C1. Consider a reaction between nitrous oxide and hydrogen that produces nitrogen and water.

The initial rates of the reaction have been observed experimentally for certain reactant concentrations given in the table
\begin{tabular}{|c|c|c|c|}
\hline \begin{tabular}{c}
Experime \
nt
\end{tabular} & \begin{tabular}{c}
$\mathrm{NO}$ \
Concentration \
$(\mathrm{mol} / \mathrm{L})$
\end{tabular} & \begin{tabular}{c}
$\mathrm{H}_{2}$ \
Concentration \
$(\mathrm{mol} / \mathrm{L})$
\end{tabular} & \begin{tabular}{c}
Rate of $\mathrm{N}_{2}$ \
formation \
$(\mathrm{mol} / \mathrm{L} / \mathrm{min})$
\end{tabular} \
\hline 1 & 6 & 1 & 18 \
\hline 2 & 6 & 2 & 36 \
\hline 3 & 1 & 6 & 3 \
\hline 4 & 2 & 6 & 12 \
\hline
\end{tabular}

Using an appropriate method, determine: (i) the order for each reactant, (ii) the overall rate equation, (iii) the overall order, and (iv) the rate constant.

Question

C1. Consider a reaction between nitrous oxide and hydrogen that produces nitrogen and water.

The initial rates of the reaction have been observed experimentally for certain reactant concentrations given in the table
\begin{tabular}{|c|c|c|c|}
\hline \begin{tabular}{c} 
Experime \
nt
\end{tabular} & \begin{tabular}{c}
$\mathrm{NO}$ \
Concentration \
$(\mathrm{mol} / \mathrm{L})$
\end{tabular} & \begin{tabular}{c}
$\mathrm{H}_{2}$ \
Concentration \
$(\mathrm{mol} / \mathrm{L})$
\end{tabular} & \begin{tabular}{c} 
Rate of $\mathrm{N}_{2}$ \
formation \
$(\mathrm{mol} / \mathrm{L} / \mathrm{min})$
\end{tabular} \
\hline 1 & 6 & 1 & 18 \
\hline 2 & 6 & 2 & 36 \
\hline 3 & 1 & 6 & 3 \
\hline 4 & 2 & 6 & 12 \
\hline
\end{tabular}

Using an appropriate method, determine: (i) the order for each reactant, (ii) the overall rate equation, (iii) the overall order, and (iv) the rate constant.

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Compare Experiments 1 and 2**: To determine the order of reaction with respect to $\mathrm{NO}$, we compare experiments 1 and 2 where the concentration of $\mathrm{H_2}$ changes while the concentration of $\mathrm{NO}$ remains constant. ‖ ‖ 2 ⋮ **Calculate the order for $\mathrm{H_2}$**: The rate of reaction doubles from 18 to 36 mol/L/min when the concentration of $\mathrm{H_2}$ is doubled from 1 to 2 mol/L. This indicates a first-order reaction with respect to $\mathrm{H_2}$. ‖ ‖ 3 ⋮ **Compare Experiments 3 and 4**: To determine the order of reaction with respect to $\mathrm{NO}$, we compare experiments 3 and 4 where the concentration of $\mathrm{H_2}$ is constant and the concentration of $\mathrm{NO}$ changes. ‖ ‖ 4 ⋮ **Calculate the order for $\mathrm{NO}$**: The rate of reaction quadruples from 3 to 12 mol/L/min when the concentration of $\mathrm{NO}$ is doubled from 1 to 2 mol/L. This indicates a second-order reaction with respect to $\mathrm{NO}$. ‖ ‖ 5 ⋮ **Write the rate equation**: With the orders determined, the rate equation can be written as $rate = k[\mathrm{NO}]^2[\mathrm{H_2}]$. ‖ ‖ 6 ⋮ **Determine the overall order**: The overall order of the reaction is the sum of the orders with respect to each reactant, which is $2 + 1 = 3$. ‖ ‖ 7 ⋮ **Calculate the rate constant $k$**: Using the rate equation and data from any experiment, we can solve for $k$. Using experiment 1, $18 = k[6]^2[1]$, we find $k = \frac{18}{36} = 0.5 \, \mathrm{L^2/mol^2/min}$. ‖ ∻1 Answer∻ ⚹ The order of the reaction for $\mathrm{NO}$ is 2, for $\mathrm{H_2}$ is 1, the overall rate equation is $rate = k[\mathrm{NO}]^2[\mathrm{H_2}]$, the overall order of the reaction is 3, and the rate constant $k$ is $0.5 \, \mathrm{L^2/mol^2/min}$. ⚹ ∻Key Concept∻ ⚹ Determining reaction order ⚹ ∻Explanation∻ ⚹ The reaction order is determined by observing how the rate of reaction changes with varying concentrations of reactants. ⚹ ∻Key Concept∻ ⚹ Rate equation and rate constant ⚹ ∻Explanation∻ ⚹ The rate equation relates the rate of reaction to the concentrations of reactants raised to their respective orders, and the rate constant is a proportionality constant in this equation. ⚹ ∻Key Concept∻ ⚹ Overall reaction order ⚹ ∻Explanation∻ ⚹ The overall reaction order is the sum of the orders with respect to each reactant in the rate equation. ⚹◊What is the rate equation for the reaction between nitrous oxide and hydrogen based on the experimental data provided?⍭ Generate me a similar question◊

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