Chapter 2 (additional) Molar density and concentration.pdf
Transcript of Chapter 2 (additional) Molar density and concentration.pdf
Molar, Density, andConcentration
AE 205 Materials and Energy Balances
Asst. Prof. Dr. Tippabust Eksangsri
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
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
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
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.
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.