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Order of Reaction

Describe the kinetic characteristics of a first-order reaction

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Order of Reaction

The damage caused by a forest fire is proportional to the amount of material to burn

Credit: Courtesy of Ramos Keith, US Fish and Wildlife Service
Source: http://commons.wikimedia.org/wiki/File:Big_tropical_forest_fire.jpg
License: CC BY-NC 3.0

How harmful are forest fires?

Forest fires cause extensive damage when they occur. Both plant and animal life are harmed during these events. The severity of a forest fire depends on how much plant life is available to burn – the more available dry plant material, the more serious the fire and the more rapidly it will spread.

Order of Reaction

In the reaction \begin{align*}A \rightarrow B\end{align*}, the rate of the reaction is directly proportional to the concentration of \begin{align*}A\end{align*} raised to the first power. That is to say, \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 \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:

\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*}

The instantaneous rate of a reaction can be measured by the slope of the tangent line at that point

Credit: CK-12 Foundation - Christopher Auyeung
License: CC BY-NC 3.0

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 \begin{align*}A\end{align*} collides with a molecule of \begin{align*}B\end{align*} to form product \begin{align*}C\end{align*}.

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

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

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

This reaction is said to be first order with respect to \begin{align*}A\end{align*} and first order with respect to \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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Image Attributions

  1. [1]^ Credit: Courtesy of Ramos Keith, US Fish and Wildlife Service; Source: http://commons.wikimedia.org/wiki/File:Big_tropical_forest_fire.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: CK-12 Foundation - Christopher Auyeung; License: CC BY-NC 3.0

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