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Consider the first-order reaction $\mathrm{A} \longrightarrow \mathrm{B}$ shown here. (a) What is the rate constant of the reaction?(b) How many A (yellow) and B (blue) molecules are present at $t$=20 $\mathrm {s}$ and 30 $\mathrm {s} ?$

(a) $k=0.0693 \mathrm{s}^{-1}$(b) at $t=20 \mathrm{s}(4 \mathrm{A}, 12 \mathrm{B}),$ at $\mathrm{t}=30 \mathrm{s}(2 \mathrm{A}, 16 \mathrm{B})$

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

Brown University

University of Toronto

Lectures

22:42

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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Consider the first-order r…

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For the hypothetical react…

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For the reaction $A \longr…

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01:52

Okay, So every drop the figure in the question and I replaced the yellow molecules with red ones, and I kept the blue ones the same. So for part A, they want us to determine. Do you make constant Okay, right. Since this is a first order reaction because they told us its first order, we need to use this equation. Ln final concentration is equal to Ellen. Oh, l A. And final concentration is go to Ellen. Initial concentration minus Katie. Now we should do is we should isolate K since they want us to solve. Okay, so if we subtract Ln initial concentration from both sides, right, we should get l and final concentration minus o in initial concentration. Go to negative, Katie. And one of the natural log rules is that if you're subtracting too natural logs to pretty much defining them, right, So promise just can be rewritten as Ellen. Final concentration over the initial concentration. All right, so and then we have minus Katie, and we want to divide negative t on both sides and we get K as Ln the final concentration over t initial concentration over negative t. Right. So they tell us that. Okay, So weaken. Yeah, they tell us that the time is 10 seconds. And we know that the official concentration of a is 16 because they're 16 red molecules in here and we don't have the final concentration is eight. Because when we go to t equals 10 we see that there is eight red ones that would just plug into the equation we get Ln initial concentration is final. Constitution is eight. Initial concentration in 16. Divided by negative CI or negative 10. And we should get, huh? We should get points. 60 0.693 per second as r K. Okay, who's now for part B? They want us to determine how many molecules of A and B are left after 20 seconds and 30 seconds. So what we do now is we just plug it into Ah ah, equation. This equation right here. So this one right here to determine our answer. Right. So we have Ellen, we see that we we don't know the final concentration of the, uh is, but we know that the initial concentration is 16 and we know that the rate constant is 0.693 per second cause we found it in the previous part right here. And we know that the time is 20 seconds, right? So we can do is we can solve for this 18 30. Final concentration. All right, so we have Ellen. Final concentration over 16 is equal to negative. 1.386 Right. So how do we get rid of log? Well, the embers of log is E Right. So if we put okay to negative 1.386 this ive pretty much cancels out the natural log and we get left with the final concentration over. The initial concentration is equal to e to the negative 1.3 a six. Now we multiply 16 on both sides so we can isolate the final concentration. Right? Some 1.386 times it by 16. Now we plug it into the calculation we should get. Hey, the final concentration is a go to for various. After 20 seconds, there will be four red ones and there will be six and there will be 12 blue ones. How do we know it's 12? Well, we see from appeared at one. Red is converted to one blue. So it's a 1 to 1 ratio. This means that if we had originally 16 red ones and we only have four left, 12 of almost I've been converted to the blue ones right now. For Part C. It's pretty much the same concept, right? So we have Ellen. The final concentration over the initial concentration is equal to negative 0.693 per second times it by 30 seconds. This time I am Lee. She gets Ellen final concentration over 16 is equal to negative 2.79 And we know that we can raised both sides. E began the final concentration is equal to six divided by 16 and you go to each of the negative 2.79 Now we multiply both sides by 16 like we did previously, and we should get this. Now. When we plug it into the calculator, we get the final concentration of a as too, and we know we started with 16 of them. My 60 minutes two is equal to 14. This means that there will be to read plus 14 blue after 30 seconds

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