The reaction AC is first-order in the reactant A and is known to go to completio

Question

The reaction AC 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:

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

Explanation / Answer

for a first order reaction A->C

-dCA/dt= KCA= dCC/dt

Rate of formation of C is equal to rate of decomposition of A.

Since absorbance is proportional toconcentration

fro first order reaction ln (C/CO)= -kt

since all the A reacted, absorbance of C formed= 1.2=This is also the propotional to A consumed

For the first 10 minutes ln {(1.2-0.444)/1.2}= -k*10

k= 0.046sec-1

for half life =0.693/k =0.693/0.046=14.98 sec

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