# 18.9: Order of Reaction

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

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

Figure 18.9.1: 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 $$\ce{A}$$ collides with a molecule of $$\ce{B}$$ to form product $$\ce{C}$$.

$\ce{A} + \ce{B} \rightarrow \ce{C}$

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

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

This reaction is said to be first order with respect to $$\ce{A}$$ and first order with respect to $$\ce{B}$$. 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.

### Contributors

• CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.