The data shown here were collected for the first-order reaction: ...

Question

The data shown here were collected for the first-order reaction: 
N2O( g)¡N2( g) + O( g) 
Use an Arrhenius plot to determine the activation barrier and 
frequency factor for the reaction. 
Temperature (K) Rate Constant (1 , s) 
800 3.24 * 10- 5 
900 0.00214 
1000 0.0614 
1100 0.955

Accepted Answer

Hi everyone for this problem we're told the following table shows various values of the rate constant K obtained at different temperatures. Use this data to construct an Iranian plot and calculate the value of the frequency factor A. And the activation energy E sub a. Okay so our goal here is to calculate the value of our frequency factor and activation energy using an Iranian plot. So let's recall that the Iranians equation and log form since we're working with a plot here is Ln of K is equal to our negative activation energy over R universal gas constant times one over our temperature in kelvin units plus Ln of A. What this translates to is y equals M X plus B. Okay. And what we can do is we can use our calculator to get the equation of the line made using this raw data and when we do that we're going to get why Is equal to negative X plus 28.75. So based off of this equation, we know what our slope is. We know that it is negative 13,434. And we know what our intercept is. So the question is asking us to calculate our frequency factor and the activation energy. So we can start by calculating the activation energy based off of our Iranians plot. We see that M is equal to negative activation energy over our so let's set that equal to each other if M equals negative activation energy over are we can plug in what we know to solve for activation energy. Okay we know what M. Is M. Is our slope. That value was given that value is negative, 13,434 is equal to negative activation energy over our our is our universal gas constant. And it's a value we should know and that is 8.314 jewels over mole times kelvin. So let's multiply both sides of our equation by our And when we do we get Negative activation energy is equal to negative 111,690 jewels per mole. So we can divide both sides by one so we can get a positive value. And when we do we get our activation energy is equal to positive 11,690 jewels per mole. Let's go ahead and convert this to kill a jewels and we can do that by using our conversion in one. Kill a jewel, there's 1000 jewels. Okay so our jewels are jewels cancel and we're left with units of kill a jewel per mole. And we get a final answer for our activation energy to be 111.7. Kill a jules per mole. So that is our activation energy. Okay, now the second part of the question asks us to solve for our frequency factor A. So based off of our Iranians plot we can see that Ln of A is equal to B. Okay, so we can set that equal to each other. So if B equals Ln of A, we know what our value for B is. It is 28.75. So this is going to equal Ln of A. So we can raise both sides to E. To get rid of that L. N. So we're going to get A. Is equal to E raised to the 28.75. So this gives us a final answer of a. Our frequency factor is equal to 3. times 10 to the 12th, second inverse. And this is going to be our final answer for our frequency factor. So we solve for activation energy and we solved for our frequency factor. That's the end of this problem. I hope this was helpful.

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