### Linear Graphs

Posted:

**Wed Mar 11, 2015 5:08 pm**Why is the graph of the half-life of a second order reaction not linear. Wouldn't the slope be 1/k with the variable being [R]o?

Thanks!

Thanks!

Created by Dr. Laurence Lavelle

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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=149&t=5437

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Posted: **Wed Mar 11, 2015 5:08 pm**

Why is the graph of the half-life of a second order reaction not linear. Wouldn't the slope be 1/k with the variable being [R]o?

Thanks!

Thanks!

Posted: **Wed Mar 11, 2015 5:42 pm**

Please specify what do you mean by 'graph of the half-life of a second order reaction' (specify x and y axis).

For a second order reaction integrated rate law is 1/[R] = kt + 1/[R_{0}]

So 1/[R] vs t will give a straight line with slope k

[R] means reactant concentration at any instant t, which is a variable and [R_{0}] is initial concentration which is a constant.

Now think from the equation how you could vary [R_{0}] to get a linear plot with slope 1/k !

For a second order reaction integrated rate law is 1/[R] = kt + 1/[R

So 1/[R] vs t will give a straight line with slope k

[R] means reactant concentration at any instant t, which is a variable and [R

Now think from the equation how you could vary [R

Posted: **Wed Mar 11, 2015 6:30 pm**

My apologies! Homework problem #14.103 says

"which of the following plots would be linear?" and one of the options is "the half-life against [A] for a second order reaction in [A]"

I am confused why this is not linear because I thought it would be, but the solutions manual does not have it listed. Thanks!

"which of the following plots would be linear?" and one of the options is "the half-life against [A] for a second order reaction in [A]"

I am confused why this is not linear because I thought it would be, but the solutions manual does not have it listed. Thanks!

Posted: **Wed Mar 11, 2015 6:46 pm**

Firstly, there was a typo in the question. It would be

g) 'the half-life against [A_{0}] for a zero order reaction in [A]'

h) 'the half-life against [A_{0}] for a second order reaction in [A]

Check the half life of a zero order reaction t_{1/2} = [A_{0}]/2k so a linear plot with 1/2k slope

Check the half life of a second order reaction t_{1/2} = 1/k[A_{0}], see t_{1/2} is inversely proportional with A_{0} , not linearly

So you will NOT get a linear plot for half life vs [A_{0}] here.

Rather you will get a linear plot for half life vs 1/[A_{0}] with 1/k slope for a second order reaction

g) 'the half-life against [A

h) 'the half-life against [A

Check the half life of a zero order reaction t

Check the half life of a second order reaction t

So you will NOT get a linear plot for half life vs [A

Rather you will get a linear plot for half life vs 1/[A

Posted: **Sun Mar 15, 2015 12:59 pm**

Oh that totally makes sense! Thank you so much and sorry for the typo!

Posted: **Tue Feb 16, 2016 5:16 pm**

There have been no graph questions in the textbook homework, so I was wondering what some examples might be to prepare should it show up on our quiz?