At a certain temperature this reaction follows first-order kinetics with a rate constant of 0.00285 s^-1: 2Cl_2 O_5 (g) rightarrow 2Cl_2 (g) + 5O_2 (g) Suppose a vessel contains Cl_2 O_5 at a concentration of 0.640 M. Calculate the concentration of Cl_2 O_5 in the vessel 280. seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits.

0.13 M

Explanation:

The rate of a reaction indicates how much of the reagent is disappearing along the time, so for a single reagent reaction:

rate = k*[reagent]ⁿ

Where k is the rate constant, [reagent] is the initial concentration of the reagent, and n the order of the reaction, which is measured experimentally. Thus, for a first-order reaction n = 1.

rate = 0.00285*0.640

rate = 1.824x10⁻³ M/s

It means that at each second, the concentration drops 1.824x10⁻³ M. So, the rate is also the concentration variation divided by time. Because the concentration is decreasing, the expression has a minus signal:

rate = - Δ[reagent]/t

1.824x10⁻³ = - ([reagent] - 0.640) / 280

- ([reagent] - 0.640) = 0.511

- [reagent] + 0.640 = 0.511

[reagent] = 0.129 M

Rouded to 2 significant digits, [reagent] = 0.13 M