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Rate of Reaction
Concepts
The concentration-time plots showed that each species in the reaction has its own rate of change in concentration. The reactants have a negative slope, because they are being consumed in the reaction. Products have a positive slope, because they are being formed in the reaction. For the hypothetical example reaction

A + 2 B   →   3 C

the stoichiometric coefficient for species B is twice that of species A; thus the concentration of B will decline twice as fast as that of species A. Similarly, the concentration of species C increases three times as fast as the concentration of A decreases.

Conceptually there should be a single, unambiguous rate for a reaction. How might such a rate be defined given the highly varied rates of change for the various species in the reaction?
The rate of reaction, r, is defined to be the slope of the concentration-time plot for a species divided by the stoichiometric coefficient of that species. Additionally, if the species is a reactant, the negative value of the slope is used, because the slope is negative and a positive rate is desired. For the example shown above

rate of reaction = r =-d [A] /dt = -d[B]/2dt= - d[C]/3dt

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