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The rate constants of some reactions double with every 10-degree rise in temperature. Assume that a reaction takes place at $295 \mathrm{K}$ and $305 \mathrm{K}$. What must the activation energy be for the rate constant to double as described?

$$519 \mathrm{kJ}$$

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

University of Central Florida

Rice University

Brown University

Lectures

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In probability theory, the conditional probability of an event A given that another event B has occurred is defined as the probability of A given B, written as P(A|B). It is a function of the probability of B, the probability of A given B, and the probability of B.

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In chemistry, kinetics is the study of the rates of chemical reactions. The rate of a reaction is the change in concentration of a reactant over time. The rate of reaction is dependent on the concentration of the reactants, temperature, and the activation energy of the reaction.

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Okay, so in this question, they tell us that t one is. He go to 298 95 Covenant and T two is equal to 305 Calvin. So what is the difference? But so the difference in temperature is 305 minus two you 95 which is 10 Calvin. And in this question, they tell us that every 10 degree increase in temperature increases the rate constant by two. Right? This means that K two is equal to double K one. So the equation that we need to use to solve this question is Ln k one over, Okay, to be able to activation energy over our times Times of by a T one minus t two over. Do you want times? T two, right, So are is a constant. It's 8.314 Jules Pro Calvin Mo nose plug in the values that we have of Ellen Que won over to K one. The reason why I put two K one is because K two is to go to K one, and if we put in to K one, we can eventually cancel out to Kate one. So this equals the activation energy over are so 8.314 I'm not gonna write the units down here so that it doesn't become messy, but the units is right here by times by t one, which is 2 95 minus 305 over t. One time teachers was 2 95 times it by 305 Right. So Ln k one over to K one can also be written as 1/2. Because the K will cancel out. This is equal to e A over 8.314 in terms of by negative 10 over to 95 times it by 305 Right, Ellen? Half is equal to six. Negative. 60.693 All right, so now we have a e a 8.314 negative. 10 over to 95 times by 305 We see that we have a negative in the front here. We see that we have a negative in here so we can cancel the two negatives out, and we get and we get this. Now, what we can do is we can isolate the activation energy. All right, So 0.693 is a go to e a over 8.314 Turn over to 95 times 305 is 899 75 Now what I'm gonna do is 0.693 years ago to e a over 8.314 times and by 1.11 times 10 to the negative for years 10 divided by $89. 975 is this. Now I divide this from both sides. All right, so I would get 0.69 3/1 0.11 times 10 to the negative. Four is you go to EA over 8.314 Now multiply both sides by 8.314 So I would you 0.693 times it by 8.314 over 1.11 times 10 to the negative for legal to deactivation energy. And when I put that into the calculator, I get the activation energy as 5.19 times 10 to the four Jules per mile, right? And it looks like they want the answer and kill Jos so we could do 5.19 times 10 to the four jewels. We know that one killed jewelers. You go to 1000 jewels, and we should get 51.9 Killer George as our answer.

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