Consider this reaction

Question

Consider this reaction:

2N₂O₅ (g) -> 2N₂O₄ (g) + O₂ (g)

At a certain temperature it obeys this rate law.

rate = (0.147 s^-1) [N₂O₅]

Suppose a vessel contains N₂O₅, at a concentration of 1.15M. Calculate the concentration of N₂O₅ in the vessel 8.30 seconds later. You may assume no other reaction is important.

Round your answer to 2 significant digits.

Answer 1

From the expression rate = 0.147 s^-1 [N₂O₅], we know the rate constant and we know the reaction is FIRST order with respect to [N₂O₅]. Knowing this, allows us to use the integrated rate law for a first order reaction to solve the problem.

Integrated rate law for 1st order reaction is

ln[A] = -kt + ln[A]_o

[A] = [A] @ time t = ?

k = rate constant = 0.147 s^-1

t = time = 8.30 s

[A]_o = initial [A] = 1.15 M

Solve for [A] ...

ln[A] = -(0.147s^-1)(8.30s) + ln[1.15]

lnA] = -1.22 + 0.14 = -1.08

[A] = 0.34 M

(be sure to check the math)