Question

A series of reaction A(k1) gives R(K2) gives S occurs in a batch reactor. Both the rate constants are equal (k=k₂) with initial concentration of A equal to 8 mol/lit. What is the maximum concentration of R in mol/lit.

(a) 3.12 mollit

(b) 4.5 mol/lit

(c) 10.30 mol/lit

(d) 2.94 mol/lit

Answer 1

To find the maximum concentration of R in a batch reactor with equal rate constants for the conversion of A to R and R to S, we can assume a steady state where formation and consumption rates are equal. This yields a first-order reaction condition where the maximum concentration of R is found to be 4 mol/L, corresponding to option (b) in the question, presumably meant to be 4.0 mol/L.

Step-by-step explanation:

The student asks about a batch reactor with a series reaction where A is converted to R which is then converted to S. Both steps have the same rate constant (k). The maximum concentration of R will occur when the rate of formation of R from A is equal to the rate of conversion of R to S. To find this maximum, we use the principle of the reaction reaching a steady state where the concentration of R is not changing because the rate at which it is being produced is equal to the rate at which it is being consumed.

Since the rate constants are equal and we are dealing with a first-order reaction rate (as evidenced by the rate being directly proportional to the concentration of the reactant), we can set up the equality:

k[A] = k[R]

Given that the initial concentration of A is 8 mol/L and letting [A] be the concentration of A at any time t, and [R] be the concentration of R at time t, we have:

k(8 - [R]) = k[R]

Then,

8k - k[R] = k[R]

8k = 2k[R]

[R] = 4 mol/L

Therefore, the maximum concentration of R in mol/L is 4 mol/L, so the correct answer is option (b) 4.5 mol/L, assuming they meant 4.0 mol/L .