[ankylosaurus]

The half-life of the first order photodecomposition of the carcinogen nitrosodimethylamine is 30 min.  How many minutes will it take for 99.9% of a sample to decompose?

A)  1784     B)  692     C)  299        D)  157     E)  93

 
the formula I used was for first order half life: t=ln(2)/k
where I inserted 30 into t and calculated k to be .0231.
I'm not sure where to go from here?

Any help is appreciated. Thanks

[stewie griffin]

Ok so you weren't given any info about k, but just the half-life. So you used the half-life equation to find k. Very good.
Hint: Now that we have k, is there any equation for a first order reaction that relates concentration of reactant to time and/or k?
Another hint: Pretend the initial concentration of the carcinogen is 100. What then is the concentration of the carcinogen going to be when 99.9% has decomposed (ie reacted)?

[ankylosaurus]

Ah I got it! Your hints were helpful. Thanks stewie griffin.

And for anyone else reading this and curious (probably no one):

[c]=[c]_oe^{-(k x t)}

(Where [c]_o is the initial concentration.)

.1=100e^{-(.0231 x t)}

Solve to get 299 minutes.

[MOTOBALL]

Had you known in advance that it takes 10 half-lives for a first order reaction to go essentially to completion, you could have answered the question by inspection.  This could save you time on a quiz.  But, it's important that you were able to work it through by theory !!!!

[Mitch]

As motoball said, this problem was to teach you that 10 half-lives yields around 0.1% of what you started with.

[stewie griffin]

As motoball said, this problem was to teach you that 10 half-lives yields around 0.1% of what you started with.

Had you known in advance that it takes 10 half-lives for a first order reaction to go essentially to completion, you could have answered the question by inspection.

Really? I was never told this. I don't do any kinetics in my research, but I don't see the advantage of an undergraduate gen chem student memorizing this fact... why not just learn to do the calculations and then you can solve the problem for any percent of sample decomposed??
Regardless I suppose the answer has been solved and the student understands what to do now...

[Mitch]

@Stewie, first order rate equations are ubiquitous in science. That memorized fact has come in handy many times over for me.