Cyclobutane can decompose to form ethylene: C4 HB(g) ⟶2 C2 H4( g) The cyclobutane concentration

step 1 In this problem, it describes the reaction of the decomposition of cyclobutane to ethylene. It s

Cyclobutane can decompose to form ethylene: C4 HB(g) ⟶2 C2...

Cyclobutane can decompose to form ethylene: $$ \mathrm{C}_{4} \mathrm{H}_{\mathrm{B}}(\mathrm{g}) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g}) $$ The cyclobutane concentration can be measured as a function of time by mass spectrometry (a graph follows). (a) Write an expression for the rate of reaction in terms of a changing concentration. (b) Calculate the average rate of reaction between $10 .$ and 30. s. (c) Calculate the instantaneous rate of reaction after $20 . \mathrm{s}$. (d) Calculate the initial rate of reaction. (e) Calculate the instantaneous rate of formation of ethylene $40 .$ s after the start of the reaction.

Cyclobutane can decompose to form ethylene:
$$
\mathrm{C}_{4} \mathrm{H}_{\mathrm{B}}(\mathrm{g}) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})
$$
The cyclobutane concentration can be measured as a function of time by mass spectrometry (a graph follows).
(a) Write an expression for the rate of reaction in terms of a changing concentration.
(b) Calculate the average rate of reaction between $10 .$ and
30. s.
(c) Calculate the instantaneous rate of reaction after $20 . \mathrm{s}$.
(d) Calculate the initial rate of reaction.
(e) Calculate the instantaneous rate of formation of ethylene $40 .$ s after the start of the reaction.

Key Concepts

Graphical Analysis in Kinetics

Graphical analysis involves plotting concentration versus time data to visually interpret and calculate reaction rates. By analyzing the graph, one can determine average rates over intervals and approximate instantaneous rates using the slope of the curve, making it a practical method for understanding kinetic behavior in experimental settings.

Reaction Stoichiometry

Stoichiometry in reaction kinetics is critical for relating the rate of change in reactant concentrations to the rate of formation of products. It involves using the coefficients from a balanced chemical reaction to ensure the calculated rates accurately reflect the consumption and production patterns dictated by the reaction's overall equation.

Instantaneous Rate of Reaction

This concept refers to the reaction rate at a specific moment in time and is determined by taking the derivative of the concentration with respect to time. It is closely associated with the slope of the tangent to a concentration versus time graph at the point of interest and gives a precise measure of reaction speed at that particular instant.

Average Rate of Reaction

The average rate of reaction is calculated by taking the difference between concentrations at two distinct time points and dividing by the time interval between them. This measurement provides an overall estimate of the reaction speed over a specified period, summarizing the net change in concentration during that interval.

Rate of Reaction Expression

This concept involves quantifying how fast the concentration of a reactant decreases or a product increases over time. It is generally expressed as the change in concentration divided by the change in time (?[Concentration]/?t for average rates or d[Concentration]/dt for instantaneous rates), with attention to the sign convention based on whether a species is being consumed or produced.

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