# equation

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```					ChE 416 – Midterm 2 – Formula Sheet

General Equations

wa / M A
xA                              where x = mole fraction, w = mass fraction, M = Molecular Weight
wa / M A  w B / M B

M  x a M A  x B M B where M is the average molecular weight, xA and xB are liquid or vapor mole fractions.

yA
kA               where k = distribution coefficient, y and x are mole fractions
xA

kA   y (1  x A )                                 AB x A
 AB        A                   or          yA                                 where is the relative volatility
k B (1  y A )( x A )                       1  ( AB  1) x A

Flash Distillation

F  L V          overall balance                               Fz  Lx  Vy component balance

Fh F  Lh L  VH V          energy balance

f V / F          fraction of feed vaporized                    q  L/F           fraction of liquid remaining

Binary Distillation
External balances:
column: overall: F  B  D                component: Fz  Bx B  Dx D                   energy: Fh F  Q R  QC  Dh D  Bh B

condenser:        overall: V1  L0  D                 energy: V1 H 1  QC  Dh D  L0 h0

Lo / D  R        reflux ratio

internal balances:
above feed (stage j): overall: V j 1  L j  D                           component: V j 1 y j 1  Dx D  L J x j
energy: V j 1 H j 1  QC  Dh D  L J h j

below feed (stage k): overall: V k  L k 1  B                           component: V k y k  Lk 1 x k 1  Bx B
energy: V k H k  Lk 1 hk 1  Bh B  Q R

Reboiler:         overall: V N 1  L N  B                               component: V N 1 y N 1  L N x N  Bx B
Energy: V N 1 H N 1  L N h N  Bh B  Q R

Feed stage:       overall: F  V  L  V  L                    component: Fz  V y f 1  Lx f 1  Vy f  L x f
Energy: Fhf  V H f 1  Lh f 1  VH f  L h f
L  L  qF and V  V  (1  q ) F
N equilibrium
Efficiency:   Eo 
N actual

Fenske Equations:

(x / x ) 
ln  A B Dist 
 (x A / xB ) R 
                                          where  AB   1 R 
1/ 2
Binary        N m in
ln  AB

       FR A Dist FR B Bott     
ln 
 1  FR  1  FR   

                             B Bot 

A Dist
multi-component:         N m in
ln  AB

 CB
N
FRC Dist
m in


FRB Bot
  CB
N

1  FRB Bot 
m in

Underwood Equations:

C
 i Fz i                       C    i Dxi , Dist
F (1  q )                             Vmin                                     Lmin  Vmin  D
i 1  i                          i 1  i  

Shira’s Equation

d i   i  1  d lk          i      d hk   
                                                    i   nk , hk     lk , hk
f i    1  f lk


   1

 f hk



```
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