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Himmelblau Chapter 1: Problems: 1.10, 1.12, 1.20, 1.21, 1.23, 1.26

Assignment #1

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Lecture 3, 2/18/2012

Chapter 2: Moles, Density, and ConcentrationObjectives: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 areatoms 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 equivalentto 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 ofthe 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 (ofany 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 aremass/length3 (kg/m3, g/cm3, lbm/ft3).

Gases (vapors) are compressible; density changes with pressure andtemperature. Solids and liquids are incompressible; density is constant withpressure 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).

Vm

=ρ

mVV =

∧

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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 =

The reference commonly used for solids and liquids is water at 4°C, which has thefollowing density:

ρref = ρH2O(l)(4°C) = 1.000 g/cm3 = 1000 kg/m3 = 62.43 lbm/ft3

For gases: ρref = air at “standard conditions”

),(),(

refrefref

A

PTPT

ρρ

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API Gravity (Crude Oil)

5.131

..

5.141

60,

60,

−

=

Fwater

Ffluidgrsp

API

ρ

ρ

In the petroleum industry the specific gravity of petroleum products is often reported in term of a hydrometer scale called ⁰API.

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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 C̊ 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

)(•

n

Flow Rate ≡ the rate at which a material (gas, liquid or solid) is transported in a process stream.

mass flow rate : is the mass (m) transported through a line per unit time (t):

Volumetric flow rate (F): is the volume (V) transported through a line per unit time (t):

Molar flow : is the number of moles (n) of a substance transported through a line

per unit time (t):

where, the “dot” above the m and n refers to a flow rate.

tmm =

•

tVF =

)(•

m

tnn =

•

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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:

Mole fraction:

Mass (weight) percent and mole percent are the respective fractions times 100.

=

totallbA lbor

totalgA gor

totalkg

mass A of

m

mAkgtotalmassxA

=

mol lbA mol lbor

molA molor

kmol

moles A of Akmol

totalmolesyA

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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 12.0CO 6.0CH4 27.3H2 9.9N2 44.8Total 100.0

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Concentration

The concentration of a component of a mixture or solution is the quantity of thiscomponent 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 themixture (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 aretypically expressed in units of parts per million (ppm) or parts per billion (ppb). If yiis 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 C̊. 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 antimonyconcentration 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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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.

Lecture 4, 2/18/2012

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Temperature

Temperature is a measure of the energy (mostly kinetic) of themolecules in a system.

The most commonly used temperature scales are two basedon a relative scale, degrees Celsius (°C) and Fahrenheit (°F), andtwo 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 freezingpoint 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:

T (°K) = T (°C ) + 273.15

T (°R) = T (°F ) + 459.67

T (°R) = T (K ) * 1.8

T( F̊) = 1.8T ( ̊C) +32

1 Δ ̊C 1 Δ ̊F 1.8 Δ ̊F 1.8 Δ°R1 Δ K 1 Δ°R 1 Δ ̊C 1 ΔK

°

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Test yourself: Temperature Conversion

Consider the interval from 20 ̊F to 80 F̊.Calculate the equivalent temperature in C̊ and the interval between them.

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Example: Temperature ConversionThe 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.