Kinetics chemistry

Question

A substance decays with zero order kinetics. What is the half-life given a rate constant that is 0.737 M^-1s^-1 and an initial concentration of 1.75 M? How much of the substance remains after 22.5 seconds? 101 seconds?

( I also want to know that for the answers that i get for each seconds, is it supposed to be negative because the substance is decaying?)

Answer 1

for a zero order reaction A → products we have d[A]/dt = –k leading to

[A] = –kt + [A]₀ where t = time (in s) and k = the rate constant (in M/s)

The value of t when [A]/[A]₀ = ½ is called the half life of the reaction and is represented as t_½

The relationship between half life (t_½) and rate constant (k) can be found by writing the expression

½[A]₀ = –kt_½ + [A]₀ and solving for t_½

Adding kt_½ – ½[A]₀ to both sides gives kt_½ = [A]₀ – ½[A]₀ = ½[A]₀ which means that

t_½ = [A]₀/2k or k = [A]₀/2t_½

In the problem we're given a rate constant 0.737 M^-1s^-1

(The units are wrong here; they should be 0.737 M s^-1)

Question 1

What is the half-life given an initial concentration of 1.75 M?

t_½ = [A]₀/2k = (1.75)/(2 × 0.737) = 1.187 s

Question 2

How much of the substance remains after 22.5 seconds? 101 seconds?

[A] = –kt + [A]₀

The decay is linear, not exponential. After two half lives (2.374 s) all of the substance is gone. So for any time t ≥ 2.374 s, [A] = 0.

Answer

There is no substance left after 22.5 seconds.

There is no substance left after 101 seconds.

The Last Question

I also want to know that for the answers that i get for each seconds, is it supposed to be negative because the substance is decaying?

The concentration can't be negative. The lowest number possible for concentration is zero.