount of
substances
Rules for percent composition:
o For gases, if not stated: it’s
either mole% or volume%
 At
the
same
temperature
and
pressure, mole% =
volume%
o For solids and liquids, if not
stated: it’s either mass% or
weight%
Collab on 08/26/21




Exam coverage
o Conversion of units
o Dimensional consistency
o Mole concept
o Density
o Mole and mass fraction
Exam details:
o 1:30-3:30
o Problem solving
o Write the problems in the
solution paper
o 2h
Mass and mole fraction
o Usually requires 4 decimal
places
“Ash”
o Not necessarily ash
o Non-combustibles
o Residual substances that did not
evaporate/ combust in the
process
o Usually minerals



For solving average molecular weights,
use the mass/mole based on the
calculations as per basis
Main vinculum must always be the
longest
In solving problems, where mole/mass
of the solution is given as well as the
mass % and mole % of the components:
o One component as mass%
o The other as mole%
o Solve for the equations for the
components’ mole and mass
o Assign variable to x to the not
given %
 If mole % of A is given,
assign mole of B as x
 If mass % of B is given,
assign mass of A as x
o Then solve for the variable using
the equations formed
Collab on 09-07-21
Collab on 9/02/21

Basis
o
o
o
o
o
o
o
o
Reference
chosen
for
calculations
Starting amount for calculations
Explicitly stated at the beginning
of the solution
Assumed values
Must be complete with label
Prefers the most convenient
basis
May be a period of time, mass of
material, and other convenient
quantity
1 or 100 is usually the best unit
basis





Sun-mon, quiz
Temperature
o How hot/cold a body is
o Defined in thermodynamics as
the average kinetic energy of
the atoms and molecules in the
system
o Usually used along with
pressure to determine the
properties
of
different
substances for various systems
o There are 4 scales commonly
used in the field of chemical
engineering
-40˚ is the temperature when Celsius is
equal to Fahrenheit
Standard temperature is 0˚C
Absolute scale
o


Reference is absolute zero
 Lowest
possible
temperature
o Best fit for physical quantities
computation
o Kelvin
 Measures the absolute
zero, 0 K
 Absolute scale that
corresponds to Celsius
 William Thompson, Lord
Kelvin
o Rankine
 Absolute scale that
corresponds
to
Fahrenheit
 William John Macquorn
Rankine
Relative scale
o Celsius
 Measured
freezing
point of water as well as
water’s boiling point;
then divided the middle
in 100 (equal parts)
 Anders Celsius
o Fahrenheit
 Measured the freezing
point of water, normal
body temperature (96.6
˚F and 32 ˚F)
 Measured
freezing
point of brine solution
(salt solution)
 Daniel
Gabriel
Fahrenheit
o Based on relative temperature
of freezing and boiling point of
substances
o Relatively assigned
Formula:
o









𝑇℃ =
(𝑇℉ −32)
1.8
o 𝑇℉ = 1.8𝑇℃ + 32
o 𝑇𝐾 = 𝑇℃ + 273
o 𝑇°𝑅 = 𝑇℉ + 460
For Kelvin, it should be 273.15 and
Rankine should be 459.67
Temperature difference
o Useful in calculations since most
basis for formula is temperature
difference
o Derivation:
∆𝑇℃ = 𝑇℃2 − 𝑇℃1
𝑇℉ − 32
𝑇℃ =
1.8
𝑇℉2 − 32 𝑇℉1 − 32
∆𝑇℃ =
−
1.8
1.8
1.8∆𝑇℃ = 𝑇℉2 − 𝑇℉1
1.8∆𝑇℃ = ∆𝑇℉
o Used for conversion of units of
constants in equations
For formula equations, temperature
difference is used
Relation between temperature scales
o ∆℃ = ∆𝐾
o ∆℉ = °𝑅
o ∆℃ = 1.8∆℉
o ∆𝐾 = 1.8∆°𝑅
Rankine still is expressed in degrees.
Only Kelvin does not have degrees
F˚ : temperature difference in
temperature
˚F : just temperature measure
0˚C is the standard conditions of
temperature
Unit degree Celsius and Kelvin are larger
than unit degree Fahrenheit and
Rankine
Collab on 09-09-21

Exam on Thursday
o
o
o



Synchronous
2:30-4:30 (1 and 45 mins)
Coverage:
 Choosing a basis
 Temperature
and
pressure
 Relating scales
to each other
o 3-4 times
o GMeet and SEB
o Copy the problem
o “Plan while copying the
problem”
o Restrict access (permits)
o SEB password is given in GMeet
Most equations are based on
temperature difference
“square of a binomial”
o For squared scales in formula
o Do not distribute
o It’s fine if another term is added
 Temperature scale in
first degree
Pressure
o Exerted on top of cylinder by
atmosphere and at the bottom
of
the
cylinder
by
water/substance
o Force applied perpendicular to
surface
or
the
normal
perpendicular force per unit
area
o SI unit is Pascals, Pa which is
N/m2
o We will only consider pressure
exerted by gases and liquids
o Exerted force per area
o Fluid has weight, weight will be
the force exerted at the bottom
of the weight
o
o
o
o
o
o
o
Discovery stemmed from welldiggers wondering why water
won’t rise beyond 10 m using
suction pumps
 They first sought Galileo
but he did not want to
be bothered lol
 Torricelli was the one
who helped them
From Torricelli’s experiment:
 Water is not pulled by
vacuum but pushed up
by local air pressure
 Therefore, maximum
height of water that
can’t
be
pumped
depends
on
atmospheric pressure
Hydrostatic pressure
 Pressure exerted by
liquid
 Pressure of fluid at
equilibrium
 Pressure at the bottom
of
the
static
(nonmoving) column of
mercury exerted at the
bottom/sealing plate
Derivation
𝑓𝑜𝑟𝑐𝑒
𝑚𝑔
𝑃=
=
𝑎𝑟𝑒𝑎
𝑎𝑟𝑒𝑎
(𝜌𝑣)𝑔 𝜌(𝑎𝑟𝑒𝑎)(ℎ)𝑔
=
=
𝑎𝑟𝑒𝑎
𝑎𝑟𝑒𝑎
𝑃 = 𝜌𝑔ℎ
Gravity used is usually gc, which
is the conversion factor
Atmospheric pressure
 Pressure exerted by air
or atmosphere
 The
barometric
pressure
𝑃𝑡𝑜𝑡 = 𝜌𝑔ℎ + 𝑃𝑎𝑡𝑚
o
o
Torricelli’s Experiment
 Fig 1
o

Patm
pushes
down liquid on
basin
and
pushes up liquid
to the tube
o

o
o
o
o
Set-up:
 Basin filled with
mercury
 A tube with a
close top and
open bottom at
the center
 Pressure exerted by the
atmosphere will cause
mercury to rise in the
tube
 The height of the rise in
mercury (fluid) is the
measured atmospheric
pressure
 The height of the fluid is
760 mm
Can be expressed in either
absolute or relative scale
Relative pressure is not the used
term, it’s called “gauge
pressure” or pressure gauge
instead
Gauge pressure
 Does not include Patm
Absolute pressure
 Patm
 𝑃𝑎𝑏𝑠 = 𝑃𝑔𝑎𝑢𝑔𝑒 + 𝑃𝑎𝑡𝑚
 19.3 psia (referred to
zero absolute pressure)
 4.6 psig (referred to
barometric pressure)
Standard pressure
 101.3 kPa, 1.000 atm,
760 mmHg
Use 1 atm as Patm if it is not given
since it is the standard
atmospheric pressure at sea
level
Head of a liquid
 A liquid column
 Head >> height of the
column of liquid
Collab on 09/13/21



Exam coverage
o Temperature
o Temperature conversion
o Homogeneity of an equation
o Equations involving (relating)
temperature
o Pressure
Pressure
o Perpendicular force per area
For fluids/ liquid
o 𝑃 = 𝜌𝑔ℎ
o H : height of the liquid
o Gravity is usually in g/gc
 Because we essentially
need to convert mass to
force
in
the
equation/formula
o
𝑔
𝑃 = 𝜌 (𝑔 ) ℎ
𝑐


Easier especially of
English units are used
 SI: g/gc = 9.81 N/kg
 AE: g/gc = 1 lbf /1 lbm
 g/gc values are from
values of g divided by gc
Force exerted by fluid
o 𝐹𝑓𝑙𝑢𝑖𝑑 = 𝑚𝑓𝑙𝑢𝑖𝑑 𝑔 = 𝜌𝑉𝑔

Absolute pressure
o The sum of pressure exerted by
fluid and pressure exerted by
atmosphere
o 𝑃𝑎𝑏𝑠 = 𝑃𝑔 + 𝑃𝑎𝑡𝑚

In exams, it will be explicitly stated if the
system is open to the atmosphere or not
It is easier and convenient to use g/gc in
English units
Manometer
o Device used to measure the
pressure of a sample gas
o U-shaped tube filled with fluid
(manometer fluid)
 Due to Patm, there is a
difference in height of
liquids
 Due
to
difference
in
pressure
o Manometer fluid
 Should be completely
immiscible to other fluid
 Creates a distinct layer
that separates the liquid
o If both manometer fluid at both
side have equal height
 no reading
 fig. 2


o
If PA > PB
 Results to difference
 fig 3
x-h
x
h


h : difference of
pressure
x : height of fluid at the
left from the opening to
o
o
o
o
the liquid/ reference
line
 x-h : height of fluid at
the right from the
opening
to
the
reference line
Used to measure pressure
difference
Sensitive to pressure of other
fluids
cheaper
Can be :
 Open-end
 Measures
relative
pressure/
relative
with
Patm
 Relative/ gauge
pressure
 Fig 6


Fluid
is
accounted with
Patm
Close-end
 Also
called
absolute
pressure
manometer
 The
measurement is
not compared
with Patm
 Fig 7

Only force is
from fluid









Take note when to add Patm and when
not
It’s easier to create open-end than closeend manometers
Bourdon Gauge
o Used by water companies
o Useful for high pressure
readings
o Used special (???)
o Used on water systems
Pressure Balance
o Pressure on the left side of the
U-tubed manometer must be
equal to the pressure on the
right side
𝑃𝑡𝑜𝑡 = 𝑃𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 + 𝑃𝑓𝑙𝑢𝑖𝑑
Density of fluid, ρ and of manometer
fluid, ρm
Height of liquids are measured relative
to the reference line
Pressure on the left side:
o 𝑃𝐴 = 𝜌𝑔𝑥
Pressure on the right side: (derivation of
pressure difference from pressure
balance)
𝑃𝐴 + 𝜌𝑔𝑥 = 𝑃𝐵 + 𝜌𝑔(𝑥 − ℎ) + 𝜌𝑚 𝑔ℎ
o






∆𝑃 = 𝑃𝐴 − 𝑃𝐵 = (𝜌𝑥 − 𝜌)𝑔ℎ
Two-fluid manometer
o 2 manometer fluids
o Fig 4

o

Only has 1 liquid but can also be
2 liquids
o Portrays how brakes work on
vehicles
Study on how formula were derived
from principles
Atmospheric pressure
o Zero point for a relative pressure
scale
Perfect Vacuum
o Zero point for absolute scale
Vacuum
o Pressure below atmospheric
pressure
o Region which the pressure is
considerably lower than the
atmospheric pressure
o 𝑃𝑣𝑎𝑐𝑢𝑢𝑚 = 𝑃𝑎𝑡𝑚 − 𝑃𝑎𝑏𝑠
o As the vacuum value increases,
the value of absolute pressure
measured decreases
Draft
o In inches H2O
o Pressure that is only slightly
below atmospheric pressure
o Not really noticeable but can be
measured
o Is also vacuum
Absolute pressure:
Patm
Derive formula using pressure
balance
Pressure balance can also be applied not
just only to U-tube manometer
problems
Fig 5
o
𝑃𝐴 + 𝜌𝑔𝑥 = 𝑃𝐵 + 𝜌𝑔𝑥 − 𝜌𝑔ℎ + 𝜌𝑚 𝑔ℎ

Can also be used in hydraulics
problem
Vacuum



0
Vacuum is positive in Pabs and negative in
Pg
Gauge pressure is negative with vacuum
Relative pressure:
0
Patm
Vacuum








Barometer
o Used to measure pressure of
atmosphere
psig : gauge pressure in pounds per
square inch
solve pressure equivalent in other units :
(P/ρ)/g (??)
Average molecular weight of air: 28.84
solve density of air:
𝜌𝑎𝑖𝑟 = 𝑖𝑑𝑒𝑎𝑙 𝑔𝑎𝑠 𝑙𝑎𝑤
𝑃𝑉 = 𝑛𝑅𝑇
𝑚
𝑃𝑉 =
𝑅𝑇
𝑀𝑊
𝑚
𝑃(𝑀𝑊) =
𝑅𝑇
𝑣
𝑚 𝑃(𝑀𝑊)
𝜌= =
𝑣
𝑅𝑇
o P is absolute pressure in atm
o T is in Kelvin
o MW is in g/mol
o R = 0.08206 L•atm/ mol•K
Percent error
o
=
o
=
|𝑡𝑟𝑢𝑒 −𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑣𝑎𝑙𝑢𝑒|



𝑔
𝑔
𝑃𝐴 + 𝜌𝑜𝑖𝑙 ( ) 𝑥 = 𝜌𝑤𝑎𝑡𝑒𝑟 ( ) ℎ
𝑔𝑐
𝑔𝑐
ℎ=




𝑥 100%
𝑡𝑟𝑢𝑒 𝑣𝑎𝑙𝑢𝑒
𝑎𝑐𝑡𝑢𝑎𝑙−𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
𝑥
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
100%
Density is usually neglected for gases like
air
Ex:



Solving z:
𝑔
𝑃𝐴 = 𝑃𝑎𝑖𝑟 + 𝜌𝑚 ( ) 𝑧
𝑔𝑐
𝑧=
If Pg is used on the left then also use Pg
on the right
x was given -_Solving h:

𝑃𝐴 − 𝑃𝑎𝑖𝑟
𝑔
𝜌𝑜𝑖𝑙 (𝑔 )
𝑐

𝑔
𝑃𝐴 + 𝜌𝑜𝑖𝑙 (𝑔 ) 𝑥
𝑐
𝑔
𝜌𝐻2𝑂 (𝑔 )
𝑐
You should be constant if you use
absolute or gauge pressure in pressure
balance
Keep track if you neglect atmospheric
pressure in the calculations
Recall that psig is without Patm
Standard atmosphere vs. atmospheric
pressure
o Standard pressure is assumed to
be in a standard gravitational
field
o Standard pressure is a fixed
value
o Standard pressure: 1 atm, 760
mmHg at 0˚C
o Atmospheric pressure is a
variable (it varies)
o Atmospheric
pressure
is
measured
(usually
from
barometers)
It’s easier to convert pressure units by
relating to atmospheric pressure
The nature of the instrument used to
make the measurement, decides
whether the pressure measured is
relative or absolute
Tank attached to a u-tubed manometer
is below atmospheric pressure when the
left leg attached to the tank is higher
than the right leg
For manometer with three fluids
o
o


Solution process is similar to
pressure balance
o Pick a reference level for
measuring pressure
o If fluid 1 and 3 are gases and
fluid 2 is Hg:
 Ignore
the
terms
involving gases
 Density of gases
are very small
and
can
therefore
be
neglected
 𝑃1 + 𝜌1 𝑑1 𝑔 = 𝑃2
o If fluid 1 and 3 are liquids and
fluid 2 is immiscible
 Fluids 1 and 3 cannot be
neglected
 𝑃1 + 𝜌1 𝑑1 𝑔 = 𝑃2 +
𝜌2 𝑑2 𝑔 + 𝜌3 𝑑3 𝑔
Pressure drop
o Experienced by flowing fluid
when it passes through a
restriction (i.e. orifice)
Examples:
o Pressure gauge on a tank of CO2
used to fill soda water bottles,
connected to a barometer
(absolute pressure)
o
Pressure difference across an
orifice (pressure drops)
Collab on 09-18-21




Ionic Compounds
o Usually already in its empirical
formula
 They do not consist
discrete molecular units
o Also
called
electrovalent
compounds
o Electrically
neutral
ionic
compound
 Zero total charge
 Subscript of cation =
anion and subscript of
anion = cation
o Metallic cation + nonmetallic
anion
Binary compounds
o Formed from only two elements
Ternary compounds
o Consists of three elements
Naming for Ionic Compounds
o Before roman numerals:
 -ous
 Cation
with
fewer positive
charges
 -ic
 Cation
with
more positive
charges
o Uses Roman Numerals for
charges (called as the “Stock
system”)
 It is much more specific
 Provides info of the
actual charge of the
cation
o



Roman numerals is the charge of
the cation i.e. the subscript of
the anion
o Metallic cation + nonmetallic
anion (-ide)
Mercury I is a diatomic ion > Hg22+
Molecular Compounds
o Contain discrete molecular units
o Formed
with
nonmetallic
elements
o Usually binary compounds
Naming Molecular Compounds
o Uses Greek prefixes to signify
number of atoms present
 Mono- : 1
 Di- : 2
 Tri- : 3
 Tetra- :4
 Penta- : 5
 Hexa- : 6
 Hepta- : 7
 Octa- : 8
 Nona- : 9
 Deca- : 10
o Nonmetallic ion + nonmetallic
ion (-ide)
o The prefix mono- may be
omitted for the first element
o For oxides: the prefixes ending
in “a” is omitted
o Exceptions:
 Molecular compounds
containing H
 B2H6 : diborane
 CH4 : methane
 SiH4 : silane
 NH3 : ammonia
 PH3 : phosphine
 H2O : water
 H2S : hydrogen sulfide
o Usually straightforward


Naming Acids
o Acids: yield H+ ions when
dissolved in water
o In gaseous or pure liquid state:
Hydrogen + nonmetallic anion
o When dissolved in water: Hydro+ nonmetallic anion (-ic) + acid
o Oxoacids: has H, O, and another
element (the central element)
 + 1 O to “-ic” acid :
“per…ic” acid
 - 1 O from “-ic” acid : “ous” acid
 - 2 O from “-ic” acid :
“hypo…ous” acid
o Oxoanions : anions of oxoacids
 All H are removed from
“-ic” acid : ends with “ate”
 – all H from “-ous” acid :
ends with “-ite”
o Anions -H but not all H : indicate
no. of H present
Parent acids
o Hydrofluoric acid, HF
o Hydrochloric acid, HCl
o Hydrobromic acid, HBr
o Hydroiodic acid, HI
o Hydrocyanic acid, HCN
o Water, H2O
o Hydrosulfuric acid, H2S
o Hydroselenic acid, H2Se
o Hydrotelluric acid, H2Te
o Chloric acid, HClO3
o Bromic acid, HBrO3
o Iodic acid, HIO3
o Nitric acid, HNO3
o Acetic acid, HC2H3O2
o Carbonic acid, H2CO3
o Sulfuric acid, H2SO4
o Selenic acid, H2SeO4
o Telluric acid, H2TeO4


o Phosphoric acid, H3PO4
o Arsenic acid, H3AsO4
o Stibinc acid, H3SbO4
Naming Bases
o Base: yields OH- ions when
dissolved in water
o Ion + hydroxide
Writing chemical equations
o Chemical
equations:
uses
chemical symbols to show what
happens in a reaction
 Shorthand expression
for
a
chemical
change/reaction
 Summarize reaction
 Display
reacting
substances
 Indicate amount of all
reacting
component
substances
 Tells you the reactants
and products involved
 Tells you the mole ratios
of involved substances
o 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 → 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠
o Includes additional info of
physical states as subscripts
 (g) : gas
 (l) : liquid
 (s) : solid
 (aq)
:
aqueous
environment
o Arrow indicates direction of
reaction (read as “yields”)
o Above the arrow:
 Additional substance /
factor supplied to the
reaction
 Delta sign : +heat
 H2O : reactant is added
to water; or substance




reacted in the presence
of water
 hv : light
 Oxidizing agents
 Solvents
 Catalysts,
energy
sources,
environmental/reaction
conditions
o Below the arrow:
 Catalyst : alters speed of
chemical reaction
o Anything above and below the
arrow is not consumed in the
reaction
o Upward arrow in products
 Evolution of a gas/gas
bubbles
 In gaseous state
o Downward arrow in products
 Formation
of
precipitate
 In solid state
Balancing equations
o Adjusting the coefficients so no.
atoms of a substance in
reactants is equal in its product
o Law of conservation of mass
o Subscripts cannot be changed or
the identity of the substance will
be altered
Know how to predict products of
chemical reactions
Molecular Formula
o Shows the exact number of
atoms of each element
Allotrope
o A distinct form of an element
o Example:
 Oxygen: oxygen gas (O2)
and ozone (O3)


Carbon: diamond and
graphite
Types of Chemical Reactions
o Combination
or
Synthesis
Reaction
 𝐴 + 𝐵 → 𝐴𝐵
 𝑚𝑒𝑡𝑎𝑙 + 𝑜𝑥𝑦𝑔𝑒𝑛 →
𝑚𝑒𝑡𝑎𝑙 𝑜𝑥𝑖𝑑𝑒
 Solid + gas = gas
 basic
 𝑛𝑜𝑛𝑚𝑒𝑡𝑎𝑙 +
𝑜𝑥𝑦𝑔𝑒𝑛 →
𝑛𝑜𝑛𝑚𝑒𝑡𝑎𝑙 𝑜𝑥𝑖𝑑𝑒
 Solid/gas + gas =
gas
 acidic
 𝑚𝑒𝑡𝑎𝑙 + 𝑛𝑜𝑛𝑚𝑒𝑡𝑎𝑙 →
𝑠𝑎𝑙𝑡
 Solid
+
gas/liquid
=
solid
 𝑚𝑒𝑡𝑎𝑙 𝑜𝑥𝑖𝑑𝑒 +
𝑤𝑎𝑡𝑒𝑟 →
𝑚𝑒𝑡𝑎𝑙 ℎ𝑦𝑑𝑟𝑜𝑥𝑖𝑑𝑒
 Solid + liquid =
aq
 basic
 𝑛𝑜𝑛𝑚𝑒𝑡𝑎𝑙 𝑜𝑥𝑖𝑑𝑒 +
𝑤𝑎𝑡𝑒𝑟 → 𝑜𝑥𝑦 − 𝑎𝑐𝑖𝑑
 Gas/solid
+
liquid = aq
 Oxy-acid: also
oxoacids/
ternary
acid
(HaXbOc)
o Decomposition Reaction
 𝐴𝐵 → 𝐴 + 𝐵
 𝑠𝑜𝑚𝑒 𝑚𝑒𝑡𝑎𝑙 𝑜𝑥𝑖𝑑𝑒 →
𝑚𝑒𝑡𝑎𝑙 + 𝑂2(𝑔)
 𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒𝑠 →
𝑚𝑒𝑡𝑎𝑙 𝑜𝑥𝑖𝑑𝑒 + 𝐶𝑂2(𝑔)


𝑏𝑖𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒𝑠 →
𝑚𝑒𝑡𝑎𝑙 𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒 +
𝑤𝑎𝑡𝑒𝑟 + 𝐶𝑂2(𝑔)
 𝑎𝑛𝑦𝑡ℎ𝑖𝑛𝑔 𝑤𝑖𝑡ℎ 𝑂 →
𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒 + 𝑂2
 Needs heat to separate
O2 gas
o Single Displacement Reaction
 𝐴 + 𝐵𝐶 → 𝐵 + 𝐴𝐶
 A is metal
 𝐴 + 𝐵𝐶 → 𝐶 + 𝐵𝐴
 A is halogen
 Requires
activity/reactivity series
 𝑚𝑒𝑡𝑎𝑙 + 𝑎𝑐𝑖𝑑 →
ℎ𝑦𝑑𝑟𝑜𝑔𝑒𝑛 + 𝑠𝑎𝑙𝑡
 𝑚𝑒𝑡𝑎𝑙 + 𝑤𝑎𝑡𝑒𝑟 →
ℎ𝑦𝑑𝑟𝑜𝑔𝑒𝑛 +
𝑚𝑒𝑡𝑎𝑙 𝑜𝑥𝑖𝑑𝑒/
ℎ𝑦𝑑𝑟𝑜𝑥𝑖𝑑𝑒
 𝑚𝑒𝑡𝑎𝑙 + 𝑠𝑎𝑙𝑡 →
𝑚𝑒𝑡𝑎𝑙 + 𝑠𝑎𝑙𝑡
 ℎ𝑎𝑙𝑜𝑔𝑒𝑛 +
ℎ𝑎𝑙𝑖𝑑𝑒 𝑠𝑎𝑙𝑡 →
ℎ𝑎𝑙𝑜𝑔𝑒𝑛 + ℎ𝑎𝑙𝑖𝑑𝑒 𝑠𝑎𝑙𝑡
o Double
Displacement
or
Metathesis Reaction
 𝐴𝐵 + 𝐶𝐷 → 𝐴𝐷 + 𝐶𝐵
 Exchange of +&- groups
 𝑎𝑐𝑖𝑑 + 𝑏𝑎𝑠𝑒 → 𝑠𝑎𝑙𝑡 +
𝑤𝑎𝑡𝑒𝑟
 Neutralization
of an acid&base
 Formation of insoluble
precipitate
 𝑚𝑒𝑡𝑎𝑙 𝑜𝑥𝑖𝑑𝑒 + 𝑎𝑐𝑖𝑑 →
𝑠𝑎𝑙𝑡 + 𝑤𝑎𝑡𝑒𝑟
 Formation of a gas
Metathesis reactions include evolution
of heat, formation of insoluble
precipitate and production of gas
bubbles in the product






Anything that reacts with oxygen gas
requires heat
No reaction for metals and salts with
metallic cation who has stronger
activity/reactivity
Activity/Reactivity Series
o Likelihood to undergo single
displacement
o SPMGC don’t displace H
 Au, Pt, Ag, Hg, Cu
o H
o Double C NLT displace H from
HA
 Co, Cd, Ni, Pb, Sn
o CIZAM displace H from H2O(g)
and HA
 Cr, Fe, Zn, Al, Mg
o NaLiBaKCa displace H from
H2O(l&g) and HA
o For halogens, arrangement is
based on electronegativity
Diatomic Ions
o H, Cl, Br, N, O, F, I
Empirical Formula
o Smallest number ratio
o Shows the elements present in
the smallest number ratio
o The simplest
Charges
o Boron: ±3
o C : +4
o Si : ±4
Collab on 9/21/21

Stoichiometry
o From Greek stoicheion, element,
and metron, measure
o





Quantitative means of relating
products to reactants
Stoichiometric Coefficients
o The relative amounts of moles
of products and reactants
Stoichiometric Ratios
o The relative proportion of
products and reactant
o Used to relate amounts of
substances from each other
Reactants
o Limiting Reactant, LR
 Theoretically first to be
completely consumed
 Has
the
smallest
maximum extent of
reaction
o Excess Reactant, ER
 Reactants that are not
the limiting reactant
Maximum extent of reaction
o Quantity based on assuming
complete reaction of each
reactant
o A straightforward way of
determining which is the LR
Solving for LR and ER
o
o

𝑛𝑓𝑒𝑒𝑑
𝑛𝑒𝑞𝑛
𝑛
𝑔𝑖𝑣𝑒𝑛
= 𝑛 𝑐𝑜𝑚𝑝𝑜𝑛 𝑒𝑞𝑛
𝑛𝑓𝑒𝑒𝑑 =
𝑐𝑜𝑚𝑝
𝑚𝑐𝑜𝑚𝑝
𝑀𝑊𝑐𝑜𝑚𝑝
𝑛𝑐𝑜𝑚𝑝 𝑜𝑛 𝑒𝑞𝑛
o Smallest ratio is the LR
Conversion
o Also termed as the degree of
completion
o Fraction of the reactant in the
feed converted to products
o In Himmelblau conversion and
degree of completion is
interchangeable, but in the SIM
conversion is for all other

reactants while degree of
completion is only for the LR
o



%𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 =
𝑛𝑢𝑠𝑒𝑑𝑅
𝑛𝑓𝑒𝑒𝑑𝑅
× 100%
Selectivity
o Ratio of moles of desired
product to undesired byproduct
Yield
o There is no universal definition
for this, but there are three
common
o Yield based on feed: amount of
desired product obtained over
amount of LR fed
o Yield based on reactant
consumed: amount of desired
product obtained over amount
of LR consumed
o Yield based on 100% conversion:
amount of product obtained
over theoretical amount of
product based on LR fed
o Third is dimensionless except for
first two
Yield and selectivity
o Measure the degree to which
desired reaction proceeds
relative
to
competing
undesirable reactions

Exam this week (Saturday)
o Stoichiometry and Material
Balance
Degree of Completion and Percent Yield
o
o




Collab on 9/28/21


𝐷𝑜𝐶 =

𝑛𝐿𝑅 𝑟𝑒𝑎𝑐𝑡𝑒𝑑
𝑛𝐿𝑅 𝑓𝑒𝑒𝑑
Numerator: calculated
from actual yield
Denominator:
calculated
from
theoretical yield
o Value of degree of completion =
value of percent yield
o They only differ on perspective
 Degree of Completion
focuses on reactant
while percent yield
focuses on products
Selectivity
o Ratio of desired product to
undesired product
o Measurement of finding of
process to select which is either
the first or second reaction
o Comparison of 2 equation
𝑆=
𝑛 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑑 𝑡𝑜 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑃
𝑛 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑑 𝑡𝑜 𝑢𝑛𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑃
Consecutive reactions
o Reactions where the product
becomes the reactant to
another reaction and so on
Material Balances
o Application
of
law
of
conservation of mass
 Matter
is
neither
created nor destroyed
o Involves accounting for material
o Always specify the system
Unlike mass, volume is generally not
conserved due to varying densities
Terms in Material Balance
o System
 A portion or the entire
process itself that is
taken for analysis
 Closed system: no
material enters/leaves
 Open or flow system:
material enters/leaves
o System boundary






A line (usually dotted)
that
encloses
the
system
taken
for
analysis
o Material
 Moles or any quantity
conserved
Components of material balance
o Initial condition (input)
o Final condition (output)
o Generation
 Occur due to chemical
reaction
o Consumption
 Occur due to chemical
reaction
o Accumulation
 Can be negative
 Sum of all materials
accumulated in the
system
over
time
interval
 Unit: mass/moles
 Unit can never be rate
(mass/mole per unit
time)
Steady-state system or process
o The amount or property of the
material is invariant (does not
change)
Pseudo steady-state
o Not entirely steady-state but is
treated as such for convenience
Quasi steady-state
o Not entirely steady-state but is
effectively behaving as such due
to its slow rate of change
Unsteady-state
or
transient
process/model
o The material in its initial
condition is different from its




final condition or material
undergo changes over time
Continuous Process
o Material enters/leaves the
system without interruption
Batch Process
o A closed process that treats a
fixed amount of material over
time
o Material enters, material is
processed, material is removed
Semi-batch process
o An open process where
materials enter but never leave
Difference equation:
o

𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 = 𝑖𝑛 − 𝑜𝑢𝑡 + 𝑔𝑒𝑛 − 𝑐𝑜𝑛
Material Balance has assumptions:
o The process are at steady-state
 Properties inside the
system does not change
 Amount/ mass
in system stays
constant
 Implies accumulation=0
o No chemical reactions
 No generation and
consumption
 Only happens
when
new
chemical
species
are
formed
 Implies gen&con=0
o Material Balance then is:
 𝑖𝑛 − 𝑜𝑢𝑡 = 0
 𝑖𝑛 = 𝑜𝑢𝑡
 𝑚𝑎𝑠𝑠 𝑖𝑛 = 𝑚𝑎𝑠𝑠 𝑜𝑢𝑡








Chemical
engineering
operations
focused on material balance
o Chemical reactions
o Fluid transport
o Size reduction and enlargement
o Heat generation and transport
o Distillation
o Evaporation
o Gas absorption
o Crystallization
o Drying
Box the overall material balance (OMB)
to set the boundary
Problems often should only use 1
component
Each component that enters the system
has its own component material balance
For multiple component material
balance, overall material balance may
not be steady-state balances, since some
other
material
accumulates
or
evaporates
In this type of material balance we are
only concerned with what goes in and
out and disregard the process
Always use linear equations for
modelling
If info is in ratio, cross multiply
o Ex: X/Y = 0.2 will become X=0.2Y
o




Collab on 9/30/21


Exam
o
o
o
o
o
2 h and 15 mins
15 mins for submission and no
extension
3 questions
1 is stoichiometry
2 is two-stage material balance

3 is material balance with
recycle stream
Bypass Stream
o Skips 1 or more stages
o Some parts are fed to the
process and some are left
unprocessed
o Used to control the composition
of the final exit stream to obtain
desired product with suitable
proportions
Recycle Stream
o Increases efficiency of process
o Gives higher yield of output
o Can offer significant economic
savings
for
high-volume
processing systems
o Usually accompanied with purge
stream
Purge Stream
o Stream is bled off
o Usually seen in reactive
systems/processes
involving
reactions
o Used
to
remove
an
accumulation of inerts or
unwanted materials that might
build up in the recycle stream
o Usually placed with recycle
streams, distillation columns
Do Overall Material Balance (OMB) of
whole system first then towards each
subsystems
Distillation Column
o Unit operations that separates a
mixture of 2 liquids with
different boiling points
Reflux
o Some part of the distillate is
returned to the distillation
column

o








Increase the concentration of
the low boiler (usually the
desired product)
Reflux/recycle ratio
o Ratio of final product and
recycle
Benzene has lower boiling point than
toluene
Crystallization
o Separation process for soluble
solids
o Lowering the solubility
o Combination of evaporation
(minimizes the solvent) and
lowering the temperature
Streams from the separator have the
same properties
K2CrO4 is nonvolatile
For product with two states and
different composition
o Mass fraction of product (mass
of stream)(mass fraction of
component in the product)
Multiple unit systems
Operations
o Mixer
 Combines two or more
streams
o Splitter
 Has 1 feed stream and
produces two or more
product streams with
the same composition
as the feed stream
 Key word is split, so
stream is only “split” to
different directions (still
of
the
same
composition)
o Separator





1 or more stream of
different composition
entering and 1 or more
streams still of different
composition leaving
 Key word is separate, so
there is separation of
different species
General rule: the basis you choose and
the unit with which you start the analysis
affect the degree of complexity of your
calculations
Distillation
o Purify or separate alcohol in the
beverage
industry
and
hydrocarbons in the petroleum
industry
o Components of liquid mixture
are separated by boiling
 Due to difference in
vapor pressure
Absorption
o Occurs in absorption of oxygen
from air
 Fermentation process,
sewage treatment plant
o Absorption of hydrogen gas for
liquid hydrogenation of oil
o A component is removed from a
gas stream by treatment with a
liquid
Drying
o of grain and other food is similar
to drying of lumber, filtered
precipitates, and rayon yarn
o volatile liquids (usually water)
are removed from solid
materials
Evaporation
o





of salt solutions (chemical) is
similar to evaporation of sugar
solutions (food)
o evaporation of volatile solvent
from nonvolatile solute
Membrane Separation
o Separation of solute from a fluid
o Using diffusion through semipermeable membrane barrier
Liquid-liquid extraction
o Solute in liquid solution is
removed by contacting with a
relatively immiscible liquid
solvent
Adsorption
o A component of a gas or liquid
stream is removed
and
adsorbed by solid adsorbent
Liquid-solid leaching
o Dissolves and remove solute
from a finely divided solid by
treating it with a liquid that does
the job
Crystallization
o Removal of solute from solution
by precipitating the solute from
solution
Collab on 10/05/21

Final Exam
o Will have about 5 problems
o Unit conversion
o Temperature
o Pressure
o Stoichiometry
o Material Balance
 Recycle
 Bypass
o
o
o
o


Multiphase systems
Ideal gas equation
On Tuesday, Oct.12
Review
previous
exam
questions
o Analytical
chemistry
:
gravimetry
Bypass Stream
o Not everything is needed to be
processed and is thus bypassed
ṁ : indicates mass flow rate
Collab on 10/08/21


Final Exam
o 1:30-4:30 pm
o Degrees of freedom
o % humidity
o 4b (multi-phase) is not included
Gas Laws
o Boyle’s Law
 At
constant
temperature, pressure
is
indirectly
proportional to volume
 As pressure increases,
volume decreases
 𝑃𝑉 = 𝑘
 𝑃1 𝑉1 = 𝑃2 𝑉2
o Charles’ Law
 At constant pressure,
temperature is directly
proportional to volume
 As
temperature
increases,
volume
increases


o
𝑉
=𝑘
𝑇
𝑉1
𝑉
= 𝑇2
𝑇1
2
Gay-Lussac’s Law

At constant volume,
temperature is directly
proportional
to
pressure


𝑃
=𝑘
𝑇
𝑃1
𝑃
= 2
𝑇1
𝑇2


o
Combined gas Law


o
o
o
𝑃𝑉
=𝑘
𝑇
𝑃1 𝑉1
𝑃 𝑉
= 2𝑇 2
𝑇1
2
Avogadro’s Law
 At
constant
temperature
and
pressure, number of
moles
is
directly
proportional to volume

o
o
𝑉
𝑛

o

(𝑃 +
𝑎𝑛2
) (𝑉
𝑉
− 𝑛𝑏) = 𝑅𝑇
o
o
=𝑘
Ideal gas Law

𝑃𝑉
𝑛𝑇

Where k is the ideal gas
constant R

𝑃𝑉
𝑛𝑇
=𝑘
=𝑅
 𝑃𝑉 = 𝑛𝑅𝑇
Dalton’s Law
 Of partial pressures
 𝑃𝑡𝑜𝑡 = 𝑃1 + ⋯ 𝑃𝑛


𝑛1 𝑅𝑇
𝑉

𝑃1 =


𝑃1 = 𝑋1 𝑃𝑡𝑜𝑡
𝑛
𝑃1 = 𝑛 1 𝑃𝑡𝑜𝑡
𝑡𝑜𝑡
Amagat’s Law
 𝑉𝑡𝑜𝑡 = 𝑉1 + ⋯ 𝑉𝑛
 𝑉1 = 𝑋1 𝑉𝑡𝑜𝑡
𝑛
 𝑉1 = 1 𝑉𝑡𝑜𝑡

𝑛𝑡𝑜𝑡

Good
for
mathematical
estimates
o Often used to estimate designs
For designs which require exact
parameters, use exact specific values for
different parameters
Real gas
o Very specific
o Has table of values
o Has different type of equations
Van der Waals equation
o Alternative for ideal gas
equation
o Ideal gas equation + correction
factors
Ideal gas equation
o Useful for alternatives of ideal
gas behaviors
o Used for rough estimates
Ideal gas
o Imaginary gas


a and b are correction factors
Correction factors are used
since real gases deviate from
properties of real gases
o Each gases have different
correction factors
No real gas exactly obeys the gas laws
Obeys ideal gas law
o Lighter gas but with negligible
deviations
o Under ordinary circumstances
o Vapor at low pressure and high
temperature exudes behavior
that approaches ideal gas
Values of R
𝐿∙𝑎𝑡𝑚
𝑚𝑜𝑙∙𝐾
𝑓𝑡 3 ∙𝑝𝑠𝑖
𝑙𝑏𝑚𝑜𝑙∙°𝑅
𝑚3 ∙𝑃𝑎
𝑚𝑜𝑙∙𝐾
𝐿∙𝑡𝑜𝑟𝑟
𝑚𝑜𝑙∙𝐾
o
𝑅 = 0.08206
o
𝑅 = 10.73
o
𝑅 = 8.314
o
𝑅 = 62.36
When using the ideal gas equation,
always state to assume ideal gas
Relative scales are preferred since it is
easy to relate and to imagine



Always assume standard condition if
pressure and temperature is not
specified, 0˚C and 1 atm
Formula weight of air sir preferred:
28.84
For specific gravity, write answers as
o



𝑔𝑎𝑠 𝑎𝑡 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑇 𝑎𝑛𝑑 𝑃
𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑔𝑎𝑠 𝑎𝑡 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑇 𝑎𝑛𝑑 𝑃
For density assuming ideal behavior, you
do not need to derive just use:
o

[𝑣𝑎𝑙𝑢𝑒]

𝜌=
𝑃(𝑀𝑊)
𝑅𝑇
Partial Pressures: Dalton
o Fictitious pressure exerted by a
single component of gaseous
mixture
o Used by engineers …
Be mindful if the percent given is in
weight or mole

Review for Analytical Chemistry, Gravimetry




Analytical Chemistry is just advance
stoichiometry
Gravimetric methods:
o Quantitative method
o Based on determining the mass
of a pure compound to which
the analyte is chemically related
 The chemical species to
be analyzed
Precipitation gravimetry
o Analyte is converted to sparingly
soluble precipitate
Precipitation gravimetry in a nutshell
o Filter, wash, heat, weigh
 Washing is to free
precipitate
from
impurities



Heating is for it to
convert to a product of
known composition
Types of reagents
o Specific reagents
 Rare
 React only with a single
chemical species
o Selective reagents
 More common
 React with limited
number of species
Characteristics of ideal precipitating
agent
o Easily filtered and washed free
of contaminants
o Sufficiently low solubility
 So no significant loss of
the analyte occurs
o Unreactive
 With constituents of the
atmostphere
o Of known chemical composition
Characteristics of favorable precipitates
(ppt) for gravimetry
o Large particle size
 Easy to filter and wash
 Usually purer than finer
precipitates
Factors that affect particle size of ppt
o Ppt solubility
o Temperature
o Reactant concentration
o Rate at which reactants are
mixed
Particle sizes
o Colloidal precipitate
 10-7 to 10-4 cm in
diameter
 Show no tendency to
settle from solution
o
o
o
 Difficult to filter
Crystalline precipitate
 At least 10-4 or greater
in cm diameter
 Settles spontaneously
 Easily filtered
Determined
by
which
process/mechanism
of
precipitate predominates
 Nucleation: a minimum
number of atoms, ion,
or
molecules
join
together to give a stable
solid
 Formed on the
surface
of
suspended solid
contaminants
 Results to a
large number of
colloids
 Particle growth: growth
of existing nuclei
 Results to small
number
of
crystalline
Determined using relative
supersaturation
 Von Weimann eqn

=






𝑄−𝑆
𝑆


Q is concentration of
solute
 S is its equilibrium
solubility
 When value is large, ppt
is colloidal
 When value is small, ppt
is crystalline
High
relative
supersaturation:
nucleation


Low relative supersaturation: particle
growth
Ways to minimize supersaturation
o Elevated
temperatures
(increase solubility)
o Dilute solutions (minimize Q)
o Slow addition of precipitating
agent (good stirring)
o Controlling pH (if solubility
depends on pH)
Supersaturated solutions
o Unstable solution
o Higher solute concentration
Colloidal particles are usually coagulated
first before filtered
Ways to hasten coagulation
o Heating
o Stirring
o Adding electrolyte to medium
Adsorption: ions are retained on the
surface of the solid; adhering to the
surface
o Primary adsorption layer: ions
on surface; usually positive
charged
o Counter-ion layer: contains
sufficient excess of negative
ions; balances charge of
particle’s surface
o Electric double layer: imparts
stability to colloidal suspension;
between primary adsorption
and counter-ion layer
Peptization: reverting a coagulated
colloid to its dispersed state
Digestion: precipitate is heated in
mother liquor
o Mother liquor: solution from
which the precipitate is formed
o Results to denser mass
o Improves coagulation


Coprecipitation:
normally
soluble
compounds that is carried out with the
precipitate
o Solubility of that compound is
not yet reached, so it appeared
as precipitate
Types of coprecipitation:
o Surface adsorption
 Soluble compound as
surface contaminant
 Improved by digestion,
washing the solution
with volatile electrolyte,
or
reprecipitation
(filtered
solid
is
redissolved
amd
reprecipitated)
o Mixed-crystal formation
 Contaminant
ion
replaces an ion in the
lattice of a crystal
 Ion must have
the
same
charge and sizes
must differ by
no more than
5%
 Countered with the use
of
a
different
precipitating agent or
by separating the ion
before
the
final
precipitation step
o Occlusion
 Foreign ions trapped in
counter-ion layer within
growing crystal
o Mechanical entrapment
 Trap portion of solution
in a pocket when




crystals
lie
close
together during growth
o First two are equilibrium
processes
o The last two are from kinetics of
crystal growth
 Countered by low rate
of ppt formation, low
supersaturation,
and
digestion
Homogeneous precipitation
o A precipitating agent is
generated in a solution of the
analyte
o Better suited for analysis
o Precipitating agent appears
gradually and homogenously
throughout the solution
o Relative supersaturation is kept
low
o Results in increased crystal size
and improved purity
Weighing form: the compound formed
after precipitate is heated
Heating precipitate
o Removes solvent and volatile
species
o Decompose solid and form
compound of new composition
Gravimetric calculations takeaways
o Calculating percent component
given mass sample and mass ppt
=
o
𝑚𝑝𝑝𝑡 (𝑀𝑊𝑝𝑝𝑡 )(𝑀𝑅)(𝑀𝑊𝑐𝑜𝑚𝑝 )
× 100%
𝑚𝑠𝑎𝑚𝑝𝑙𝑒
Calculating mass of component
given
mass
of
another
component
= 𝑚𝑜𝑡ℎ𝑒𝑟𝑐𝑜𝑚𝑝 × 𝑀𝑊𝑜𝑡ℎ𝑒𝑟𝑐𝑜𝑚𝑝 ×
𝑛𝑐𝑜𝑚𝑝
× 𝑀𝑊𝑐𝑜𝑚𝑝
𝑛𝑜𝑡ℎ𝑒𝑟𝑐𝑐𝑜𝑚𝑝

o
Molar ratio is just
formula based, number
of moles in component
and other component
are dependent of each
other
 Ex: 1 mol of
Pb3O4 is to 3
mol pf PbO2
 Focus
on
central atom or
main common
component
Determining which weighing
form gives greatest mass of
precipitate
 Calculate
mass
of
common
component/molecule/a
tom from mass of each
weighing form then
compare values
= 1 𝑔 𝑐𝑜𝑚𝑝 × 𝑀𝑊𝑐𝑜𝑚𝑝 ×
𝑛𝑊𝐹
× 𝑀𝑊𝑊𝐹
𝑛𝑐𝑜𝑚𝑝
%𝑝𝑝𝑡
= 𝑚𝑠𝑎𝑚𝑝𝑙𝑒 (
)(𝑀𝑊𝑝𝑝𝑡 )(𝑀𝑅)(𝑀𝑊𝑐𝑜𝑚𝑝 )
100%

Insoluble Ions
Except in
Alkali metals, Ca, Sr, Ba, NH4+
Alkali metals, NH4+
Alkali metals, NH4+
Alkali metals, Ca, Sr, Ba, NH4+
Alkali metals
2-
S
CO32PO43OH
O2
Normally soluble ions, but can be
insoluble
-
Cl
BrISO42
Insoluble with
Ag+, Pb2+, Hg22+
Ag+, Pb2+, Hg22+
Ag+, Pb2+, Hg22+
Ba2+, Pb2+, Ca2+, Sr2+
Soluble Ions
o Nitrates, NO3o Acetates, CH3COO
o Chlorates, ClO3o Perchlorates, ClO4-

o
𝑚𝑠𝑎𝑚𝑝𝑙𝑒 =
o
Highest
yield
will
produce the greatest
mass
Determining minimum mass of
the sample given %content of
precipitate and mass of
component
 Use lowest % and solve
𝑚𝑐𝑜𝑚𝑝 (𝑀𝑊𝑐𝑜𝑚𝑝 )(𝑀𝑅)(𝑀𝑊𝑝𝑝𝑡 )
%𝑝𝑝𝑡 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒
Determining
maximum
precipitate mass given mass of
component and %ppt
 Use largest %
References
Brown, L.S., & Holme, T.A. (2011). Chemistry for
engineering students, 2nd ed. Cengage Learning.
Brown, T.L., Lemay, H.E., Bursten, B.E., Murphy, C.J.,
& Woodward, P.M. (2012). Chemistry: The central
science, 12th ed. Prentice Hall.
Geankopolis, C.J. (1993). Transport process and unit
operations, 3rd ed. Prentice-Hall.
Himmelblau, D.M., & Riggs, J.B. (2012). Basic
principles and calculations in chemical engineering,
8th ed. Pearson Education.
Professor: Engr. Ramiro Amon
Compiled by: F.D.