You wish to determine the activation energy for the following
fi...

Question

You wish to determine the activation energy for the following 
first-order reaction: 
AS B + C 
(b) How would you use these data to determine the activation 
energy?

Accepted Answer

hi everyone for this problem, it reads for the following first order reaction. What information is needed and how will it be used to calculate the reaction's activation energy. So we have two things that we want to answer here. The first is the information needed and how it will be used to calculate the reaction's activation energy. Okay, so for the first part, what we want in terms of information is going to be the change in concentration of X versus time at different temperatures. So that is the information that is going to be needed in order to solve this problem. Now, step two or the second part asks how will this information be used to calculate the reaction's activation energy? So for part two of this problem, we can use the Iranians equation to calculate the activation energy and we're going to use the Iranians equation and linear form and that is Ln of K. Is equal to negative activation energy over gas constant R times one over temperature plus Ln of A. So let's just talk about what this means. K. Is the rate constant, activation energy is in joules, per mole gas constant is a value of 8.314. Joules per mole kelvin, T. Is temperature in kelvin and A is the Iranians constant or frequency factor. And when we write this out in linear form, what this equates to is Y equals M X plus B. Okay, Where M is the slope. And so if we look at it this way we see that M is equal to negative activation energy over our and B is the Y intercept. Okay, so B is equal to Ln of A. So what we're going to do is step two is we're going to plot Ln of X, which is L n f K versus one over T which is X. Okay, so let me just write that out what I just said. So we're going to plot Ln of X versus T for each temperature. Okay. And from each linear graph, we're going to calculate the rate constant at each temperature. So let's write that out from each linear graph. We're going to calculate the rate constant And remember our rate constant is K. We're going to calculate the rate constant at each temperature using Okay, where K is equal to negative slope. Alright, so that's step two. Alright. Now, to calculate K at the different temperatures, what we're going to need to do is for a first order reaction. Remember we're told that this is a first order reaction. So to calculate K at the different temperatures for a first order reaction, we're going to need the following equation, which is Ln of concentration at time, T is equal to negative rate constant times time plus Ln of the initial concentration. Okay, and what this equates to in linear form is why equals M X plus B. Okay, where M is equal to the slope, which is negative K. Okay. And B is the Y intercept. Okay, so that means the next thing that we're going to do in terms of the step is we're going to plot Ln of K versus one over time than using the graph, we're going to calculate the activation energy using activation energy is equal to negative slope times are Okay. So we're going to have these these this is what's going to be used to calculate the reaction's activation energy. So part one, What information is needed? The information that's needed is the measuring the change in concentration of X versus time at different temperatures. And then step two. We're going to plot the Ln of the change in concentration versus time. Time for each temperature. And then from each linear graph, calculate the rate constant at each temperature using K equals the negative slope. And then the last thing that we're going to do is plot L n f k versus one over temperature. Then using the graph, calculate the activation energy. Using activation energy is equal to negative slope times are so that is it for this problem. I hope this was helpful

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