Assignment #1
Himmelblau Chapter 1:
Problems: 1.10, 1.12, 1.20, 1.21, 1.23, 1.26
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Lecture 3, 2/18/2012
Chapter 2: Moles, Density, and Concentration
Objectives:
1.Define a kilogram mole, pound mole, gram mole.
2. Convert from moles to mass and vise versa.
3. Calculate molecular weight.
4. Define density and specific gravity and calculate the density of a liquid and solid.
5. Convert the composition of a mixer from mole fraction to mass fraction and vise versa.
6. Transform a material from one measure of concentration to another.
7. Calculate the mass or number of moles of each component in a mixture given the percent
composition and vise versa.
8. Convert a composition given in mass percent to mole percent and vise versa.
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Moles and Molecular Weights
Mole ≡ the amount of a substance that contains as many elementary entities as there are
atoms in 0.012 kg of carbon 12. In SI system, one mole of any species contains 6.02 x 1023
(Avogadro’s number) molecules of that species.
Moles can also be expressed as kg-moles or lb-moles, e.g. 27.0 kg of aluminum is equivalent
to 1 kg-mole, and 1 lb-mole of magnesium has a mass of 24.3 lb.
We will use the designation of g mole for the SI mole.
Molecular Weight ≡ the sum of the atomic weights of the atoms that constitute a molecule of
the compound (same as molar mass); units of the form kg/kmol, g/mol or lbm/lb-mole;
molecular weight (MW) =mass/mole
Molecular weight is the conversion factor that relates the mass and the number of moles (of
any kind, e.g. kg-moles)of a quantity of a substance.
atomic weight - atomic mass .... Appendix B - pg 1030
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Example: Moles and Molecular Weight
Silver nitrate is a white crystalline salt, used in marking inks, medicine and chemical analysis.
How many kilograms of silver nitrate (AgNO3) are there in :
a. 13.0 lb mol AgNO3.
b. 55.0 g mol AgNO3
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Test yourself: Moles and Molecular Weight
Calcium carbonate is a naturally occurring white solid used in the manufacture of
lime and cement. Calculate the number of lb moles of calcium carbonate in:
a. 50 g mol of CaCO3.
b. 150 kg of CaCO3.
c. 100 lb of CaCO3.
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Density, Specific Gravity, API Gravity
Density (ρ) ≡ mass (m) per unit volume (V) of a substance; units are
mass/length3 (kg/m3, g/cm3, lbm/ft3).
m
ρ=
V
Gases (vapors) are compressible; density changes with pressure and
temperature. Solids and liquids are incompressible; density is constant with
pressure and varies slightly with temperature.
Specific volume (1/ρ) ≡ volume occupied by a unit mass of a substance;
Units are length3/mass (reciprocal of density).
∧
V
V=
m
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Specific Gravity
Specific gravity (SG) ≡ ratio of the density (ρ) of a substance to the
density (ρref) of a reference substance at a specific condition; dimensionless;
Sp.gr. of A =
ρ A (T , P)
ρ ref (Tref , Pref )
The reference commonly used for solids and liquids is water at 4°C, which has the
following density:
ρref = ρH2O(l)(4°C) = 1.000 g/cm3 = 1000 kg/m3 = 62.43 lbm/ft3
For gases: ρref = air at “standard conditions”
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API Gravity (Crude Oil)
In the petroleum industry the specific gravity of
petroleum products is often reported in term of a
hydrometer scale called ⁰API.

141.5
API =
 ρ fluid , 60 F
sp.gr.
ρ
 water , 60 F




− 131.5
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Example: Density and specific gravity
The density of a liquid is 1500 kg/m3 at 20 °C.
a. What is the specific gravity 20°C/4°C of this material ?
b. What volume (ft3) does 140 lbm of this material occupy at 20°C ?
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Test yourself: Density and specific gravity
The specific gravity of mercury at 20 C
̊ is 13.546. Calculate the density of
mercury in lbm/ft3. Calculate the volume in ft3 occupied by 215 kg of mercury.
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Flow Rate
.
Flow
Rate ≡ the rate at which a material (gas, liquid or solid) is transported in a process stream.
•
mass flow rate
(m): is the mass (m) transported through a line per unit time (t):
•
m=
m
t
Volumetric flow rate (F): is the volume (V) transported through a line per unit time (t):
•
V
F=
t
Molar flow ( n) : is the number of moles (n) of a substance transported through a line
per unit time (t):
•
n
n=
t
where, the “dot” above the m and n refers to a flow rate.
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Mole Fraction and Mass (Weight) Fraction
The following terms may be used to define the composition of a mixture of
substances, including a species A:
Mass fraction:
mass of A  kg A
gA
lb m A 


xA =
or
or
total mass  kg total g total lb m total 
Mole fraction:
yA =
moles of A  kmol A mol A lb mol A 
or
or


lb mol 
total moles  kmol
mol
Mass (weight) percent and mole percent are the respective fractions times 100.
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Analyses of Multicomponent Solutions and Mixtures
In this text book, the composition of gases will always be presumed to be
given in mole percent or fraction unless specifically stated otherwise.
In this text book, the composition of liquids and solids will be given by mass
(weight) percent or fraction unless otherwise specifically stated, as is the
common practice in industry.
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Example: Flow rate and Mole Fraction
The feed to an ammonia synthesis reactor contains 25 mole% nitrogen and the
rest is hydrogen. The flow rate of the stream is 3000 kg/h. Calculate the rate of
flow of nitrogen into the reactor in kg/h.
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Example: Mole and Mass Fraction
A liquefied mixture of n-butane, n-pentane and n-hexane has the
following composition in weight percent.
n - C4H10 = 50 %
n - C5H12 = 30 %
n - C6H14 = 20 %
Calculate the weight fraction, mole fraction and mole percent of each
component and also the average molecular weight of the mixture.
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Test yourself: Mole and Mass Fraction
A mixture of gases is analyzed and found to have the following composition. How
much will 3 lb mol of this gas weigh ?
CO2
CO
CH4
H2
N2
Total
12.0
6.0
27.3
9.9
44.8
100.0
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Concentration
The concentration of a component of a mixture or solution is the quantity of this
component per unit volume of the mixture.
Mass Concentration ≡ mass of a component per unit volume of the mixture (g/cm3,
lbm/ft3, kg/in3,…)
Molar Concentration ≡ number of moles of the component per unit volume of the
mixture (kmol/m3, lb mol/ft3,…)
Molarity ≡ molar concentration expressed in moles solute/liter solution
Trace species (species present in minute amounts) in mixtures of gases or liquids are
typically expressed in units of parts per million (ppm) or parts per billion (ppb). If yi
is the fraction of component i, then
ppmi = yi x 106
ppbi = yi x 109
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Example: Concentration
A solution of HNO3 in water has a specific gravity of 1.10 at 25 C
̊ . The
concentration of HNO3 is 15 g/L.
What is the mole fraction of HNO3 in the solution ?
What is the ppm (wt) of HNO3 in the solution ?
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Test yourself: Concentration
The 1993 Environmental Protection Agency (EPA) regulation contains standards for 84
chemicals and minerals in drinking water. According to the EPA one of the most
prevalent of the listed contaminants is naturally occurring antimony. The maximum
contaminant level for antimony and nickel has been set at 0.006 mg/L and 0.1 mg/L
respectively.
A laboratory analysis of your household drinking water shows the antimony
concentration to be 4 ppb (parts per billion) and that of nickel to be 60 ppb.
Determine if the drinking water is safe with respect to the antimony and nickel levels.
Assume density of water to be 1.00 g/cm3
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Lecture 4, 2/18/2012
Chapter 4: Temperature
Objectives:
1. Define what temperature is.
2. Explain the difference between absolute and relative temperature.
3. Convert a temperature in any of the four common scales to any others.
4. Convert an expression involving units of temperature to other units of temperature.
5. Know the reference points for the temperature scales.
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Temperature
Temperature is a measure of the energy (mostly kinetic) of the
molecules in a system.
The most commonly used temperature scales are two based
on a relative scale, degrees Celsius (°C) and Fahrenheit (°F), and
two based on an absolute temperature scale, degrees Kelvin (K)
and Rankine (°R).
Relative scales are based on a specified reference temperature
(32 ̊F or 0 ̊C) that occurs in an ice-water mixture (the freezing
point of water).
Absolute scales are defined such that absolute zero has
a value of 0 (lowest temperature attainable in nature:
-273.15°C and -459.67°F).
The size of the degree is the same as the Celsius degree (Kelvin scale) or a Fahrenheit degree
(Rankine scale).
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Temperature Conversion
Temperatures expressed in one of these scales may be converted to equivalent
temperatures in another scale by using the following relationships.
Comparison of magnitudes of various temperature units:
°
1 Δ ̊C
1ΔK
1 Δ ̊F
1 Δ°R
1.8 Δ ̊F
1 Δ ̊C
1.8 Δ°R
1 ΔK
T (°K) = T (°C ) + 273.15
T (°R) = T (°F ) + 459.67
T (°R) = T (K ) * 1.8
T( F̊ ) = 1.8T ( C
̊ ) +32
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Test yourself: Temperature Conversion
Consider the interval from 20 ̊F to 80 F̊ .
Calculate the equivalent temperature in C
̊ and the interval between them.
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Example: Temperature Conversion
The specific heat capacity of toluene is given by following equation:
Cp = 20.869 + 5.293 × 10-2 T
where Cp is in Btu/(lb mol) (° F), and T is in ° F.
Express the equation in cal/(g mol) (K) with T in K.
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