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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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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 $A \rightarrow B$ , the rate of the reaction is directly proportional to the concentration of  $A$ raised to the first power. That is to say, $[A]=[A]^1$ . 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 ( Figure below ). The graph of concentration versus time is curved. The reaction rate $\left(\frac{\Delta [A]}{\Delta t} \right)$ 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:

$\text{rate}=-\frac{[A]_{\text{final}}-[A]_{\text{initial}}}{\Delta t}=-\frac{0.35 \text{ M} - 0.63 \text{ M}}{3.0 \text{ s} - 1.0 \text{ s}}=0.14 \text{ M/s}$

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.

The rates of some reactions depend on the concentrations of more than one reactant. Consider a reaction in which a molecule of  $A$ collides with a molecule of  $B$ to form product $C$ .

$A+B \rightarrow C$

Doubling the concentration of  $A$ alone would double the reaction rate. Likewise, doubling the concentration of  $B$ alone would also double the rate. The rate law must reflect the rate dependence on both reactants.

$\text{rate}=k[A][B]$

This reaction is said to be first order with respect to  $A$ and first order with respect to $B$ . 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.

#### Practice

Read the material at the link below and answer the following questions:

1. What is a zero-order reaction?
2. What is a second-order reaction?
3. How is the order of a two-reactant reaction determined?

#### 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?