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Ch.14 - Chemical Kinetics
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All textbooksMcMurry 8th EditionCh.14 - Chemical KineticsProblem 40a

Chapter 14, Problem 40a

The following reaction is first order in A (red spheres) and first order in B (blue spheres): A + B → Products Rate = k[A][B]

(a) What are the relative rates of this reaction in vessels (1)–(4)? Each vessel has the same volume.

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Hi everyone. This problem reads the reaction that is described below is first order in both y green spheres and Z orange spheres. If the volume in each vessel is the same, what are the relative rates of this reaction? And one through four. So we want to know the relative rates of this reaction. Okay, so let's take a look at the rate that's given up here. So we have rate is equal to the rate constant times the concentration of Y times the concentration of Z. Since this is the rate, the rate is proportional to the product of the number of why molecules and the number of Z molecules. So let's go ahead and calculate this for each 1123 and four. So for one, The concentration of why we're gonna count how many spheres we have and it is 12. And the concentration of Z is to So when we rewrite the rate, what we're going to get is the rate is equal to K. Times 24. Okay, For the second image we get the concentration of Y is equal to eight and the concentration of Z is equal to six. So when we rewrite this rate, we get, the rate is equal to K times 48. For the 3rd image, the concentration of Y is equal to and the concentration of Z is equal to six. So when we write the rate we get, the rate is equal to K times 60. And lastly we're going to get the concentration of why for the fourth image, the concentration of Y is equal to 12 and the concentration of Z is equal to three. So when we rewrite the rate we get, the rate is equal to K times 36. Alright, so let's take a look at these ratios. So the ratio is 24-48-60-36. So what we're going to do is we're going to get the smallest ratio by dividing the relative rates by 12. So when we do that, what we get is 245 and three. Okay, so the relative rates of this reaction in vessels one, 2, 4, R., 2, 4, 5 and three. That is it for this problem? I hope this was helpful.
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The following reaction is first order in A (red spheres) and first order in B (blue spheres): A + B → Products Rate = k[A][B]

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