Page 222 - Modeling of Chemical Kinetics and Reactor Design

192 Modeling of Chemical Kinetics and Reactor Design

A B
Amount at t = 0 n n
AO BO
Amount at t = t n n
A B
Amounts that have reacted (n – n ) n – n
AO A B BO
and from stoichiometry 3(n AO − n A ) = (n − n BO ) . Total moles at
B
time t = n = n + 3( n AO − n ) + n BO , although n BO = 0. If the gas law
A
T
A
applies, then n = pV/RT, and at constant V and T:
P = p + ( 3 p AO − p )
T
A
A
= p + 3 p − 3 p
A AO A
P = 3 p − 2 p
T AO A
or

1 P )
p = (3 p −
A AO T
2
where P = total pressure
T
p = partial pressure of A (paraldehyde) at time t
A
p AO = partial pressure of A at time t = 0
Table 3-13 shows the relationship between the ratio of p /p AO versus
A
time t.
A plot of ln p /p AO against time t (Figure 3-23) gives a straight
A
line with the slope equal to the rate constant k . Therefore, the
1
assumed first order for the reaction is correct. The relationship between
the ratio of p /p AO versus time t is represented by the model equation
A
Y = Ae BX .
The computer program PROG1 determines the rate constant k from
1
the slope of Y = Ae BX . The constants for the equation are:

• A = 1.0082
• B = –0.47105
• Correlation Coefficient = 0.99972

The slope B = k . Therefore, the model equation Y = Ae BX is
1
–1
0.471 hr .