Integrated Rate Law question...?

[R W A P]

The rate constant for a certain reaction is = 1.20×10−3 s^-1.
If the initial reactant concentration was 0.750, what will the concentration be after 6.00 minutes?
The answer is 0.487 M, but I would like to know HOW to arrive at that answer? (i.e. ...could you show me how it's done?)

 

[Harry S]

From the units of your rate constant (s^-1), you know that your reaction is first order. For first order reactions, the rate of the reaction is given by the following. Rate = -d[A]/dt = k[A]. This is calculus for the change in the concentration of A with respect to the change in time = the rate constant times the concentration of A. Now, rearrange the equation to get the variables on one side. -d[A]/[A] = k dt. Integrate both sides! The first side should be done on the interval of [A initial] to [A final]. The right hand side should be integrated on the interval of 0 to t. I'm assuming you know how to integrate. Your answer is ln[A final]-ln[A initial] = kt. Solve for [A final]. Hope this helps.