Question

The rate constant for a given reaction is k = 0.312 m⁻¹s⁻¹. If the initial concentration of reactant is 1.00 M, then what is the length of the third half-life (in seconds)?

a. 2.22 s
b. 4.44 s
c. 6.66 s
d. 8.88 s

Answer 1

To calculate the length of the third half-life for a second-order reaction with rate constant k = 0.312 m⁻¹s⁻¹ and initial concentration 1.00 M, you use the formula for second-order reactions. The result for the third half-life, starting with a concentration of 0.25 M, is 12.82 seconds.

Step-by-step explanation:

The question deals with a second-order reaction, where the rate constant (k) is given, and you're asked to calculate the length of the third half-life.

For second-order reactions, the formula for the half-life (t1/2) is t1/2 = 1 / (k x [A]), where [A] is the concentration of the reactant at the beginning of the half-life period. Unlike first-order reactions, the half-life of a second-order reaction depends on the initial concentration and changes over time as the concentration decreases.

For the first half-life, the initial concentration is 1 M, so t1/2 = 1 / (0.312 x 1) = 3.205 s.

For the second half-life, the concentration starts at 0.5 M, so t1/2 = 1 / (0.312 x 0.5) = 6.41 s.

Therefore, for the third half-life, the starting concentration is 0.25 M, so t1/2 = 1 / (0.312 x 0.25) = 12.82 s.