he decomposition of acetaldehyde, CH3CHO, was determined to be a second order reaction with a rate constant of 0.0771 M-1 s-1. If the initial concentration of acetaldehyde is 0.358 M, what will the concentration be after selected reaction times

The concentration is [-1 + sqrt (1+0.11t) ]/0.1542 M

Explanation:

Let the concentration of CH3CHO after selected reaction times be y

Rate = Ky^2 = change in concentration of CH3CHO/time

K = 0.0771 M^-1 s^-1

Change in concentration of CH3CHO = 0.358 - y

0.0771y^2 = 0.358-y/t

0.0771ty^2 = 0.358 - y

0.0771ty^2 + y - 0.358 = 0

The value of y must be positive and is obtained in terms of t using the quadratic formula

y = [-1 + sqrt (1^2 - 4 (0.0771t) (-0.358) ]/2 (0.0771) = [-1 + sqrt (1+0.11t) ]/0.1542 M