He second-order decomposition of hi has a rate constant of 1.80 x 10-3 m-1s-1. how much hi remains after 27.3 s if the initial concentration of hi is 4.78 m?

a. 4.55 m

b. 0.258 m

c. 3.87 m

d. 2.20 m

e. 2.39 m

c. 3.87 M. After 27.3 s, the concentration of the remaining HI is 3.87 M

Whenever a question asks you, "How long to reach a certain concentration?", you must use the appropriate integrated rate law expression.

The integrated rate law for a second-order reaction is

1/[A]t = 1/[A]0 + kt

where

• [A]t = the concentration of A at time t

• [A]0 = the concentration of A at time 0 (i. e., at the beginning of the reaction)

• k = the rate constant for the reaction

1/[A]t = 1 / (4.78 M) + 1.80 * 10^ (-3) M·s^ (-1) x 27.3 s

= 0.2092 M^ (-1) + 0.04914 M^ (-1) = 0.2583 M^ (-1)

[A]t = 1/[0.2583 M^ (-1) ] = 3.87 M