The rate constant (k) for a reaction was measured as a function
o...

Question

The rate constant (k) for a reaction was measured as a function
of temperature. A plot of ln k versus 1>T (in K) is linear and has
a slope of -7445 K. Calculate the activation energy for the reaction.

Accepted Answer

Hi everyone for this problem we're told a reaction was carried out in replicates. Each replicate reaction was carried out at a different temperature. While keeping the rest of the conditions identical, multiple values of K were obtained at different temperatures. A plot of L N f K versus one over temperature in kelvin units has a downward slope with a value of negative 6453 kelvin. What is the activation energy for the reaction? Okay, so our goal here is to find the activation energy for this reaction. Let's take a look at what we're given in the problem. We're told we have a downward slope and were given the value of that downward slope, it is negative 6453 kelvin. We're also told we have a plot of L N f K versus one over temperature. So the equation that we can use to solve this problem for activation energy is the Iranians equation in log form and that equation is Ln of K. Is equal to negative activation energy over R. Universal gas constant R times one over temperature plus Ln of A. And what this translates to is Y equals M X plus B. Where y is R. L N F K. M is our negative activation energy over R. Universal gas constant. T is our our exes are one over T and L N of A. Is R B. Okay, so what we want to solve for here is activation energy which is represented by M. Our slope. And so what this translates to is our slope is equal to negative activation energy over are we know what are slow hope is what M. Is because that value was given. They tell us that our slope is negative 6453 Calvin. We don't know what our activation energy is, but we do know what r universal gas constant R is, that is 8. Jules over more Times Kelvin. This our value is one that we should have memorized. It's not going to be given in the problem. So essentially now we have everything that we need to solve for our activation energy. So let's go ahead and do that. We'll multiply both sides of our equation by 8.314. So we can isolate our activation energy. So when we do that we get our activation energy is equal to negative kelvin times 8. jewels over more times kelvin. Okay, so we get negative activation energy is equal to negative 53,650. So we can divide both sides by negative one. So we can get a positive value here and what we get is activation energy is equal to positive 53, jewels over more. Okay, so We can convert this to kill a jewels so that we can have a simpler number. So to convert this from Jules to from jewels to kill a jewels and one kill a jewel, we have 1000 jewels, so we'll go ahead and divide this value by 1000 and our jewels will cancel, and we'll be left with killer joules per mole. And so we get 53.65 Kila jewels. So we get a final answer of activation energy is equal to 53.65 killer jewels. So this is going to be our final answer and that is the end of this problem. I hope this was helpful.

The rate constant (k) for a reaction was measured as a function of temperature. A plot of ln k versus 1>T (in K) is linear and has a slope of -7445 K. Calculate the activation energy for the reaction.

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