Solve 2nd Order Reaction Kinetics: Mn(CO)sub5 → Mnsub2 (CO)sub10

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Homework Statement

The second order reaction 2Mn(CO)sub5 → Mnsub2 (CO)sub10 has a rate constant equal to
3.0 *10^9 M^-1s^-1 at 25oC. If the initial concentration for Mn(CO)sub5 is 1.0 * 10^-5 M, how long will it take for 90% of the reactant to disappear?

Homework Equations

Rate Law = k*[Mn(CO)sub5]

The Attempt at a Solution

Not sure what they want me to do here? If its a half life thing I understand, but it is not stated anywhere in the problem and I assume we're not expected to know such things. I can find the rate most certainly, and the units would be what they are, but how exactly do I relate such things in an equation to find how long it would take for 90% of the reaction to disappear? Can someone point me in the right direction? I have work for the day so I won't have as much time as I'd like to work it out, but if someone could just give me a nudge I'd be fine! Thanks.

 

[epenguin]

Homework Statement

The second order reaction 2Mn(CO)sub5 → Mnsub2 (CO)sub10 has a rate constant equal to
3.0 *10^9 M^-1s^-1 at 25oC. If the initial concentration for Mn(CO)sub5 is 1.0 * 10^-5 M, how long will it take for 90% of the reactant to disappear?

Homework Equations

Rate Law = k*[Mn(CO)sub5]

The Attempt at a Solution

Not sure what they want me to do here? If its a half life thing I understand, but it is not stated anywhere in the problem and I assume we're not expected to know such things. I can find the rate most certainly, and the units would be what they are, but how exactly do I relate such things in an equation to find how long it would take for 90% of the reaction to disappear? Can someone point me in the right direction? I have work for the day so I won't have as much time as I'd like to work it out, but if someone could just give me a nudge I'd be fine! Thanks.

Looks like you've stated the wrong rate law.
For that reaction what is the most plausible rate law?
More conclusively have you noticed the units quoted for the rate constant?

Because of the → symbol and no other indications if you have quoted the question completely I think you can assume the reaction irreversible, i.e. goes to completion.

The concentration-independent half-life concept is valid only for first-order kinetics.

Although the question is maybe not extremely easy you can do it with a bit of knowledge of integration; otherwise it is standard chemical kinetics theory found in any physical chemistry textbook of medium level.