The temperature dependence of the rate constant for a reaction
i...

Question

The temperature dependence of the rate constant for a reaction 
is tabulated as follows:
Temperature (K) k 1M 1 s1 2 
600 0.028 
650 0.22 
700 1.3 
750 6.0 
800 23
Calculate Ea and A.

Accepted Answer

hi everyone for this problem, it reads the rate of a chemical reaction increases as the temperature is increased. The following table shows how the value of the rate constant K. Changes as the temperature is increased. Using the data in the table calculate the value of the activation energy and a frequency factor. Okay so this is our goal here is to find the value of both of these and to solve this problem, we need to plot the given data in order to find those values. And when we plot the given data, the Iranians equation for the plot is going to be L. N. Of K. Is equal to negative activation energy over R. Times one over T plus Ln. Of A. And what this equates to is Y equals M. X plus B. Okay, so after we plot the given data, the regression equation for the plot that we're going to get is why is equal to negative 328.98 X plus or minus. Excuse me -2.4378. So when we plot the data this is what we're going to get. Okay. And we are looking for activation energy and frequency factor. Okay, so these two values here so because we have the regression equation for a plot we can set our variables equal to each other to solve for what we're looking for. So we know that M is equal to negative activation energy over our. Okay, so because we know that what we can do is plug in the values that were given in our regression equation to solve for negative activation energy. So we know that R. M. is equal to negative 328.98. So what we can do here is multiply both sides of our equation by our okay. And that is going to give us our activation energy. So our new equation is going to be negative activation energy is equal to negative 328.98 times are Now we already know the value of our that's a constant that we should know. So we'll have negative activation energy is equal to negative -328.98 times 8.314 Jewels over Mole Times Kelvin. So we get negative activation energy is equal to negative 35.14 jewels over more. Okay so we need to convert this to kill a jules. And when we do that In one, kill a jewel we have 1000 jewels. So our jewels cancel and we're left with killer jewels. So we get negative 2.74 Killer Jules Permal. So if we divide both sides by negative one we'll get a positive activation energy. So let's go ahead and do that. So we get a final activation energy equal to 2.74 killer jewels per mole. So that is our answer for our activation energy were also asked to solve for our frequency factor A based off of our regression line and are Iranians equation, we know that B. Is equal to Ln. Of A. And from our regression line, R. Ln of A. Is equal to negative 2.4378. So we have everything that we need to solve four A. Here are frequency factor so A. Is going to equal to get rid of the L. N. We need to take E to the negative 2.4378. By doing that will cancel out the L. N. And so when we plug this into our calculator A equals E. Raised to the negative 2.4378 gives us a frequency factor of 0.874, which is our answer for frequency factor. So those are the two values were asked to solve and those are the answers to the to this problem. And that's the end of this problem. I hope this is helpful.

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