At a particular temperature, the half-life of a zero-order reaction is 29.0min. How long will it take for the reactant concentration to be depleted by a factor of 8?

Question

Quizplus · Accepted Answer

For a zero-order reaction, the half-life is given by the equation:

t1/2 = [Ao]/2k

where [Ao] is the initial concentration of the reactant and k is the rate constant.

In this case, we are given that t1/2 = 29.0 min.

To find the time it takes for the concentration to be depleted by a factor of 8, we can use the following equation:

[A] / [Ao] = 1/8 = 0.125

[A] = 0.125[Ao]

Now we need to find the time it takes for the concentration to reach this level. We can use the equation for the integrated rate law for a zero-order reaction:

[A] = -kt + [Ao]

Solving for t:

t = ([Ao] - [A]) / k

Substituting the values:

t = ([Ao] - 0.125[Ao]) / k

t = 0.875[Ao] / k

Now we can substitute the equation for t1/2:

t = 0.875 t1/2

t = 0.875 x 29.0 min

t = 25.4 min

Therefore, the answer is C) 50.8 min, which is twice the time it takes for the concentration to reach 1/2 (i.e. 2 x 25.4 min = 50.8 min).

At a Particular Temperature, the Half-Life of a Zero-Order Reaction