3.
(a) In chemical reaction kinetics, state what is meant by
(i) rate of reaction
(ii) reaction order
(iii) rate constant
Illustrate your answer by referring to the general gas phase reaction $\mathrm{A}+\mathrm{B} ightarrow \mathrm{C}$
(b) Briefly, giving the relevant mathematical detail, describe two experimental methods for determining rate laws
(c) Cyclopropane isomerizes into propene when heated to $500^{\circ} \mathrm{C}$ in the gas phase. The extent of conversion for various initial pressures $\left(P_{0} ight)$ has been followed by allowing the reaction to proceed for a given time $(t)$ and then recording the final partial pressure $(P)$ of cyclopropane. The experimental data collected are:
\begin{tabular}{lcccccc}
$P_{0}(\mathrm{~Pa})$ & 20000 & 20000 & 30000 & 30000 & 50000 & 50000 \
$t(\mathrm{~s})$ & 100 & 200 & 100 & 200 & 100 & 200 \
$P(\mathrm{~Pa})$ & 18650 & 17300 & 27800 & 26000 & 46550 & 43300
\end{tabular}
(i) Using the data above, calculate the fractional conversion in each case and hence find the order of reaction with respect to cyclopropane.
(ii) What is the rate constant for the reaction under these conditions?
(iii) If you had data at a different temperature, how would you find the parameters in the Arrhenius expression for the rate constant?

Question

3.
(a) In chemical reaction kinetics, state what is meant by
(i) rate of reaction
(ii) reaction order
(iii) rate constant
Illustrate your answer by referring to the general gas phase reaction $\mathrm{A}+\mathrm{B} ightarrow \mathrm{C}$
(b) Briefly, giving the relevant mathematical detail, describe two experimental methods for determining rate laws
(c) Cyclopropane isomerizes into propene when heated to $500^{\circ} \mathrm{C}$ in the gas phase. The extent of conversion for various initial pressures $\left(P_{0}ight)$ has been followed by allowing the reaction to proceed for a given time $(t)$ and then recording the final partial pressure $(P)$ of cyclopropane. The experimental data collected are:
\begin{tabular}{lcccccc}
$P_{0}(\mathrm{~Pa})$ & 20000 & 20000 & 30000 & 30000 & 50000 & 50000 \
$t(\mathrm{~s})$ & 100 & 200 & 100 & 200 & 100 & 200 \
$P(\mathrm{~Pa})$ & 18650 & 17300 & 27800 & 26000 & 46550 & 43300
\end{tabular}
(i) Using the data above, calculate the fractional conversion in each case and hence find the order of reaction with respect to cyclopropane.
(ii) What is the rate constant for the reaction under these conditions?
(iii) If you had data at a different temperature, how would you find the parameters in the Arrhenius expression for the rate constant?

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Define rate of reaction**: The rate of reaction is the speed at which reactants are converted into products. For the reaction $\mathrm{A} + \mathrm{B} \rightarrow \mathrm{C}$, the rate can be expressed as the change in concentration of A or B (or C) with respect to time. ‖ ‖ 2 ⋮ **Define reaction order**: The reaction order is the exponent to which the concentration of a reactant is raised in the rate law. It indicates how the rate is affected by the concentration of that reactant. ‖ ‖ 3 ⋮ **Define rate constant**: The rate constant, $k$, is a proportionality constant in the rate law equation that relates the rate of reaction to the concentrations of reactants. It is specific to a particular reaction at a given temperature. ‖ ‖ 4 ⋮ **Experimental methods for determining rate laws**: Method 1: Initial rates method involves measuring the initial rate of reaction at various initial concentrations of reactants. Method 2: Integrated rate laws method uses the concentration of reactants or products as a function of time to determine the order of reaction. ‖ ‖ 5 ⋮ **Calculate fractional conversion**: Fractional conversion is calculated using the formula $\frac{P_0 - P}{P_0}$. Apply this formula to each set of data to find the fractional conversion. ‖ ‖ 6 ⋮ **Determine reaction order**: Plot the data appropriately (e.g., a plot of ln(conversion) vs. time for a first-order reaction) to determine the slope and thus the order of the reaction. ‖ ‖ 7 ⋮ **Calculate rate constant**: Once the order of reaction is known, use the appropriate integrated rate law to calculate the rate constant, $k$, from the slope of the plot. ‖ ‖ 8 ⋮ **Arrhenius expression parameters**: If data at a different temperature were available, plot ln($k$) versus $1/T$ (where $T$ is the temperature in Kelvin) to find the slope and intercept, which correspond to the activation energy and the frequency factor, respectively, in the Arrhenius equation. ‖ ∻a Answer∻ ⚹ (i) Rate of reaction: speed at which reactants turn into products. (ii) Reaction order: exponent of reactant concentration in rate law. (iii) Rate constant: proportionality constant in rate law. ⚹ ∻b Answer∻ ⚹ Initial rates method and integrated rate laws method are two experimental methods for determining rate laws. ⚹ ∻c Answer∻ ⚹ (i) Fractional conversions calculated. (ii) Rate constant determined using integrated rate law. (iii) Arrhenius parameters found using ln($k$) vs. $1/T$ plot. ⚹ ∻Key Concept∻ ⚹ The rate of reaction, reaction order, and rate constant are fundamental concepts in chemical kinetics that describe how fast a reaction occurs and how reactant concentrations affect the rate. ⚹ ∻Explanation∻ ⚹ The rate of reaction indicates the speed of a chemical reaction. The reaction order shows the dependence of the rate on reactant concentrations, and the rate constant is a unique value for each reaction at a given temperature, relating the rate to the concentrations. Experimental methods like initial rates and integrated rate laws help determine these values, and the Arrhenius equation relates the rate constant to temperature. ⚹◊What is the formula to calculate the rate of reaction in a chemical reaction⍭ Generate me a similar question◊

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