8. The half-life of a reaction was found to be inversely dependent on the concentration of the starting material. Thus, we can say that

a. the reaction is zero order b.the reaction is first order
c.the reaction is second order

d. the reaction starts out first order and changes to second order after one half-life.

e. the reaction starts out second order and changes to first order after one half-life.

I think that the answer is the reaction is second order. Is this correct?

Here are the equations for half life for

order 0, order 1, and order 2. I didn't include order 3 because those reactions are not very common.
zero order:
half life = (Ao)/2ak

1st order:
half life = ln 2/ak

2nd order:
half life = 1/ak(Ao)

note: a and k are constants.l (Ao) is starting material concn.

You are right; it is second order. That is the only one for which the starting material is inversely dependent on the starting material, (Ao).

To determine the order of a reaction, we need to analyze the relationship between the reaction rate and the concentration of the starting material. In this case, the given information states that the half-life of the reaction is inversely dependent on the concentration of the starting material.

The half-life of a reaction refers to the time it takes for the concentration of the reactant to decrease by half. So, if the half-life is inversely proportional to the concentration of the starting material, it means that as the concentration of the starting material decreases, the half-life increases.

By observing this relationship, we can conclude that the reaction is first order. In a first-order reaction, the half-life is inversely proportional to the concentration of the reactant. As the concentration decreases, the half-life increases.

Therefore, the correct answer is b. the reaction is first order.