FORMULAE SHEET
Chapter 4
General Balance Equation
ACCUMULATION=INPUT-OUTPUT+GENERATION-CONSUMPTION
Balance on Continuous Steady State Processes
INPUT+GENERATION =OUTPUT+CONSUMPTION
Limiting Reactant: A reactant is limiting if it is present in less than its stoichiometric proportion
relative to every other reactant.
n  ns
Fractional Excess: Fractional Excess =
,
where ns is the stoichiometric amount
ns
Percentage Excess:
Percentage Excess = 100 * Fractional Excess
moles reacted
f 
Fractional and Percentage Conversion:
, Percentage Conversion = f  100
moles fed
Moles of desired product formed
Yield:
YIELD=
Moles that would have been formed if there were no side
reactions and the lim iting reac tan t had reacted completely
Moles of desired product formed
Selectivity:
SELECTIVITY=
Moles of undesired product formed
Theoretical Oxygen: The moles (batch) or molar flow rate (continuous)of O2 needed for complete
combustion of all the fuel fed to the reactor, assuming that all carbon in the fuel is oxidized to CO 2
and all hydrogen is oxidized to H2O.
Theoretical Air: The quantity of air that contains the theoretical oxygen.
 (moles air ) fed  (moles air ) theoretica l 
  100%
Percent Excess Air: = 
(moles air ) theoretica l


Chapter 5

Ideal Gas Law
PV  nRT or
PV  RT
Gas Law Constant R=0.08206 L.atm/(mol.K) = 82.057 cm3.atm/(mol.K) = 8314.34 m3.Pa/(kmol.K)
Temperature: T(K)=T(C)+273.15, T(R)=T(F)+459.67, T(R)=1.8T(K), T(F)=1.8T(C)+32
1 K = 1 ºC = 1.8 ºR = 1.8 ºF
Standard Conditions:
Ts=273 K, Ps=1 atm, Vˆ s=22.4 L/mol
p AV  n A RT , V A  n A  y A , VA  VB    y A  y B V  V
Ideal Gas Mixtures
V
n
p
n
PVA  n A RT , A  A  y A , p A  pB    y A  y B P  P
P
n
P
Van der Waals equation:
RT
a
 2
Vˆ  b Vˆ
where a 
27 R 2Tc2
RT
, b c
64 Pc
8Pc
where P and Pc are in atm, T and Tc are in K, Vˆ is in L/mol, R = 0.08206 Latm/(molK).
P  RT V  b  a V V  b
SRK (Soave-Redlich-Kwong) Eq.




a  0.42747 R 2Tc2 Pc , b  0.08664 RTc Pc , m  0.48508  155171
.
  015613
.
2


  1  m 1  T TC

2
and  is the Pitzer Acentric Factor.
where P and Pc are in atm, T and Tc are in K, Vˆ is in L/mol, R = 0.08206 L.atm/(mol.K).

PV  znRT or PV  zRT
Compressibility Factor Equation of State:


VP
V
 c
Reduced Variables:
Tr  T T , Pr  P P , Vr 
c
c
RTc Pc RTc
Pseudocritical Constants for Hydrogen or Helium:
Tc adjusted  Tc  8 K , Pc adjusted  Pc  8 atm
1
Tc  ya Tca  yb Tcb  yc Tcc 
Pc  ya Pca  yb Pcb  yc Pcc 
 '  y a a  yb b  yc c  
Pseudocritical Temperature for a Gas Mixture:
Pseudocritical Pressure for a Gas Mixture :
Pitzer Acentric Factor () for a Gas Mixture
Chapter 6
Saturation Condition - Single Condensable Species:
pv  yv P  pv (T )
Superheated Condition - Single Condensable Species:
pv  yv P  pv (T )
pv  y v P  pv (Tdp )
Dew Point Condition when a Gas is Cooled at Constant Pressure:
Degrees of Superheat = T - Tdp
Relative Saturation (Relative Humidity):
RH or sr hr  
pv
pv
T 
 100%
p A  y A P  x A pA T 
B
log 10 p   A 
Antoine Equation:
where p* is the vapor pressure of a pure substance
T C
in mm Hg, T is temperature in C and A, B, and C are constants to be supplied.
Hˆ v
ln p   
 B where p* is the vapor pressure of a pure
Clausius-Clapeyron Equation:
RT
 H v is the energy required to vaporize one mole of liquid, T is the absolute
substance,
temperature, R is the gas constant.
The Phase Rule:
F = 2 + m -  where F is the number of degrees of freedom,  is the number of
phases, m is the number of chemical species in a system.
Raoult’s Law:
Conversion Factors
Length
Density
1 m (meter) = 100 cm = 3.2808 ft = 39.37 in
1 m (micrometer)= 10-6 m = 10-4 cm = 10-3 mm
1  (angstrom) = 10-10 m = 10-4 m
1 in = 2.540 cm
1 ft = 12 in
1 mile = 5280 ft
1 g/cm3 = 62.43 lbm/ft3 = 1000 kg/m3 =
8.345 lbm/U.S. gal
1 lbm/ft3 = 16.0185 kg/m3
Mass
1 lbm = 453.59 g = 0.45359 kg = 16 oz = 7000
grains
1 kg = 1000 g = 2.2046 lbm
1 ton (short) = 2000 lbm
1 ton (long) = 2240 lbm
1 ton (metric) = 1000 kg
Volume
1 L (liter) = 1 dm3 = 1000 cm3
1 in3 =16.387 cm3
1 ft3 =0.028317 m3 = 28.317 L (liter) = 7.481
U.S. gal
1 m3 = 1000 L (liter) = 264.17 U.S. gal
1 U.S. gal = 4 qt = 3.7854 L (liter) = 3785.4 cm3
1 British gal = 1.20094 U.S. gal
Pressure
1 Pa (pascal) = 1 N/m2
1 bar = 1  105 Pa
1 psia = 1 lbf/in2 = 6.89476103 Pa = 2.0360
in Hg at 0oC = 2.311 ft H2O at 70oF =
51.715 mm Hg at 0oC = 6.89476104
dyn/cm2 = 6.89476  104 g/cms2
1 atm = 14.696 psia = 1.01325105 Pa =
1.01325 bar = 760 mm Hg at 0oC =
29.921 in Hg at 0oC = 33.90 ft H2O at
4oC
1 dyn/cm2 = 2.0886  10-3 lbf/ft2
1 lbf/ft2=4.7880x 102 dyn/cm2=47.880 N/m2
Heat, Energy, Work
1 J (joule) = 1 N.m = 1 kgm2/s2 = = 023901 cal
= 9.48610-4 Btu = 0.7376 ft-lbf =
2.77810-7 kWh=107 gcm2/s2 (erg)
2