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

[@samchung9596]

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

[@sofiadeumacansandoval3352]

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

[@jimmyf8390]

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

[@EricZuckerman1]

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: kzbin.info/aero/PLsQ-ZBkwv0dfZNhaHH8UCnTRsRdifZKaZ These are in the order in which I have my class watch the videos. Best of luck in your chemistry endeavor.

[@saintvendetta2022]

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

[@EricZuckerman1]

My pleasure. Hope you crush your studies of chemical kinetics!! Best of luck :)

[@HMistry100]

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

[@drashar841]

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?

[@simpforme.]

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

[@EricZuckerman1]

Glad you found the video helpful. Good luck in all your studies!!

[@simpforme.]

thank you!

[@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!

[@EricZuckerman1]

The little "a" is the stoichiometric coefficient of the reactant. In this case, the reaction is written as 2M --> P, so a = 2. That same 2 is what you saw "divided" later. So sorry I missed this comment years ago, when it would have helped you.

[@alisaid8364]

@@EricZuckerman1 it helped me know thanks mr

[@fatemehhosseini3669]

this video saved me thank you so much!

[@Vunami]

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

[@mostafaalsaw9771]

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

[@EricZuckerman1]

Do you have the concentration of B at a variety of times or just a single time? What other information is known?

[@mostafaalsaw9771]

@@EricZuckerman1 I have the concentration of B at a variety of times But I do not know what is the initial concentration A and concentration A ? for exempel 0 0 8 0,091 16 0,156 24 0,202 28 0,218 30 0,227 32 0,236 ∞ 0,334

[@EricZuckerman1]

Mostafa Alsaw97 It seems to me that at t = infinity, all of the initial A has reacted to produce all of the measured B. So, you can use stoichiometry to determine the concentration of A, initially. It would look something like this: # mole A/L = (0.334 mole B/L) * (2 mol A/1 mol B) = 0.668 mol A/L = 0.668 M.

[@mostafaalsaw9771]

@@EricZuckerman1 How can you calculate the concentration for A?

[@EricZuckerman1]

Mostafa Alsaw97 In the previous comment, I did calculate the initial concentration of A. Using dimensional analysis in the exact same way can tell you what concentration of A was used to create each data point of B. Subtracting that used amount of A from the initial amount of A will yield the remaining amount of A at each time. Imagine it like a bicycle. Every two wheels can make a bicycle. So we could say 2Wheels = 1 Bicycle. Now imagine I told you I had 42 wheels in my shop to start (the initial concentration). 30 minutes later, you see I have 12 bicycles prepared. You can now see that I used 24 wheels to make the twelve bicycles and must have 18 wheels remaining. The calculations would be: # wheels used = 12 bicycles * (2 wheels/1 bicycle) = 24 Wheels used # wheels remaining = 42 wheels initially - 24 wheels used = 18 wheels remaining. The key thing is the amount of B is always connected to the amount of A used, because the only way to get B is by using up 2 A’s, according to the reaction you provided.

[@ellaannechii]

Thanks Sir! YOu helped a lot!

[@omoralsuny5755]

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?

[@EricZuckerman1]

Suny, unfortunately, I am not a researcher in the kinetics realm. While I had heard of sorption kinetics, I have never read or studied the topic. After a cursory glance, it is an interesting topic that would require a long study for me to give you any guidance. I wish I could help you, but my assistance will be guesswork at this time. Good luck.

[@omoralsuny5755]

@@EricZuckerman1 Thanks for reading my comment! I appreciate your generous attitude! I am searching for the solution. Hopefully I will find a solution! And again thanks for wishing me luck. Stay safe and sound!

[@DaivyDjimbi]

Hello 2M is the initial quantity of products right?

[@EricZuckerman1]

In the example, the reaction is 2M --> P. That is, two moles of the substance M react to form a single mole of substance P. Initially, there is no substance P in the container.

[@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

[@EricZuckerman1]

William, the equations I show are for a gas phase, unimolecular equation. In no way do I consider myself up on the engineering aspects of kinetics. Still, I think the main difference lies in the necessity to take into account the flow rate and the volume of the liquid when the reaction is done in aqueous or liquid forms. The flow associated with these techniques means that the reactants are not necessarily present during the experiment and may flow beyond the sensors, etc. I wish I knew more about the techniques you are using and could be of actual benefit. Good luck and I hope that someone out there has an adequate explanation to help you make the connections.

[@wv_rosales]

Eric Zuckerman Thanks prof., Your answer was a lot faster than what I was expecting. I will research it and post here as soon as I get the answer to help other classmates with the same issue.

[@Aminulchem]

Great.

[@Thiyagadhayalan]

very clear explanation, thanks

[@EricZuckerman1]

Glad it helped!!

[@guustvb]

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

[@EricZuckerman1]

There are a number of methods used to determine the order of a reaction. For a unimolecular process as described in the video, a graph is the easiest way. So you could make these same graphs by hand. Note that in the example here we are given concentration and time data, which is a clue that graphing the data would help. Another method you might try and can find in my videos is the method of initial rates. Instead of the data being concentration vs. time, you would have initial concentration and rate. Rate and time are related but not the same thing (for example, the larger the rate the less time some process takes). You can also use half life information to deduce the order for unimolecular processes, but I don't have a video that discusses that topic.

[@tranquoclan5043]

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

[@EricZuckerman1]

Pressure data implies that we're dealing with gases. PV=nRT is our common approximate relationship. Well, if you rearrange that to solve for n/V, you have an expression for concentration (moles per liter). So, n/V = P/RT. That means each and every pressure is proportional to the concentration. If you have the temperature and pressure, you can directly compute the concentration and run the exact same analysis. But for first order you can just use the pressure data as is. Why? Because the RT factor cancels when making a ratio.

[@tranquoclan5043]

@@EricZuckerman1 thanks for the comment, but I mean the concentration of P (product) data column instead of the concentration of M data column in the table.

[@EricZuckerman1]

@@tranquoclan5043 I see. That is a different story. But an easy one to fix. Because you can balance the reaction, you can easily use stoichiometry to determine the [A] from every data point of [P]. For example, suppose that the rxn is A --> 2P. This means that at every instant, [P] is twice that of [A]. If you had a data point where [P] = 0.40 M, then the work to find [A] is as follows: # mol A/L = 0.40 mol P/L * 1 mol A/2 mol P = 0.20 moles A/L = 0.20 M

[@tanzirahmed63]

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.

[@EricZuckerman1]

If you know the reaction, then the moles of product made can be converted to moles of reactant used by stoichiometry. At every time, the concentration of the reactant is Initial concentration less the amount used.

[@tanzirahmed63]

@@EricZuckerman1 I have conc vs time data provided by a researcher which contains 2 reactions in series (A to B to C). The first reaction is ignored (A to B) because thr data shoes it is so fast so the second (as it is so slow) is being used to determine the rate expression and constant. I've been advised to ignore the consumption of B as it will require me to take into account both the consumption and formation of B and so I was told focus on the consumption of C. Are you saying that I should convert the concentrations of C at each time to moles and then find moles of reactant B using stoichiometry and then convert them to concentrations of B at those same times, and then use the integrated laws to find the rate constant and order?

[@EricZuckerman1]

@@tanzirahmed63 It seems that B is formed so quickly that we can ignore that time with respect to the overall time. If the reactions are truly written as A --> B --> C, then the stoichiometry is 1:1. That is, for each mole of C created, one mole of A was used. Suppose you started with [A]0 = 1.00 M. after t=1.0 seconds you might have produced [C] = 0.05M. Thus, at t = 1.0 s, you have [A] = 1.00 M - 0.05 M = 0.95 M. For each time you have, you can do the same thing and create a table of [A] and t. From that, the video shows how to determine both the order and rate constant. Hope this is helpful.

[@tanzirahmed63]

@@EricZuckerman1 thanks Eric, you are a legend! Just to confirm, the final rate expression I obtain will be the rate law with respect to the consumption of A right? As I have converted the [C] to [A] now?

[@EricZuckerman1]

@@tanzirahmed63 Yes. I've also assumed that there was no change in volume during the reaction.

[@stephanyecastelblanco7316]

Thanks you!

[@naviitaramro3474]

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

[@EricZuckerman1]

For this example (where the stoichiometric coefficient is 2), first order would tell us that m = -2k. So k = -m/2. The slope would be given in the linear equation (by MS Excel) as a negative number, so the negative sign would cancel the negative portion of m. It's important to note that negative rate constants don't seem to make much physical sense.

[@barbarawilk3973]

Thank you! Thank you! :)

[@mannmohan3009]

its xool. thanks Eric.

[@nizettedugue9621]

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

[@EricZuckerman1]

Are you saying that you cannot select different columns? Are you using a PC or Mac?

[@EricZuckerman1]

On Windows select the first column, then hold control while selecting the other column you want. On a Mac, select the first column as usual and select the other column by holding command.

[@nizettedugue9621]

@@EricZuckerman1 Yes i got it work, thank you so much. But another question I have is that is when i plotted the points, it gave me two separate lines and not just one line in a scatter plot

[@EricZuckerman1]

@@nizettedugue9621 You have most likely created a "Line plot" and not a "Scatter plot". Make sure you are selecting Insert > Chart > X Y (Scatterplot)

[@amin9245]

Life saver

[@EricZuckerman1]

Glad it helped!!

[@zillousgrom4332]

i love you