Chemistry MATH question 2

Question

The first-order decomposition of N₂O₅ at 328 K has a rate constant of 1.70 × 10^-3 s^-1. If the initial concentration of N₂O₅ is 2.88 M, what is the concentration of N₂O₅ after 12.5 minutes?

Answer 1

First order decay has a half life = 0.693/k

So, we will first have to find the half life, i.e. t_1/2

t_1/2 = 0.693/1.70x10^-3 s^-1

t_1/2 = 407.6 s

To find the fraction remaining, we can use

Fraction remaining = 0.5ⁿ where n = the number of half lives that have elapsed.

12.5 minutes x 60 seconds/min = 750 s

750 s x 1 half life/407.6 s = 1.84 half lives have elapsed

Fraction remaining = 0.5^1.84 = 0.279

Concentration remaining = 2.88 M x 0.279 = 0.804 M