Order of Reaction from Halflife times

[JwdePhysics]

Homework Statement

A -> Products
The two half-lives are 34 minutes and 68 minutes respectively. Find the order of the reaction.

So I and my friends are having disagreements over whether this is first order or second order or not.

Homework Equations

For first order half-life, t = 0.693/k
For second order half-life, t = 1/([A]₀k)

The Attempt at a Solution

I say it's first order because the first half life occurs at 34 minutes. Then the second half life occurs at 68 minutes (34 minutes after the first half-life). Therefore the half-life doesn't change and you would have a first-order half-life

My friends say it's second order because they interpret the problem as the second half-life occurring 68 minutes after the first half-life. And so if that were true, the half-life would double in time according to the second order half-life equation ([A]₀ would get cut in half from the first half life, doubling the entire right side of the equation and therefore doubling the time).

Who is right?

 

[Borek]

Looks like it is more about ambiguity and poor wording than about chemistry.

 

[mjc123]

Strictly speaking, the answer is second order. If the concentration has fallen to half the initial value after t1, and to a quarter after t2 (from the start), then the first half life is t1 and the second half life is (t2-t1). t2 is not a half life, but a quarter-life. So your friend is right, but I'm not sure the framer of the question was using language so precisely. I must admit I assumed it was first order on first reading the question.
(On a pedantic point of style, the half life is a length of time, not a point in time. So the first half life is 34 minutes, it does not "occur at" t = 34 minutes. This may be aiding the confusion.)