# D32.2 Relative Rates of Reaction

The rate of a reaction can be expressed in terms of the change in concentration of any reactant or product, and therefore depends on the stoichiometry of the reaction. Let’s use the ammonia decomposition reaction as an example:

_{3}(

*g*) ⟶ N

_{2}(

*g*) + 3 H

_{2}(

*g*)

From the balanced reaction, we can see that one N_{2} molecule is produced for every two NH_{3} molecules that have reacted. Therefore, the formation of N_{2} is half as fast as disappearance of ammonia:

The negative sign accounts for the fact that NH_{3 }(reactant) concentration is decreasing while N_{2 }(product) concentration is increasing. The fraction ½ accounts for the stoichiometry.

Similarly, because 3 mol H_{2} forms during the time required for formation of 1 mol N_{2}:

The concentrations vs. time graphs for this reaction is shown below. At any time, the instantaneous rates for reactants and products are related by the reaction stoichiometry. For example, at 500 s, the rate of H_{2} production is three times greater than that for N_{2} production.

The rate of a reaction is therefore defined by taking the change in concentration per unit time of a reactant or a product and multiplying by the reciprocal of the stoichiometric coefficient for that reactant or product. The reaction rate determined this way is the same regardless of which reactant or product is measured during an experiment. For a generic reaction:

*a*A +

*b*B →

*c*C +

*d*D

where lower-case letters are stoichiometric coefficients and upper-case letters represent chemical formulas, the rate of the reaction is:

**Exercise: Definition of Reaction Rate
**

**Exercise: Reaction Rate and Stoichiometry
**

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