## Graphs of rate laws

$aR \to bP, Rate = -\frac{1}{a} \frac{d[R]}{dt} = \frac{1}{b}\frac{d[P]}{dt}$

Baoying Li 1B
Posts: 113
Joined: Sat Aug 17, 2019 12:18 am

### Graphs of rate laws

Hey, can someone describe the characteristics of the graph of rate laws? Like what’s the between the first order and the second order? What about the zero order?

Parker Smith
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Joined: Thu Jul 25, 2019 12:15 am

### Re: Graphs of rate laws

A first order rate law forms a linear relationship when the natural log of [A] is plotted over time. A second d order rate law forms this relationship when 1/[A] is graphed over time. We derive these relationships from the integrated rate laws of each order of reaction. Since a 0th order rxn doesn't depend on the concentration, the relationship of simply [A] over time gives a linear graph

Posts: 103
Joined: Sat Aug 17, 2019 12:18 am

### Re: Graphs of rate laws

All of the graphs will be linear, but the slopes will vary. For instance, the graph of a first-order and zero-order reaction will have a decreasing slope of -k while a second-order reaction will have an increasing slope of k.

405268063
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Joined: Thu Jul 25, 2019 12:17 am

### Re: Graphs of rate laws

For zero order, the rate law makes a linear graph, which means that the rate just goes at constant k (slope). For first order reactions, the graph is also linear if you plot ln[A] versus time. For second order reactions, the graph is linear is you plot 1/[A] versus time.

MeeraBhagat
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Joined: Sat Aug 24, 2019 12:15 am

### Re: Graphs of rate laws

Depending on the different rate laws for the different ordered reactions, plotting the corresponding term on the y-axis against time will yield a straight line instead of a curve. For example, if given a graph with the y-axis as 1/ln[A] plotted against time, and the graph is a straight line, then you know it is a second order reaction. The same goes for a first and zero order reactions with y-axis ln[A] and [A], respectively.

Gabriella Bates 2L
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Joined: Thu Jul 11, 2019 12:15 am

### Re: Graphs of rate laws

The graphs for the different rate laws will all be linear, but what is plotted on the y axis varies. For a 0th order reaction, [A] vs time is linear, and the slop is equal to -k. For a 1st order reaction, ln[A] vs time is linear and the slope is equal to -k. For a 2nd order reaction, 1/[A] vs time will be linear and the slope is equal to k. The differences are important because looking a the graph can help us determine the order of the rate law for a given reaction.

Justin Quan 4I
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Joined: Sat Sep 14, 2019 12:17 am

### Re: Graphs of rate laws

Here's a diagram depicting the graphs of the three rate laws, zeroth, first, and second order reactions.

105335337
Posts: 103
Joined: Sat Aug 24, 2019 12:15 am

### Re: Graphs of rate laws

If you graph [R] v time & get a straight line: zero order

if you graph ln[R] v time & get a straight line: first order

if you graph 1/[R] v time & get a straight line: second order

pmokh14B
Posts: 107
Joined: Sat Aug 17, 2019 12:15 am

### Re: Graphs of rate laws

The first order graph is of ln[A] vs time, and the second-order is 1/[A], whichever is linear is the order of the reaction.