The reaction A rightarrow B is carried out in a laboratory reactor. According to

Question

The reaction A rightarrow B is carried out in a laboratory reactor. According to a published article the concentration of A should vary with time as follows: C_A = C_AO exp(-kt) where C_AO is the initial concentration of A in the reactor and k is a constant. If C_A and C_AO are in lb-moles/ft^3 and t is in minutes, what are the units of k? The following data are taken for C_A(t): Verify the proposed rate law graphically (first determine what plot should yield a straight line), and calculate C_AO and k. Convert the formula with the calculated constants included to an expression for the molarity of A in the reaction mixture in terms of t (seconds). Calculate the molarity at t = 200 s.

Explanation / Answer

Given equation is

Where

andare in lb-moles/ft3

t is in min

Which can be rearranged to find the units of constant “k” as follows

Taking logarithm on both the sides

The units of constant “k” now can be found by simple dimensional analysis which states that dimensional units on the left hand side of the equation are the same as the dimensional units on the right hand side of the equation.

dimensional units on the right hand side of the equation are calculated by substituting relevant terms in equation

Which shows that the units of constant k are or

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