Question

The following reactions take place in a batch reactor:

A+B--> C (desired product)

B+C-->D (hazardous product)

As the reaction proceeds, D builds up in the reactor and could cause an explosion if its concentration exceeds 15 mol/L. To ensure the safety of the plant personnel, the reaction is quenched (e.g., by cooling the reactor contents to a low temperature) and the products are extracted when the concentration of D reaches 10mol/L.

The concentration of C is measured in real-time, and samples are periodically taken and analyzed to determine the concentration of D. The data are shown below:

Cc (mol/L)	Cd (mol/L)
2.8	1.4
10	2.27
20	2.95
40	3.84
70	4.74
110	5.63
160	6.49
220	7.32

(a) What would be the general form of an expression for Cd as a function of Cc?(a) Calculate the natural logarithms of these two variables

(b) Plot using the values calculated in (a), then derive the expression that relate these two variables.

(c) At what concentration of C is the reactor stopped?

(d) Someone proposed not stopping the reaction until Cd=13 mol/L, and someone else strongly objected. What would be the major arguements for and against that proposal?

Please a step by step answer would be appreciated!

Answer 1

(a)

From the data above, we can deduce that D is in function of C as follows:

To confirm this, we can plot [D] vs. [C]

(b)

(c)

The next one is a plot of ln [D] vs. ln [C]

If unable to use a program to find out the equation, you could always use the old-school method. First we can calculate the slope. Consider 'y' as ln[D] and 'x' as ln [C].

Then it is possible to know the intercept with y axis using any x and y pair of values.

Then,

Please note a slight difference in b value, due to the use of less decimal values.

(d)

Reaction stops when [D] = 10 mol/L. Therefore,

(e)

When [D] = 13 mol/L,

The main argument for raising the limit of D in reactor from 10 M to 13 M is that the production of C will be doubled; against this point of view is the closeness between the explosion line with this new limit; if the reactor is unable to cool for a given situation, the risk of explosion is way higher.