The following data were collected for the reaction of cyclobutane, C4 H8(g), to form ethylene, C

The following data were collected for the reaction of...

The following data were collected for the reaction of cyclobutane, $\mathrm{C}_{4} \mathrm{H}_{8}(g)$, to form ethylene, $\mathrm{C}_{2} \mathrm{H}_{4}(g)$. Make a graph of concentration versus time for the formation of $\mathrm{C}_{2} \mathrm{H}_{4}$ and the decomposition of $\mathrm{C}_{4} \mathrm{H}_{8}$ on the same graph. What are the rates of formation of $\mathrm{C}_{2} \mathrm{H}_{4}$ at $t=1.00 \times 10^{3} \mathrm{~s}$ and $t=9.00 \times 10^{3} \mathrm{~s}$, and the rates of decomposition of $\mathrm{C}_{4} \mathrm{H}_{8}$ at $t=1.00 \times 10^{3} \mathrm{~s}$ and $t=9.00$ $\times 10^{3} s$ ? What can be said about the relationship between the values of the rates of formation and decomposition?

The following data were collected for the reaction of cyclobutane, $\mathrm{C}_{4} \mathrm{H}_{8}(g)$, to form ethylene, $\mathrm{C}_{2} \mathrm{H}_{4}(g)$. Make a graph of concentration versus time for the formation of $\mathrm{C}_{2} \mathrm{H}_{4}$ and the decomposition of $\mathrm{C}_{4} \mathrm{H}_{8}$ on the same graph. What are the rates of formation of $\mathrm{C}_{2} \mathrm{H}_{4}$ at $t=1.00 \times 10^{3} \mathrm{~s}$ and $t=9.00 \times 10^{3} \mathrm{~s}$, and the rates of
decomposition of $\mathrm{C}_{4} \mathrm{H}_{8}$ at $t=1.00 \times 10^{3} \mathrm{~s}$ and $t=9.00$
$\times 10^{3} s$ ? What can be said about the relationship between the values of the rates of formation and decomposition?

Key Concepts

Data Analysis in Chemical Kinetics

Analyzing experimental kinetic data often involves constructing graphs, calculating slopes to approximate the instantaneous rates at particular time points, and comparing these rates to deduce mechanistic information. This concept emphasizes the techniques used to interpret time-dependent concentration data to reveal the underlying reaction dynamics.

Stoichiometric Relationships

Stoichiometric relationships in a chemical reaction indicate the fixed proportions in which reactants are consumed and products are formed. These relationships are crucial for relating the rates of change of different species; for example, the rate of formation of a product is directly related to the rate of decomposition of a reactant according to their stoichiometric coefficients.

Concentration vs Time Graph

This graph plots the concentration of reactants and products against time, allowing one to visually analyze the dynamics of a chemical reaction. It helps in identifying key features such as the rate at which concentrations change, points of maximum or minimum concentrations, and patterns that might indicate equilibrium or steady-state behavior.

Instantaneous Rate of Reaction

The instantaneous rate is defined as the rate at which the concentration of a reactant or product changes at a specific moment in time. It is mathematically represented as the derivative of concentration with respect to time (d[Species]/dt). This concept is key in determining how fast a reaction is proceeding at any given point on the concentration versus time graph.

Reaction Kinetics

Reaction kinetics is the study of the rates of chemical reactions and the factors that affect them. It involves analyzing how concentrations of reactants and products change over time, determining rate laws, and understanding the mechanisms by which reactions occur. This subject underlies the methods used to estimate reaction rates from experimental data.

Transcript

00:01 So in this question, we need to find the rate of formation and decomposition of the reactants and products for the reaction of psychobutane to form ethylene.

00:19 So we're given the data as time and minutes and malarity of the reactant.

00:28 So for this problem, we need to change the time to seconds because we're.

00:34 Trying to find the rates of formation and decomposition at time is equal to 1 ,000 second and 9 ,000 seconds.

00:43 You can see from the balanced chemical reaction, one mole of reaction gives two moles of product.

00:48 So for every one mole of reacting use up, two moles of product are formed.

00:52 The rate of formation of a product is therefore going to be twice the rate of decomposition of the reactant.

01:01 So if we find the rate of decomposition, we can find the rate of formation.

01:06 So here is the graph, if we just graph the data based off of the time in seconds or the time in minutes.

01:21 So here i've already converted the x -axis to seconds, but if you graph it in minutes, it should look similar.

01:31 And how i got the graph for the product was that since you know that one mole of reacting gives two moles of the product, we're going to, at each time, subtract the molarity of the reactant from the initial molarity, and this difference is going to multiply by two, and that's going to give you the molarity of the product.

02:01 Because basically, for example, at time is equal to 4 ,000 minutes, we're going to take the initial molarity of c4h8, and we're going to subtract the molarity at that time.

02:17 And then the difference needs to be multiplied by two because for every one mole of reactant, we get two moles of products, and then that is going to equal the molarity of the product that is formed at time is equal to 4 ,000 minutes.

02:35 So then we can just convert time from minutes to seconds by multiplying by 60.

02:48 And that changes our units on the x -axis.

02:51 So you can see that this is a bit crowded...

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