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### 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!

### Re: Linear Graphs

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/[R0]
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 [R0] is initial concentration which is a constant.

Now think from the equation how you could vary [R0] to get a linear plot with slope 1/k !

### Re: Linear Graphs

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!

### Re: Linear Graphs

Posted: Wed Mar 11, 2015 6:46 pm
Firstly, there was a typo in the question. It would be
g) 'the half-life against [A0] for a zero order reaction in [A]'
h) 'the half-life against [A0] for a second order reaction in [A]
Check the half life of a zero order reaction t1/2 = [A0]/2k so a linear plot with 1/2k slope
Check the half life of a second order reaction t1/2 = 1/k[A0], see t1/2 is inversely proportional with A0 , not linearly
So you will NOT get a linear plot for half life vs [A0] here.

Rather you will get a linear plot for half life vs 1/[A0] with 1/k slope for a second order reaction

### Re: Linear Graphs

Posted: Sun Mar 15, 2015 12:59 pm
Oh that totally makes sense! Thank you so much and sorry for the typo!

### Re: Linear Graphs

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?