Rate constant \( k = 4.5 \times 10^{-2}\ \mathrm{L^2\ mol^{-2}\ s^{-1}} \), then what is the order of reaction?
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Memorize these common units of rate constant: zero order \(=\mathrm{mol\ L^{-1}\ s^{-1}}\), first order \(=\mathrm{s^{-1}}\), second order \(=\mathrm{L\ mol^{-1}\ s^{-1}}\), and third order \(=\mathrm{L^2\ mol^{-2}\ s^{-1}}\).
Step 1: Understanding the Concept:
The units of the rate constant $k$ depend on the overall order of the reaction ($n$). Step 2: Formula Application:
The general unit for $k$ is $(\text{mol L}^{-1})^{1-n} \text{ s}^{-1}$. Step 3: Explanation:
The given unit is $\text{L}^2 \text{ mol}^{-2} \text{ s}^{-1}$, which can be rewritten as $(\text{mol L}^{-1})^{-2} \text{ s}^{-1}$.
Comparing the powers: $1 - n = -2$
$n = 1 + 2 = 3$. Step 4: Final Answer:
The reaction is of the 3rd order.