Consider the reaction: C 4 H 8 ( g) → 2 C 2 H 4 ( g) The tabulated data were collected for the concentration of C 2 H 4 as a function of time: a. What is the average rate of the reaction between 0 and 10 s? Between 40 and 50 s?

Hey everyone in this example, we need to calculate the average rate for the reaction between zero and 10 seconds and then between 30 and 40 seconds based on the gathered data. So we have cycle hexane producing two moles of propane. And according to our chart we have the change in concentration of cyclo hexane at given times. So we want to first write out our rate expression where we would have our change in concentration of cycle hexen or cyclo hexane, sorry, divided by the change in time. Now, according to our given reaction, we have a coefficient of one in front of our cyclo hexane. So that's right here and we want this because it's a reactant and we're going to be losing this to produce our product protein to be negative. So we would have negative one. So for first the rate between 0.10 seconds we would say that we should have negative one times the final concentration of cyclo hexane in our numerator, which would occur at 10 seconds being according to the chart, 0.902 molar minus the initial concentration of cyclo hexane given in the chart at zero seconds being 1.0 molar. And then in our denominator we want to plug in the difference in time. So that would be according to the prompt from 10 seconds to final time minus the initial time. Zero seconds. And so what we would get here is a value equal to 9.8 times 10 to the negative third power. And we have units of polarity times inverse seconds since seconds are in the denominator. So this would be our first answer that we've calculated here for the rate between zero and 10 seconds. And then according to the prompt, we also need to find for the rate of cyclo hexane between 30 and 40 seconds. So what we would have is negative one. And then in our numerator we're focusing on the difference between 40 and 30 seconds. So we should have the final concentration which at 40 seconds 0.686 molar for cyclo hexane subtracted from the initial concentration of cyclo hexane at 30 seconds being 0.75 to moller. Then in a in the denominator we should have the difference in time. So according to the prompt that's calculated between the final time, 40 seconds minus the initial time being 30 seconds. And so what we would get here For our rate is a value of 6.6 times 10 to the negative third power. And we have units of molar itty times inverse seconds. And this would be our second answer for our rate of cyclo hexane between 30 and 40 seconds. So everything highlighted in yellow represents our final answers. I hope that everything I reviewed was clear. But if you have any questions, please leave them down below and I will see everyone in the next practice video

Ch.14 - Chemical Kinetics

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Tro 4th Edition

Ch.14 - Chemical Kinetics

Problem 31a

Chapter 14, Problem 31a

Consider the reaction: C₄H₈( g) → 2 C₂H₄( g) The tabulated data were collected for the concentration of C₂H₄ as a function of time: a. What is the average rate of the reaction between 0 and 10 s? Between 40 and 50 s?

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Determine the change in concentration of C_2H_4 between the given time intervals.

For the interval 0 to 10 s, calculate \( \Delta [C_2H_4] = [C_2H_4]_{10s} - [C_2H_4]_{0s} \).

For the interval 40 to 50 s, calculate \( \Delta [C_2H_4] = [C_2H_4]_{50s} - [C_2H_4]_{40s} \).

Calculate the time interval \( \Delta t \) for each case: \( \Delta t = t_{final} - t_{initial} \).

Use the formula for average rate of reaction: \( \text{Average Rate} = \frac{\Delta [C_2H_4]}{\Delta t} \) for each time interval.

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Key Concepts

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

Reaction Rate

The reaction rate is a measure of how quickly reactants are converted into products in a chemical reaction. It is typically expressed as the change in concentration of a reactant or product over a specific time interval. Understanding how to calculate the average rate involves determining the difference in concentration at two time points and dividing by the time elapsed.

Concentration

Concentration refers to the amount of a substance (solute) present in a given volume of solution or mixture. In the context of gas reactions, concentration can be expressed in terms of moles per liter (Molarity) or partial pressure. Monitoring changes in concentration over time is crucial for calculating reaction rates and understanding the dynamics of the reaction.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced based on the balanced chemical equation. In this reaction, the stoichiometry indicates that 4 moles of C4H8 produce 2 moles of C2H4, which is essential for understanding the relationship between the concentrations of the reactants and products.