UNIT 1
UNITS AND DIMENSIONS
Unit is any measure or amount used as a standard for measurement. It is a means of the
measurable extent of a physical quantity. The derived unit is a combination of primary units.
The derived quantity is a combination of two or more primary dimensions. Their units are a
combination of primary units.
TABLE 1
PRIMARY DIMENSIONS AND UNITS IN DIFFERENT SYSTEM OF UNITS
Quantity
Units
Symbol
Dimension
FPS
MKS
CGS
FPS
CGS
CGS
Length
Foot
metre
centimeter
ft
m
cm
L
Mass
Pound
kilogram
Gram
lb
kg
g
M
Time
Second
second
Second
S
S
S
T
Temperature
Fahrenheit
Celsius
Celsius
0
F
0
C
0
C
K
TABLE 2
DERIVED UNITS IN SI
Quantity
Units (symbolic abbreviation in bracket)
Dimension
SI
MKS/CGS
FPS
(based on
SI)
Area
square metre
(m2)
square centimetre
(cm2)
square feet (ft2)
L2
Volume
cubic metre
(m3)
cubic centimetre
(cm3), litre (L)
cubic feet (ft3)
L3
Density
kilograms per
cubic metre
grams per cubic
centimetre (g cm-3)
pounds per cubic
foot (lb ft -3)
ML-3
grams per second
pounds per hour
MT-1
(g s-1)
(lb h-1)
(kg m-3)
Mass flow
rate
Quantity
kilogram per
second (kg s-1)
Units (symbolic abbreviation in bracket)
Dimension
(based on SI)
SI
MKS/CGS
FPS
Molar flow
rate
moles per second (mol s-1)
moles per second
(mol s-1)
pounds per hour (lb
h-1)
nT-1
Volumetric
flow rate
cubic metres per second
cubic
centimetres per
second (cm3 s-1) ,
litre per second
(L s-1)
cubic feet per hour
L3T-1
(m3 s-1)
(ft3 h-1)
Mass flux
moles per square metre per
second
(mol s-1 m-2)
moles per square
metre per second
(mol s-1 m-2)
pound moles per
hour per square
foot (lb-mol h-1 ft-2)
nT-1L-2
Force
newton (N)
kilogram-force
(kgf )
pound force (lbf)
MLT-2
Pressure
newton per square metre or
pascal (N m-2 or Pa)
kilogram force
per square
centimetre (kgf
cm-2)
pound force per
square foot (lb ft-2)
ML-1T-2
Quantity
Units (symbolic abbreviation in bracket)
Dimension
(based on SI)
Energy
SI
MKS/CGS
FPS
joule (j)
metre kilogram force
foot pound force (ft
lbf)
ML2T-2
(m kgf)
Power
watts or joules per
second (W or J s-1)
horse power (HP)
foot pound force per
second (ft lb s-1)
ML2T-3
Heat,
Enthalpy
Joules (J ) British
kilocalories (Kcal )
Thermal Unit (Btu)
ML2T-2
Heat capacity
joules per
kilogram per
degree kelvin (J
kg-1 K-1)
kilocalories per
kilogram per degree
celsius (kcal kg-1 0C-1)
Btu per pound per
degree Fahrenheit
(Btu lb-1 0F-1)
L2T-2K-1
Molar heat
capacity
Joules per mole
per degree kelvin
(J mol-1 K-1)
Kilocalories per mole
per degree celsius
(kcal mol-1 0C-1)
Btu per pound per
degree Farenheit
ML2T-2K-1N-1
joules per square
metre per second
(J s-1 m-2 W m-2 )
kilocalories per hour
per square metre
(kcal h-1 m-2)
Btu per hour per
square foot (Btu h-1
ft-2)
Heat flux
(Btu lb mol-1 0F-1)
MT-3
Conversion factors
1) Length: 1ft = 12 inches
1 inch = 2.54 cm, 1ft = 30.48 cm, 1 yard= 36 inch = 3 feet, 1 mile=1.609
km
2) Mass: 1 kg = 1000 g,
1 lb = 453.59 g = 0.45359 kg
1 ton = 1000 kg
3) Temperature: K= °C+ 273
°C= 5/9 (°F-32)
°R = °F + 460
4) Pressure: 1 bar = 1x105 N/m2 = 750 mmHg
1 N/m2 = 1 Pa
1atm = 1.01325 x 105 N/m2 = 760 mmHg = 33.91ft water = 14.696 psi =
29.92 inches Hg
1 mm Hg = 1 torr
5) Force: 1 kgf = 9.806 N
6) Energy: 1 calorie =4.184 J
1 Btu = 252 calorie
1 J = 1 kgm2/s2 = 107 erg
1 Btu =1055 J
7) Volume: 1cc = 1 ml
1 L = 1000 cc
8) Power: 1 Hp = 745.7 W. 1W = 1J/s. 1 W = 1 N.m
9) Density: 1 g/cc = 1000 kg/m3 = 1 kg/L
Value of Universal gas constant
R= 8.314 J/(gmol.K)
= 1.987 (cal/gmol.K)
= 0.082 atm.L/(gmol.K)
= 8.314 m3Pa/(gmol.K)
= 8.314 m3KPa/(kgmol.K)
Temperature scale:
1) ∆°C= ∆°R
2) ∆°C= ∆K
3)
∆°C =1.8 ∆°F
4)
∆°K =1.8 ∆°R
Pressure scale:
1) Absolute pressure = gauge pressure + atmospheric pressure
2) Absolute pressure = gauge pressure + barometric pressure
3) Absolute pressure = atmospheric pressure – vacuum pressure
UNIT 2
GRAM ATOM
Used to specify the amounts of chemical elements. It is defined as the mass in grams of an
element which is equal numerically to its atomic weight.
gram atoms of an element =
wt . in grams
− − − − − − − (1)
atomic weight
Similarly, the mass in kilograms of a given element that is numerically equal to its atomic
weight is called a kilogram-atom.
Similarly, kilogram atoms of element
kg atoms of an element =
wt .in kg
− − − − − − − (2)
atomic weight
For chemical compounds, a mole is defined as the amount of substance equal to its molecular
weight / formula weight.
GRAM MOLE
Used to specify the amount of chemical compounds.It is defined as the mass in grams of
substance that is equal numerically to its molecular weight.
gmoles of compound
=
wt .in g
− − − − − − − (3)
molecular weight
Gram mole of a substance is the mass in grams of the substance that is numerically equal to its
molecular weight.
Similarly,
kgmoles
of compound
=
wt .in kg
molecular weight
− − − − − − − (4)
Mole is defined as the amount of substance equal to its molecular weight.
(1) Calculate the kilogram atoms of carbon which weighs 36 kg
Solution: 36 kg carbon
Atomic weight of carbon = 12
katom of carbon =
wt .in kg
36
=
=3
atomic weight of carbon
12
(2) Calculate the kilograms of ‘Na’ of which the amount is specified as 3 katom.
Solution: 3 katom Na
Atomic weight of Na = 23
katom of Na =
wt .in kg of Na
atomic weight of Na
∴ Kg of Na = katom of Na x Atomic weight of Na = 3 x 23 = 69
(3) How many kilograms of ethane are there in 210 kmol?
Solution: Basis: 210 kmol ethane.
Atomic weights: C=12, H=1, Chemical formula of ethane = C2H6
Molecular weight of ethane = 2x12+1x6 = 30
kmol of C 2 H 6 =
wt .in kg of C 2 H 6
mol . weight of C 2 H 6
∴ kg of ethane (C2H6) = kmol of ethane x Molecular weight of ethane = 210 x 30 =
6300 kg
∴ 210 kmol of ethane = 6300 kg ethane
(4) Convert 88 kg of carbon dioxide into its amount in molar units.
Solution: Basis: 88 kg of carbon dioxide
Molecular formula of carbon dioxide = CO2
Atomic weights: C=12, O=16
Molecular weight of CO2 = (1x12) + (2x16) = 44
kmol of CO 2 =
88 g of CO2 = 2 kmol CO2
wt .in kg of C O 2
88
=
= 2
mol . weight of CO 2 44
(5) Find the moles of oxygen present in 500 grams
Solution: Basis: 500 g of oxygen
Molecular weight of O2 = 2 x 16 = 32
kmoles
of O 2 =
500
= 15 . 625
32
(6) Convert 499 g of CuSO4.5H2O into moles.
Solution: Basis: 499 g of CuSO4.5H2O
Atomic weights: Cu=63.5, S=32, O= 16 and H = 1
Molecular weight of CuSO4.5H2O
= (1x63.5)+(1x32)+(4x16)+5(2x1+1x16) = 249.5
Moles of CuSO4.5H2O = 499 = 2 mol
249.5
kmoles of CuSO 4 .5H 2 O =
499
= 2
249 . 5
The relationship of a compound and its constituents is given for some compounds as follows:
Each mole of NaOH contains one atom of Na
1 mol of NaOH≡ 1 atom of Na ≡ 1 atom of H
Each mole of NaOH contains 1 atom of Na. The sign ≡ refers to ‘equivalent to’ and not ‘equal
to’.
Similarly for H2SO4 and ‘S’
1 mol of H2SO4 = 1 atom of S (atom is written for gram-atom).
1 mol of H2SO4 = 1 atom of S (atom is written for gram-atom)
1 kmol of H2SO4 = 1 katom of S (katom is written for kilogram-atom)
i.e., each mole of H2SO4 contains 1 atom of S.
For CuSO4.5H2O and CuSO4
1 mol of CuSO4.5H2O ≡ 1 mol CuSO4
1 kmol of CuSO4 . 5H2O ≡ 1 kmol of CuSO4
(7) How many kmoles of H2SO4 will contain 64 kg S
Solution: Basis: 64 kg of S
Atomic weight of S = 32
atoms
of S =
kg of S
64
=
= 2
katom
32
Each moles of H2SO4 contains one atom of S.
1 kmol of H2SO4≡ 1 katom of S
moles of H 2 SO 4 =
1
x 2 = 2 kmol
1
(8) Find kmoles of K2CO3 that will contain 117 kg of K?
Solution: Basis: 117 kg of K
Atomic weight of K = 39
atoms of K =
117
= 3 katom
39
Each mole of K2CO3 contains 2 atom of K
2 atom of K ≡ 1 mole of K2CO3
2 katom of K ≡ a kmol of K2CO3
moles
of K 2 CO 3 =
1
x 3 = 1 . 5 kmol
2
(9) How many kilograms of carbon are present in 64 kg of methane?
Solution: Basis: 64 kg of methane
Atomic weight of C = 12
Molecular weight of CH4 = 16
1 katom of carbon ≡ 1 kmol of CH4
∴ 12 kg of carbon ≡ 16 kg of CH4
i.e., in 16 kg of CH4, 12 kg of carbon are present.
So amount of carbon present in 64 kg of methane = 12 x 64 = 48
16
(10) Find equivalent moles of Na2SO4 in 644 kg of Na2SO4.10H2O crystals
Solution: Basis: 644 kg of Na2SO4.10H2O crystals
Molecular weight of Na2SO4 = 2x23+1x32+4x16 = 142
Molecular weight of Na2SO4.10H2O
= (2x23)+1x32+4x16+10 (2x1+1x16) = 322
moles of Na 2 SO 4 .10H 2 O =
644
= 2 mol
322
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