Question

In the lab you were told that the hydrolysis of tert-butylchloride reacts via an S_N1 mechanism and your graphs were constructed assuming a first-order reaction. Describe how one can graphically determine whether a reaction is 1^st order or 2^nd order?

Answer 1

Concept: Graphical methods for determining reaction order

Concept Overview:

All of the concentration-time reactions can be rearranged to give equations that form a straight line:

Zero Order: [A]_t = -kt + [A]₀
First Order: ln[A]_t = -kt + ln[A]₀
Second Order: 1/[A]_t = kt + 1/[A]₀

These relationships are very powerful, because in one graph, you can determine both the reaction order and the rate constant. The reaction order is determined when you choose the graph that is linear. For example, if you have a first order reaction, a plot of concentration versus time will not be linear--to obtain a straight line, you must plot the natural log of concentration versus time. To determine your reaction order, you like likely have to plot [A] vs t, ln [A] vs t, and 1/[A] vs t. From those plots, choose the one that is the best line to determine your reaction order. Be careful to plot all of the data! You need to long time points to tell between first and second order.

Note also that the slope of all of these graphs is either k or -k. The rate constant is determined simply by solving the slope of your graph! The slope is only positive for the second order reaction, so a graph that rises to the right is easily singled out as second order.