Kinetics: Using the Integrated Rate Laws and Graphs to Determine the Rate Law

For a unimolecular chemical reaction, a single set of data can reveal the order of reaction. This data is concentration vs. time data and must be graphically analyzed. We start by creating integrated rate laws from the potential rate laws: zero, first, second and third order. This step requires using integral calculus, which is why the four equations that result are called "integrated rate laws".

The integrated rate laws can be put in a linear form in which a function of concentration vs. time could yield a line. "Could" is there because a first order reaction will only yield a linear graph when using the first order integrated rate law. Same for a second order reaction, where it will only be linear when plotted with the proper axis for a second order integrated rate law.

This video walks you through a set of sample data to determine the order of reaction. All four graphs are made so that you can see only one of the four is linear, and that must be the order.

[EricZuckerman]

Hi wakinguptooearly.  Most textbooks assume the stoichiometric coefficient in a unimolecular process is 1.  The integrated rate laws I utilize do not make that assumption.  The lower case 'a' represents the stoichiometric coeffiecient in my integrated rate laws, which for the given reaction is a 2...2 M produces one 1 P.  For the example, then

If you notice, there are 4 possible orders shown for the reaction data (0 through 3rd) and their integrated rate laws for each possible order are also displayed.  After linearizing each integrated rate law, there is a correlation between the equation of a line and the constants and variables of the equation for the line.  I color coded the correlation in the video.

Plotting the data for a second order integrated rate, which is a plot of 1/[M] vs. t, results in a straight line, and that is why the order of the reaction is 2 order.  If the first order plot had been linear (ln[M} vs. t), then the reaction would have been 1st order.  In both cases, the lower case 'a' is still 2, because it is not related to the kinetics of the reaction, only to the balanced reaction.

To get the rate constant, I used the linearized second order rate law and the equation of a line to see that m = a k.  Go back to the video and see if you can identify this relationship for second order.  If you look at first order, you'll find that m = -ak.  From the best fit line that Excel gave us, we can get the slope...m.  We just rearrange the relationship m = ak to k = m/a, and substitute.  Since a = 2, we thus have k = m/2 in this example.

Hope this helps.  And, feel free to look over my full set of kinetics videos found in my youtube channel:  
These are in the order in which I have my class watch the videos.  Best of luck in your chemistry endeavor.

[wakinguptooearly]

Hi, I found this video through google, so I'm not sure if there's background information mentioned elsewhere in another video.

Is "a" the order number? Is the reason you divided "m" by 2 because the slope was linear graph, therefore, making the data set indicative of a second order? Thanks!

[drashar]

Excellent video! One simple question, you divide 0.1908 by 2 because it is second Order right? if third order we need to divide m by 3?

[jimmyf]

I'm taking an online class and this video helped more than anything that the teacher provided, thank you!

[sofiadeumacansandoval]

Thank you so much! I struggled to make my graphs until I watched your video!

[samchung]

Thx a lot~I have struggled in this rate law plotting technique for quite a while. Thx Eric!

[omoralsuny]

Dear Professor,
Hope you are doing well. I am working on Soil Phosphorus Sorption Kinetics. After calculation, I have found both adsorption and desorption simultaneously and the equilibrium point has not followed any definite pattern and the equilibrium point is not obvious too. While plotting them on pseudo-first-order, pseudo-second-order, elovich equation, I can't take each value as that shows error, eliminationg those values I tried to plot, this time R squared value is too low(even 0.008). For first order, I have plotted -log(qe-qt) vs t where as t/qt vs t for second order and qt vs ln(t) for Elovich equation. I can't understand what should I do? Will you please help me?

[HMistry]

Thank you so much You have no idea how much this helped!!

[saintvendetta]

Thanks so much! You did a fantastic job explaining this and making it easy. :)

[simpforme.]

Thank you so much! You saved my life and your explanation was clear and easy.

[mostafaalsaw]

Request in reaction speed.
Hello
I need your help
I have a problem calculating the initial concentration.
The reaction equation 2A==> B
I have the concentration of B but I want to calculate the concentration of A. Every time it gets wrong.
Sincerely.
Mostafa Elsawi
@Eric Zuckerman

[DaivyDjimbi]

Hello 2M is the initial quantity of products right?

[guustvb]

Professor is it possible to calculate the order and the k value without computer?

[wv_rosales]

Hello Professor,

Thanks for the class. If possible, I would like to ask you something. In the exercise resolution you’ve used the equations for different order reactions. Even understanding that the reactor's equation differs of the kinetics’ reaction equation, I would like to understand better that difference and when to apply each of them.

For example, BDO's decay is usually described by a first order reaction, although the 1st order decay has different forms if we're working with PFR, CSTR, or Batch Reactor. I've seen that you've only used the concept of kinetics equation for the different orders without the necessity of talking about the peculiarities about each reactor. My doubt is when to use that or to use the reactor’s decay equation, since when we are working with BDO's remediation in a river we utilize both PFR and CSTR equations to describe it depending on the river shape, flow type, objective, distance, time and others.

So, that is the doubt. Why to consider that when talking about the river, and not here, talking about the kinetics, as they have different describing equations.

Thanks,

William

[tanzirahmed]

if we were given concentration of the product vs time, how could we use this to find the order and value of rate constant? someone said to me you need to convert the concentrations of the product to reactant concentrations but i dont know how.

[Vunami]

not all heroes wear cape... this guy explained this too well

[naviitaramro]

If it were a first Order would finding the slope be m/2?

[tranquoclan]

What if P data column vs time instead of M data column vs time? Thanks alot!

[fatemehhosseini]

this video saved me thank you so much!

[nizettedugue]

I am not able to select the separate numbers on excel and its driving me crazy