help please i need and explanation with answers

Question

The reaction, 2 N₂O(g) → 2 N₂(g) + O₂(g), has a rate constant equal to 0.76 s^-1 at 1000 K. How long will it take for the concentration of N₂O to decrease to 35% of its initial concentration?

Answer 1

Since the rate constant has units of s^-1, we can tell that it is a first order reaction. The integrated rate law for a first order reaction is [A] = [A]_oe^-kt and t_1/2 = 0.693/k

t_1/2 = 0.693/0.76 = 0.912 seconds

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

0.35 = 0.5ⁿ

log 0.35 = n log 0.5

n = 1.51 half lives

Time it takes = 1.51 half lives x 0.912 seconds/half life = 1.38 seconds