Chapter 8: Multiple Reactions

What Type of Reaction is Taking Place?


Three species were found in a CSTR. The following concentration data were obtained as a function of temperature. The initial concentration of the single reactant, A, was the same at all temperatures. Both B and C are products.

CA0 = 2moles/dm3

Run
T (oC)
CA (mole/dm3)
CB (mole/dm3)
CC (mole/dm3)
1
30
1.7
0.01
0.29
2
50
1.4

0.03

0.57
3
70
1.0
0.1
0.90
4
100
0.5
1.25
1.25
5
120
0.1
1.80
0.1
6
130
0.01
1.98
0.01

Explain the above data, what type of reaction is taking place, independent, complex, series or parallel ?

Hint 1: What are the trends?

Hint 2: What do the trends suggest?

Full Solution


 

 

 

 

 

 


Hint 1

Observations

At low temperatures

                        1)   Little conversion of A

                        2)   Little B formed

                        3)   Mostly C formed (but not too much because of the low conversion - 15 to 30% - of A)

At high temperatures

                        1)   Virtually complete conversion of A

                        2)   Mostly B formed

A graph with X on the y-axis and T on the x-axis. The graph shows a single blue curve that starts at a lower value and gradually increases over time.   

A graph with Ci on the y-axis and T on the x-axis, showing two curves labeled C_B and C_C. The blue curve (C_B) starts low and increases over time, while the pink curve (C_C) rises to a peak and then declines.
Back to Problem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hint 2

Data suggest 2 reactions

(1) \( A \xrightarrow{k_1} B \) \(-r_{1A} = k_1 C_A = C_A A_1 e^{-E_1 / RT} = r_B \)

(2) \( A \xrightarrow{k_2} C \) \(-r_{2A} = k_2 C_A = C_A A_2 e^{-E_2 / RT} = r_C \)

Back to Problem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Solution

Observations

At low temperatures

                        1)   Little conversion of A

                        2)   Little B formed

                        3)   Mostly C formed (but not too much because of the low conversion - 15 to 30% - of A)

At high temperatures

                        1)   Virtually complete conversion of A

                        2)   Mostly B formed

A graph with X on the y-axis and T on the x-axis. The graph shows a single blue curve that starts at a lower value and gradually increases over time.   

A graph with Ci on the y-axis and T on the x-axis, showing two curves labeled C_B and C_C. The blue curve (C_B) starts low and increases over time, while the pink curve (C_C) rises to a peak and then declines.

Data suggest 2 reactions

(1) \( A \xrightarrow{k_1} B \) \(-r_{1A} = k_1 C_A = C_A A_1 e^{-E_1 / RT} = r_B \)

(2) \( A \xrightarrow{k_2} C \) \(-r_{2A} = k_2 C_A = C_A A_2 e^{-E_2 / RT} = r_C \)

                            

Reaction (1) is dominant at high temperatures

\( k_1 = A_1 e^{-E_1 / RT} \)

with

\( k_2 \gg k_1 \) \( A_2 \gg A_1 \)

Reaction (2) is dominant at low temperatures

\( k_1 \gg k_2 \) \( E_1 > E_2 \)

\(-r_A = \left( k_1 + k_2 \right) C_A = \left( A_1 e^{-E_1 / RT} + A_2 e^{-E_2 / RT} \right) C_A \)


A graph with -r_A on the y-axis and T on the x-axis. The curve starts at a low value and increases upward in a nonlinear fashion.

A graph with ln(-r_A) on the y-axis and 1/T on the x-axis. The curve has two distinct linear regions with different slopes. The first segment, labeled 'A → B,' has a slope of E1, and the second segment, labeled 'A → C,' has a slope of E2.

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