Green Chemical Engineering

185Homogeneous Reactors

The rate equation is

((,))−=rx TkC

AA

A

n

where k = k

0

e

−ΔE/RT

and C

A

= C

A0

(1 − x

A

)

Substituting appropriate terms into the heat balance Equation 3.221, we have

00

{}

+

{}

+− −

{}

=+

{}

QHVrxT

d

dt

MC T

RA

AP

()()((,))[]∆

(3.222)

where

M: mass hold of the reactor (kg)

C

P

mean specic heat (kJ/kg°C)

Rearranging Equation 3.222, we get

dT

dt

H

C

rx T

Q

MC

R

P

AA

P

=

−∆













−

()

+

()

(,)

ρ

(3.223)

The molal balance equation (or the design equation) for the batch reactor is

−=−

()

dC

dt

rx T

A

AA

(,)

which is written in terms of conversion x

A

as

−=

−

()

dx

dt

rx T

C

A

AA

A

(,)

0

(3.224)

Solving the rst-order differential Equations 3.223 and 3.224 simultaneously, we obtai ...