Question

The reaction A→C is first-order in the reactant A and is known to go to completion. The product C is colored and absorbs light strongly at 550 nm, while the reactant and intermediates are colorless. A solution of A was prepared, and the absorbance of C at 550 nm was measured as a function of time. (Note that the absorbance of C is directly proportional to its concentration.)

Use the following data to determine the half-life of the reaction:

Time (s)	Absorbance
0	0.000
10	0.444
20	0.724
100	1.188
200	1.200
500	1.200

You don't need to do the math, but what equations/methods should I use to solve this?

Answer 1

As absorbance is directly proportional to concentration and given the reaction follows first order kinetics

So, first draw a Plot of ln (absorbance) vs time .

Find the the bestline linear equation .

Then the slope of the equation = - K

Where, K is rate constant .

Integrated rate law of first order equation is

ln[A] = ln [A]o - Kt ...(1)

Now, for first order reaction

Half life = (0.693/K) .....(2)

Using the calculated value of K half life can be calculated by Eq.2