The tabulated data were collected for this reaction at a certain temperature: X 2 Y → 2 X + Y c. What is the concentration of X after 10.0 hours?

everyone in this example, we're given the below reaction and were given data values according to the time and concentration of our react in A. B three in polarity. We need to determine after eight hours the concentration of our product B. So what we should first begin with is plotting a graph first for a zero order reaction. And we should recall that this graph is going to be equal to the concentration of our reactant being a B three at a given time versus time. So this is what we would plot next. We want to recall our graph for a first order reaction. And so to generate this graph, we would plot the Ln of our concentration of our react in a. B three at a given time versus time. And then our last thing we want to recall is our second order reaction graph. Which we can generate from the data values given by plotting One over our concentration of our react in a. b. three. and sorry about that. That's a three at a given time versus time. So for our first graph for the zero order reaction We are going to get our equation of our line being why equal to our slope negative 9.06857 times x. Or sorry, that would be times 10 to the negative third power. And then times X. And then we would add this to our Y intercept given in our calculators at 0.103338. Now we also would get for our correlation coefficient which we should recall is r squared a value equal to 0.97856. And based on this value for our correlation coefficient, we would definitely be able to verify that this is a plot for a zero order reaction. So moving on to our next plot here for a first order reaction, we would get an equation of our line equal to y equal to negative 0.117178 X. Which is our slope times X. And then added to our Y intercept being negative 2.24467. And then for our correlation coefficient for a first order reaction in our calculators, we would get a value of 0.95597. Lastly moving on to our last plot for equation of our line, we're going to get Y is equal to 2.99 81 times X added to the Y intercept 10.36. And then for our correlation coefficient r squared we're going to get a value equal to 0.9999. And based on this value being 0.9999, we would say that this is going to be therefore the order of our reaction. And so for our reaction given we can say that we have a second order reaction. So relating our equation of our line to our integrated rate law for a second order reaction, we can determine that one over our concentration of our react in A. B three Is equal to Y. And so that would mean that we can say our why? Or sorry, our slope given in our equation of our line being 2. at times X. Where in place of X. We're going to plug in from the prompt the time eight hours. So then this is added to our Y intercept 10.36. And what we would be able to simplify to is One over our concentration of our reactant is equal to 33.9884. And so we want to get our concentration of reactant. So we're going to Switch places with these two values so that we can get that our concentration of our react in A. B. three is equal to 1/33 0.9884, which is equal to 0.2942. And it's going to be in units of morality. So now we're going to utilize our data set and we can pick any time. So let's just start where the time is at zero seconds or zero hours rather which corresponds to the concentration of A. B three being 30.100 solar. So utilizing this, these data values, we can say that our change in concentration of our react in A. B three is going to be equal to our concentration of our reactant A. B three when the time is zero hours minus our concentration of our reactant, A. B. Three after eight hours, which will just represent us t here and so what we would be able to do, plugging in our values from the data set is that we have at zero hours of concentration of 00.100 moller subtracted from our concentration of after eight hours, which we calculated to be 0.0 to 94 to moller. And so for our change in concentration of our react in a. B three, we're going to get a value equal to 0.7058 moller. Now we want to refer to our given reaction and because we need to determine our concentration of our product B. We're going to see that according to our given reaction, we produce three moles of B. We also want to recall that our units of polarity can be interpreted in moles per liter. So below, with our concentration or change in concentration of our reaction maybe three. We can reinterpret this value as 0.7058 moles per liter of solution. And we're going to multiply by the molar ratio where above we get that from our reaction and we see that we have for one mole of a B. 33 moles of B that is produced. And so we can plug that in as a molar ratio conversion factor. So in our denominator we will have our one mole of a B three, Our reactant producing three moles of our product B. And here we should have moles of a B three. So what this means is that we can cancel out our units moles of a B three, leaving us with moles of our product B as the final unit. And this is going to give us a value here equal to 0.212 Moller as our concentration of B after eight hours. And so this would be our final answer here to complete this example. So I hope that everything I explained was clear. If you have any questions, just leave them down below and I will see everyone in the next practice video.

Ch.15 - Chemical Kinetics

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Tro 6th Edition

Ch.15 - Chemical Kinetics

Problem 90c

Chapter 15, Problem 90c

The tabulated data were collected for this reaction at a certain temperature: X₂Y → 2 X + Y c. What is the concentration of X after 10.0 hours?

Verified step by step guidance

Determine the rate law for the reaction. This involves understanding how the concentration of reactants affects the rate of the reaction.

Use the integrated rate law that corresponds to the order of the reaction. For example, if it's a first-order reaction, use the first-order integrated rate law: \( [A] = [A]_0 e^{-kt} \).

Identify the initial concentration of X, \([X]_0\), from the data provided.

Calculate the rate constant \(k\) using the data provided and the appropriate rate law.

Substitute the values of \([X]_0\), \(k\), and \(t = 10.0\) hours into the integrated rate law to find the concentration of X after 10.0 hours.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Chemical Reaction Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. In the given reaction, X<sub>2</sub>Y decomposes into 2 moles of X and 1 mole of Y, indicating the molar relationships between the substances. Understanding these ratios is essential for determining the concentration of products formed over time.

Concentration and Molarity

Concentration refers to the amount of a substance in a given volume of solution, commonly expressed in molarity (moles per liter). To find the concentration of X after a specified time, one must consider the initial concentration of reactants and how they change as the reaction proceeds. This concept is crucial for quantifying the amount of X produced after 10.0 hours.

Reaction Kinetics

Reaction kinetics studies the rates of chemical reactions and the factors affecting them. The time factor in the question (10.0 hours) is significant, as it influences how much of the reactants have converted into products. Understanding the kinetics of the reaction helps predict the concentration of X at a specific time point.