The reaction of nitric oxide with hydrogen at $1280^{\circ} \mathrm{C}$ is
$$
2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)
$$

From the following data collected at this temperature, determine (a) the rate law, (b) the rate constant, and (c) the rate of the reaction when $[\mathrm{NO}]=12.0 \times 10^{-3} \mathrm{M}$ and
$$
\left[\mathrm{H}_{2}\right]=6.0 \times 10^{-3} \mathrm{M} \text {. }
$$
\begin{tabular}{cccc}
Experiment & {$[\mathbf{N O}](M)$} & {$\left[\mathbf{H}_{2}\right](M)$} & Initial Rate $(M / \mathbf{s})$ \
\hline 1 & $5.0 \times 10^{-3}$ & $2.0 \times 10^{-3}$ & $1.3 \times 10^{-5}$ \
2 & $10.0 \times 10^{-3}$ & $2.0 \times 10^{-3}$ & $5.0 \times 10^{-5}$ \
3 & $10.0 \times 10^{-3}$ & $4.0 \times 10^{-3}$ & $10.0 \times 10^{-5}$
\end{tabular}

Question

The reaction of nitric oxide with hydrogen at $1280^{\circ} \mathrm{C}$ is
$$
2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)
$$

From the following data collected at this temperature, determine (a) the rate law, (b) the rate constant, and (c) the rate of the reaction when $[\mathrm{NO}]=12.0 \times 10^{-3} \mathrm{M}$ and
$$
\left[\mathrm{H}_{2}\right]=6.0 \times 10^{-3} \mathrm{M} \text {. }
$$
\begin{tabular}{cccc} 
Experiment & {$[\mathbf{N O}](M)$} & {$\left[\mathbf{H}_{2}\right](M)$} & Initial Rate $(M / \mathbf{s})$ \
\hline 1 & $5.0 \times 10^{-3}$ & $2.0 \times 10^{-3}$ & $1.3 \times 10^{-5}$ \
2 & $10.0 \times 10^{-3}$ & $2.0 \times 10^{-3}$ & $5.0 \times 10^{-5}$ \
3 & $10.0 \times 10^{-3}$ & $4.0 \times 10^{-3}$ & $10.0 \times 10^{-5}$
\end{tabular}

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Determine the order with respect to NO**: Compare experiments 1 and 2 where the concentration of $\mathrm{H_2}$ is constant. Calculate the rate order with respect to $\mathrm{NO}$ by using the initial rates and concentrations of $\mathrm{NO}$. ‖ ‖ 2 ⋮ **Determine the order with respect to H₂**: Compare experiments 2 and 3 where the concentration of $\mathrm{NO}$ is constant. Calculate the rate order with respect to $\mathrm{H_2}$ by using the initial rates and concentrations of $\mathrm{H_2}$. ‖ ‖ 3 ⋮ **Write the rate law**: Using the orders determined in steps 1 and 2, write the rate law expression. ‖ ‖ 4 ⋮ **Calculate the rate constant (k)**: Use the given rate constant value to confirm the rate law. ‖ ‖ 5 ⋮ **Calculate the rate of the reaction**: Use the rate law and the given concentrations of $\mathrm{NO}$ and $\mathrm{H_2}$ to calculate the rate of the reaction. ‖ ∻1 Answer∻ ⚹ The rate law is Rate = $k[\mathrm{NO}]^2[\mathrm{H_2}]$ ⚹ ∻2 Answer∻ ⚹ The rate constant (k) is $6.0 \times 10^3 \, \mathrm{M^{-2}s^{-1}}$ ⚹ ∻3 Answer∻ ⚹ The rate of the reaction is $4.32 \times 10^{-4} \, \mathrm{M/s}$ ⚹ ∻Key Concept∻ ⚹ The rate law for a reaction relates the rate of the reaction to the concentrations of the reactants and includes a rate constant (k) and reaction orders (m and n). ⚹ ∻Explanation∻ ⚹ The rate law is determined by comparing the initial rates and reactant concentrations from different experiments. The rate constant is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants raised to their respective orders in the rate law. ⚹◊What are the orders of the reaction with respect to nitric oxide and hydrogen in the rate law equation provided?⍭ Generate me a similar question◊

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