Textbook 7.21

[Andrea_Perez_2F]

Based on this question,
7.21 Which of the following plots will be linear? (a) [A] against time for a reaction that is first order in A; (b) [A] against time for a reaction that is zeroth order in A; (c) ln [A] against time for a reaction that is first order in A; (d) 1/[A] against time for a reaction that is second order in A; (e) kr against temperature; (f) initial rate against [A] for a reaction that is first order in A; (g) half-life against [A] for a reaction that is zeroth order in A; (h) half-life against [A] for a reaction that is second order in A.
I was wondering how to approach this question, how do we know if something would be linear or not?

[Ysabelle Magat 1E]

You can tell if the plot will be linear by knowing the order of the reactant A:

If A is zero-order: plot will be linear when [A] vs. t
If A is first-order: plot will be linear when ln[A] vs. t
If A is second-order: plot will be linear when 1/[A] vs. t

Hope this helps!

[Phoebe 1H]

For rate orders and their corresponding graphs, the easiest way is to honestly memorize them. What equation goes with what graph, etc. The plots that we went over during lecture for each of the ordered reactions and their half-lives really help. This will come in handy for 14BL as you actually set up an experiment and determine rate laws and their corresponding graphs!