# Thread: Integrated Rate Law

1. ## Integrated Rate Law

I found the order (first order) but I don't see how I can calculate the value of the rate constant without a rate! I only have time and M(right column). How do I calculate it? I know k= (A) and I haven't a clue on how to predict the concentration at 280 s. Will someone explain to me please?

The data below show the concentration of versus time for the following reaction:

Time M
0 1.000
25 0.822
50 0.677
75 0.557
100 0.458
125 0.377
150 0 .310
175 0.255
200 0.210

Determine the value of the rate constant: ???

Predict the concentration of at 280: ?????

2. ## Exponential

Your concentration should be undergoing an exponential decay, right: $M(t)=M_0e^{-rt}$? Take the natural log of both sides:
$\ln{M}=\ln(M_0e^{-rt})$
$\ln{M}=\ln(M_0)-rt$
Thus the relationship between ln(M) and t is linear, with -r the slope of the line. You can take the logarithms of your M values, and then fit a line to that versus t with a standard least-squares linear regression and extract a value for r in the equation, and using the fact that $\frac{dM}{dt}=-r\cdot{M}$, obtain your rate constant.

--Kevin C.