Molar, Density, andConcentration

AE 205 Materials and Energy Balances

Asst. Prof. Dr. Tippabust Eksangsri

Molar (n)

Molecular Weight (MW)

• The atomic weight of an element is the mass of anatom based on the scale that assigned a mass ofexactly 12 to the carbon isotope 12C.

• The molecular weight of a compound is the sum ofthe weights of atoms of which the compoundcomposed.

• In SI, MW is presented in a unit of g/gmol.

• In British system, MW is presented in a unit oflbm/lbmol.

Example 1: Calculation of Molecular Weight

Recently, a superconductivity material in a formof YBa2Cu16O24 was invented. What is themolecular weight of the superconductor?

Given: The Periodical Table in the next slide

Periodical Table of Elements

Example 2:

Use molecular weight to convert moles to mass

How many pounds of NaOH are in 7.5 gmol of NaOH?

Given: MW of NaOH = 40.0 g/gmol

Density ()

Density of solution

Specific gravity (sp. gr.)

Example 3: Calculation of solution density

If you add 50 g of sugar to 500 mL of water, how do you

calculate the density of the sugar solution?

Given: Density of water = 1 g/mL

Flow Rate

Concentration

1. Mass (or weight) fraction & Mole fraction

n

ii

x1

1 and

n

ii

y1

1

Example 4: Calculation of the mass fraction

The microstructure of nanosized particles has proved to be important in

nanotechnology in developing economic magnetic performance of nano-

composites. In a ternary alloy such as Nd4.5Fe77B18.5 ,the average grain size is

about 30 nm. By replacing 0.2 atoms of Fe with atoms of Cu, the grain size can

be reduce to 17 nm.

(a) What is the molecular formula of the alloy after adding Cu to replace Fe?

(b) What is the mass fraction of each atomic species

Given information; Neodymium (Nd) has a MW of 144.24

Iron (Fe) has a MW of 55.85

Boron (B) has a MW of 10.81

Copper (Cu) has a MW of 63.55

Example 5:

Conversion between mass fraction and mole fraction

An industrial-strength drain cleaner contains 5.00 kg water

and 5.00 kg of NaOH. What are the mass fraction and mole

fraction of each component in the cleaner?

Example 6: Changing basis for calculation

A medium grade bituminous coal analyzes as follows:

The mole ratio of C and H in the residuum is 9. Calculate the mass fraction of

each component of the coal with ash and moisture-free basis.

Component % by mole

S 2

N 1

O 6

Ash 11

Water 3

Residuum (C & H) 77

Total 100

Concentration

2. ppm & ppb: The unit of ppm (parts per million) and ppb (parts per billion) are used to express concentrations of trace species. The definition may refer to mass ratio (for liquid and solid) or mole ratio (for gas).

For liquid & solid;

For gas;

solution g 10

solute 1gppm 1

6

solution g 10

solute 1gppb 1

9

solution gmol 10

solute 1gmolppm 1

6

solution gmol 10

solute 1gmolppb 1

9

Example 6: Use of ppm

The current OSHA 8-hour limit for HCN in air is 10.0 ppm.

A lethal dose of HCN in air is 300 mg/kg air at room

temperature.

5.1) How many mg HCN / kg air is 10.0 ppm?

5.2) What fraction of the lethal dose is 10.0 ppm?

* OSHA = Occupational Safety and Health Agency

Concentration

3. Other ways to express concentration

- Mass per unit volume; kg/m3, lb/ft3, g/L

- Mole per unit volume; gmol/cm3, gmol/L, lbmol/ft3

- Molarity

- Molality

- Normality

- etc.

Example 7: Calculation of concentration and flow rate

In the production of a drug having MW = 192, the exit

stream from the reactor flows at a rate of 10.5 L/min. The

drug concentration is 41.2% (in water), and the specific

gravity of the solution is 1.024.

Calculate the concentration of the drug (in kg/L) in the exit

stream, and the flow rate of the drug in kg mol/min.

Temperature and Pressure

AE 205 Materials and Energy Balances

Asst. Prof. Dr. Tippabust Eksangsri

The zeroth law of Thermodynamics

Two bodies are in thermal equilibrium if both have the same temperature reading even if they are not in contact.

Temperature ?

Freezing point (ice point) : a mixture of ice and water in equilibrium with saturated air at 1 atm

Boiling point (steam point) : a mixture of liquid water and water vapor in equilibrium at 1 atm

Temperature Scales

Absolute zero

Boiling point of water at 760 mm Hg

Freezing point of water at 760 mm Hg

180 scales

100 scales

212

32

[°F] [R] [K] [°C]

0

-40

492

672

460

420

373

273

255

233

0

100

-18

-40°F = °C

Thermodynamics Temperature Scales

• British System;Rankin scale (R)T (R) = T (F) + 459.67T (R) = T (°F)

• S.I. System;Kelvin scale (K)T (K) = T (C) + 273.15T (K) = T (°C)

• Conversion factors;T (°F) = 1.8 T (°C) + 32

Relative and Absolute Temperature

1. Relative temperature; based on relative scales andexpressed in degree Fahrenheit [°F] and degreeCelsius [°C]

2. Absolute temperature; based on absolutetemperature scales and expressed in Rankine [R]and Kelvin [K].

Example 8: Conversion of temperature unit

The heat capacity of sulfuric acid has the unit of

J/(gmol)(°C), and is given by the relation as shown below

Heat capacity = 139.1 + (1.56 x 10-1) T

Where T is expressed in [°C]. Modify the formula so that

the resulting expression has the associated units of

Btu/(lbmol)(R), with T expressed in [R].

Pressure

Pressure (P)Pressure is a force exerted by fluid per unit area

Or P = F/A

SI;

Unit of pressure is Pascal (1 Pa =N/m2)English; Unit of pressure is psi, (1 psi = 1lbf/in

2)

“Pressure in a fluid does not change in horizontal direction”

W

x

z

P1

P2

Assuming fluid density () is constant

0 zz maF

xPxPFz 12

When,

zxm

gaz

zgPPP 12 gageP

012 zxgxPxP

If fluid density () is a function of elevation, =fn(z)

W

x

z

P1

P2

From

012 zxgxPxP

Divide by xz, then taking the limit z --> 0

gdz

dP

2

1

gdzP

dz2

1

dW= xdz

Absolute pressure (Pa) actual pressure at a given position

Atmospheric pressure (Patm) local atmospheric pressure

Gauge pressure (Pgage) pressure read from measuring device

Pabs = Pgage + Patm

Definition of pressure

The Manometer measure Pg

1 2

hGAS

gasP

Assume;

Constant at any point

and

21 liqgas PP

1gasgas PP

ghPP liqliqgas 2

therefore

The Barometer

Atmospheric pressure (Barometric pressure) = weight of air above the location per unit surface area

Batm PP

A1

A2

A3

BBB

Wh gh

A

ghA

A

WPB

2

2

2

2

ghA

ghA

A

WPB

1

1

1

1

ghA

ghA

A

WPB

3

3

3

3

Standard atmosphere at 1 atm

• Pressure of 760 mm. height of mercury column(Hg = 13,595 kg/m3)

• Temperature of 0 C• Gravitational acceleration of 9.807 m/s2

1 atm = 760 torr

= 1.013x105 Pa

= 1.013 bars

= 14.696 psi

Standard atmospheric pressure:

Example 9: Calculation of pressure

Small animals such as mice can live at reduce air pressure

down to 20 kPa absolute. In a test, a mercury manometer

attached to a tank reads 64.5 cm. Hg and the barometer

reads 100 kPa. Will the mice survive?

Differential pressure measurement

• For a certain type of liquid (with constant density), the pressure is the same at any point lied on the same height.

• For gas at a constant temperature, its density can be considered constant. The gas pressure at every points in the same container is equal.

Example 10: Calculation of pressure difference

A differential manometer is used to determine the pressure

difference across the orifice plate. The flow rate was to be

calibrated with the observed pressure drop. Calculate the

pressure drop (P1 P2) in Pascals for the manometer

reading in the following figure.

Example 11: Calculation of gas pressure

Air flows through a duct under a draft of 4.0 cm H2O. The

barometer indicated the atmospheric pressure of 730 mm

Hg. What is the absolute pressure of the air in the unit of

inches of mercury?