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# Order of Reaction

## Describe the kinetic characteristics of a first-order reaction

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Order of Reaction

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### Order of Reaction

In the reaction AB\begin{align*}A \rightarrow B\end{align*}, the rate of the reaction is directly proportional to the concentration of A\begin{align*}A\end{align*} raised to the first power. That is to say, [A]=[A]1\begin{align*}[A]=[A]^1\end{align*}. A first-order reaction is a reaction in which the rate is proportional to the concentration of only one reactant. As a first-order reaction proceeds, the rate of reaction decreases because the concentration of the reactant decreases (see Figure below). The graph of concentration versus time is curved. The reaction rate (Δ[A]Δt)\begin{align*} \left(\frac{\Delta [A]}{\Delta t} \right)\end{align*} can be determined graphically by the slope of a tangent to the curve at any point. The rate of the reaction at the time shown with the red triangle is given by:

rate=[A]final[A]initialΔt=0.35 M0.63 M3.0 s1.0 s=0.14 M/s\begin{align*}\text{rate}=-\frac{[A]_{\text{final}}-[A]_{\text{initial}}}{\Delta t}=-\frac{0.35 \text{ M} - 0.63 \text{ M}}{3.0 \text{ s} - 1.0 \text{ s}}=0.14 \text{ M/s}\end{align*}

Credit: CK-12 Foundation - Christopher Auyeung

This graph shows how the concentration of a reactant changes as a reaction proceeds. The rate of the reaction is determined at any point by measuring the slope of a tangent to the curve.[Figure2]

The rates of some reactions depend on the concentrations of more than one reactant. Consider a reaction in which a molecule of A\begin{align*}A\end{align*} collides with a molecule of B\begin{align*}B\end{align*} to form product C\begin{align*}C\end{align*}.

A+BC\begin{align*}A+B \rightarrow C\end{align*}

Doubling the concentration of A\begin{align*}A\end{align*} alone would double the reaction rate. Likewise, doubling the concentration of B\begin{align*}B\end{align*} alone would also double the rate. The rate law must reflect the rate dependence on both reactants.

rate=k[A][B]\begin{align*}\text{rate}=k[A][B]\end{align*}

This reaction is said to be first order with respect to A\begin{align*}A\end{align*} and first order with respect to B\begin{align*}B\end{align*}. Overall, it is a second-order reaction. The rate law and the order of a reaction must be determined experimentally.

### Summary

• A first-order reaction is described.

### Review

1. What is a first-order reaction?
2. How is the instantaneous rate determined?
3. How do we determine rate law and reaction order?

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