## First Order Reactions Graph

$\frac{d[R]}{dt}=-k[R]; \ln [R]=-kt + \ln [R]_{0}; t_{\frac{1}{2}}=\frac{0.693}{k}$

Clarissa Cabil 1I
Posts: 66
Joined: Fri Sep 28, 2018 12:19 am

### First Order Reactions Graph

During lecture, Professor Lavelle mentioned how first order reactions produce straight line plots of ln[reactant] vs time with a slope that equals -k. However, he proceeded on with lecture and then mentioned how first order reactions produce exponential curves that are decreasing. Can someone explain the graph of first order reactions? Are they linear or decreasing curves?

JiangJC Dis2K
Posts: 72
Joined: Fri Oct 12, 2018 12:16 am

### Re: First Order Reactions Graph

The graph of ln[A] vs. time is linear for first order reactions, but the graph of [A] vs time is exponential decay, because e is applied to undo the ln. That is the difference between the two graphs but both of them are for first order reactions, the only difference is the two variables.

Kelsey Warren 1I
Posts: 60
Joined: Fri Sep 28, 2018 12:15 am

### Re: First Order Reactions Graph

Both graphs really mean the same thing and can be about the exact same reaction, you're just plotting [A] vs time and then ln[A] vs time (which produces a linear graph from the exponential decay).

gwynlu1L
Posts: 62
Joined: Fri Sep 28, 2018 12:19 am

### Re: First Order Reactions Graph

pay attention to the y axis of a graph, since it can tell you what order rxn it is. but for the most part, associate ln[A] with first order rxns.