5.

The following concentration vs. time data were obtained for the irreversible liquid phase reaction in a batch reactor at constant temperature:
$$
A \stackrel{k}{\rightarrow} 2 \mathrm{~B}
$$
\begin{tabular}{|c|c|}
\hline Time (s) & Concentration $(\mathrm{mol} / \mathrm{L})$ \
\hline 0 & 5.1 \
\hline 36 & 4.0 \
\hline 72 & 3.2 \
\hline 108 & 2.6 \
\hline 144 & 2.1 \
\hline 180 & 1.8 \
\hline 234 & 1.4 \
\hline 324 & 0.9 \
\hline 468 & 0.6 \
\hline 576 & 0.4 \
\hline
\end{tabular}
a) Apply an appropriate method to find the rate law for the above reaction. Justify and explain your method chosen (max 100 words).
b) Using your rate law and an initial reactor composition of only species $A$ at a concentration of $(2000+(z \times 100)) \mathrm{molm}^{-3}$ calculate the fractional conversion of $A$ and the composition of the reactor after $1 \mathrm{~min}$. Assume that no side reactions occur and the same constant temperature was used.
Here
$z=$ the 4 th digit of your URN

Question

5.

The following concentration vs. time data were obtained for the irreversible liquid phase reaction in a batch reactor at constant temperature:
$$
A \stackrel{k}{\rightarrow} 2 \mathrm{~B}
$$
\begin{tabular}{|c|c|}
\hline Time (s) & Concentration $(\mathrm{mol} / \mathrm{L})$ \
\hline 0 & 5.1 \
\hline 36 & 4.0 \
\hline 72 & 3.2 \
\hline 108 & 2.6 \
\hline 144 & 2.1 \
\hline 180 & 1.8 \
\hline 234 & 1.4 \
\hline 324 & 0.9 \
\hline 468 & 0.6 \
\hline 576 & 0.4 \
\hline
\end{tabular}
a) Apply an appropriate method to find the rate law for the above reaction. Justify and explain your method chosen (max 100 words).
b) Using your rate law and an initial reactor composition of only species $A$ at a concentration of $(2000+(z \times 100)) \mathrm{molm}^{-3}$ calculate the fractional conversion of $A$ and the composition of the reactor after $1 \mathrm{~min}$. Assume that no side reactions occur and the same constant temperature was used.
Here
$z=$ the 4 th digit of your URN

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Determine the order of the reaction**: To find the rate law, we can use the method of initial rates or integrate the rate law. Given the data, we can plot concentration vs. time and look for a pattern that matches zero, first, or second-order kinetics. ‖ ‖ 2 ⋮ **Plot and analyze data**: By plotting the given data, we can determine if the plot of concentration vs. time, ln(concentration) vs. time, or 1/concentration vs. time gives a straight line, which would indicate zero, first, or second-order kinetics, respectively. ‖ ‖ 3 ⋮ **Calculate the rate constant**: Once the order is determined, we can use the slope of the appropriate plot to calculate the rate constant $k$. ‖ ‖ 4 ⋮ **Determine the fractional conversion**: The fractional conversion of A after 1 minute can be calculated using the rate law and the initial concentration. The fractional conversion $X$ is given by $X = \frac{[A]_0 - [A]}{[A]_0}$, where $[A]_0$ is the initial concentration and $[A]$ is the concentration after 1 minute. ‖ ‖ 5 ⋮ **Calculate the composition of the reactor**: Using the fractional conversion and the stoichiometry of the reaction, we can calculate the composition of the reactor after 1 minute. For every mole of A that reacts, 2 moles of B are formed. ‖ ∻1 Answer∻ ⚹ The rate law and the rate constant need to be determined by analyzing the concentration vs. time data. The fractional conversion and the composition of the reactor can then be calculated using the rate law and the initial concentration. ⚹ ∻Key Concept∻ ⚹ Determining the rate law involves analyzing how the concentration of reactants changes over time and finding a mathematical relationship that describes this change. ⚹ ∻Explanation∻ ⚹ The rate law expresses the rate of a chemical reaction in terms of the concentration of reactants. By analyzing the given data, we can determine the order of the reaction and calculate the rate constant, which can then be used to find the fractional conversion and the composition of the reactor after a certain time. ⚹◊What is the overall order of the reaction A → 2B based on the given concentration vs. time data?⍭ Generate me a similar question◊

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