Concentration Changes Over Time

A zero order reaction loses concentration at a constant rate, so [A] versus t is already a straight line sloping down. First and second order reactions both slow down as reactant runs out, so their [A] versus t plots curve — just in different ways. That curve alone can't tell you the order. Instead, each order has an integrated rate law, a rearranged version of the rate law that expresses concentration as a function of time. Plug concentration data into the matching transformation and, if you picked the right order, the plot straightens into a line.

For zero order, [A] vs t is linear with slope -k. For first order, ln[A] vs t is linear with slope -k, because the integrated law ln[A]t = ln[A]0 - kt has that exact linear form. For second order, 1/[A] vs t is linear with slope +k, from 1/[A]t = 1/[A]0 + kt. So the test for order is mechanical: make all three plots, see which one is straight, and read the order off that.

This sits right after writing rate laws from initial rates and right before using the rate constant you find from a slope to predict concentrations or half-lives. The slope of whichever plot comes out straight hands you k directly, and the intercept hands you the starting concentration — so this topic is really the bridge between knowing a reaction's order and being able to calculate anything about it over time.