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Process Variables
To design or analyze a process, we need to know the
amounts, compositions, and condition of materials
entering, leaving, and within the process.
The quantities used to describe a process are called
process variables. These must be measured or
computed.
In this class we will be concerned with a number of
process variables, including:
y Mass and Volume
y Flow Rate
y Chemical Composition
y Pressure
y Temperature
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MASSAND VOLUME
Density
Density is the mass per unit volume of a substance
kg/m3,g/cm3, lbm/ft3 (symbolized by the Greek letterV)
Density relates mass and volume of a substance.
density = (mass)/(volume) m =V V
EXAMPLE:Determine the mass of 200 cm3
ofCCl4and the volume (in cm
3) of 6.20 lbm ofCCl4
(=1 595kg/m3)
Gas/vapor densities depend heavily on Pressure and
Temperature -V(P,T). Liquid and solid densities cannormally be looked up in a table.
Densities of pure solids
and liquids also vary
when pressure and
temperature change, butmuch less.
Solid and liquid densities
are often treated as
constants.
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In most applications assume the density of water as
1.0 g/cm3- strictly true only for a specific temperature.
Specific Volume
The specific volume of a substance is the volume perunit mass, the reciprocal of the density.
Specific Gravity
The specific gravity is the ratio of the density of a
substance to that of a reference substance. - a dimensionless quantity.Usually reference for solids and liquids is water at 4
oC
V = 1.000 g/cm3
= 1 000 kg/m3
= 62.43 lbm/ft3
For gases usual reference density is air.
Since density varies with temperature- specify the
temperatures involved:
e.g.
this means "the specific gravity of the substance at
20oC is 0.73 times that of water at 4
oC".
In CGS the numerical values of the density and s.g.
are the same
s.g. = 0.6 = 0.6 g/cm3
1V
!
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EXAMPLE: If dibromopentane has a sg of 1.57, what
is the density in a) g/cm3
b) lbm/ft3
c) kg/m3
EXAMPLE:A drum contains 8.00 liters of toluene.
What is the mass of the liquid?
EXAMPLE:A drum 700 lbm of a liquid mixture of
benzene and toluene. The density of the mixture is
measured to be 0.850 g/ml. Estimate the mass andvolumes of the two hydrocarbons in the drum
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Flow Rates
Expressed as
y the mass flow rate, , mass per unit timey the molarflow rate, , moles per unit timey the volumetric flow rate, , volume per unit time
m = mass kg
n = moles kg V = volume m
3
volumetric flow rate can be converted to mass flow
rate by using the density:
Vm V!
Most industrial flow measurement devices measure
the flow velocity. The volumetric flow rate is then
calculated from the velocity and the cross-sectionalarea of the pipe:
vAV !
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Chemical Composition
Moles
AMole is a measure of the number of particles(6.02x10
23) or quantity of substance.
Agram-mole (mol, gmol) of a substance is the amount
of a substance that contains as many elementary
entities as there are atoms in 0.012 kg of carbon 12.
A substance whose mass in grams is numerically the
same as its molecular (or atomic) weight contains
6.02x1023
particles and thus equates to one mole of the
substance.
Carbon Dioxide has a molecular weight of 44, so
1 mol ofCO2 contains 44 grams and 6.02x1023
molecules ofCO2
EXAMPLE:1.505x10
24
molecules of a substance has amass of 34.5 grams. What is the molecular weight of
the substance?
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Kilogram-moles (kgmol) andpound-moles (lbmol,
mole) are also used. These are defined the same way
but using different mass units.
1 gmol ofCO contains grams1 lbmol ofCOcontains grams
Ifthe molecular weightofa substance is M,then there
are Mgrams pergram-mole. This means you can use
the molecular weight as a conversion factor for goingfrom mass to moles.
EXAMPLE: How many a) lb moles and b) gmol in
2.00 pounds ofNaOH?
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Use the same conversion factors for the different units
of mole as for converting mass units
(1 lbmole = 454 g-mole, etc.).
The molecular weight is used to convert from mass tomoles, so it is logical that it is also used to convert
between mass and molar flow rates:
MW
mn
!
Most material streams in process units are mixtures of
compounds. Composition of streams can be described
in various ways.
Composition Fractions
Composition fractions can be based on mass (x) or on
moles (y).
mass fractionxi
Ax or or
!
mole fraction yi
Ay or or
!
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Convert from "fraction" to "percent" by multiplying
by 100.
The units of mass measurement used don't make a
difference, as long as the top and bottom of the ratiouse the same units:
0.25 0.25 0.25 0.25
Ax etc! ! ! ! !
EXAMPLE:A stream contains 20 g of oxygen gas, 70
g of nitrogen, 5 g of helium, and 5 g of hydrogen.
Find the mass and mole fractions and the mass and
mole percent compositions.
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Parts per Million (PPM) and
Parts per Billion (PPB)
A concentration unit often seen in environmental
usage isparts permillion orppm. For solids andliquids it is the grams of solute in 1 million grams of
solution. For gases it is the number of particles
(moles). PPM (or ppb) is a special kind of mass (or
mass) fraction
Used to express the concentration oftrace species
Signifies how many parts (grams, moles) of the
species are present per million or billion parts (grams,
moles) of the mixture.
Parts perMillion (ppm) = xA*106 or yA*106Parts per Billion (ppb) = xA*10
9or yA*10
9
EXAMPLE: The current OSHA 8 hour limit for HCN
in air is 10.0 ppm. Convert to mg HCN/kg air
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Given a mass composition in percentorfraction form
convertto molar composition or vice-versa
assume a basis of 1 kg, 100 mol, etc.
E.G.:Air is 78 mole% nitrogen, 21 mole% oxygen,and 1 mole% argon. What is its mass composition?
Basis:
Component moles mol wt mass mass fraction
The Average MolecularWeightof a mixture is
computed from the molar composition and the
molecular weight. It is a weighted average -- themolecular weights are averaged using the mole
fractions as weights.
!!compnentsall
iiMyMyMyM -
1111
and, using mass fractions
!!componentsall
i
i
Mx
Mx
Mx
M.
2
2
1
11
EXAMPLE:Calculate the average molecular weight of
air.
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Do NOT try to calculate average densities or average
specific gravities using a weighted arithmetic mean,
use a weighted harmonic mean.
Concentration
composition and concentration used interchangeably.
Concentration is based on volume and is one way of
expressing composition. The mass concentration is
the mass of a component per unit volume, similarly
molar concentration is the moles per unit volume.
The following are some ways to expressconcentration, where the numerator signifies the solute
and the denominator signifies the solution.
Mass Concentration: g/cm3, lbm/ft
3, kg/in
3
MolarConcentration: kmol/m3, lb-mol/ft
3, g-mol/L
The last molar concentration listed, g-mol/L is the
Molarity of the solute in the mixture.
Molarity of component A, MA = g-molA/Ltotal
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