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The reaction rate is a quantity that defines how the concentration of a reactant or product changes with time. The rate is defined to be a positive number. If we consider a reaction such as

A + B -> C + D
we can ask how the concentration of A, B, C and D change over time. The average reaction rate is therefore the simple expression
average reaction rate = change in concentration/change in time
For example, in the above reaction the reaction rate expression can be written as
rate = D[C] /DT
Since the rate of production of C is the same as the rate of production of D (One molecule of D is produced when one molecule of C is produced), and is the negative of the change in A and B (For each molecule of C, one A and one B get used up.), we also have
rate = D[C] /DT = - D[D] /DT = -D[A] /DT = -D[B] /DT

For more complex reactions, we have to take into account the fact that some species are produced or used up faster than others: consider the reaction

2N2O5 -> 4NO2 + O2
In this reaction, NO2 is produced twice as fast as N2O5 is used up, and oxygen is produced only 1/2 as fast. Therefore the relationships between the rates of change for the various species is
-D[N2O5] = D[NO2/2] = D[O2]/0.5
The rate expression for this reaction is therefore
rate = -D[N2O5]/DT = D[NO2]/2DT = D[O2]/0.5DT
The graph below shows the various concentrations as a function of time:

Example: If we study the reaction of nitrogen and hydrogen gases to form ammonia, we find that the nitrogen is disappearing at a rate of 0.100 mol/L*min. What is the rate expression of the reaction and what is the rate of disappearance of hydrogen and appearence of ammonia?

N2 + 3H2 -> 2NH3

Solution: The nitrogen in this reaction is disappearing at a rate of 0.100 mol/L*min. The rate is therefore

rate = -D[N2]/DT = 0.100 mol/L*min
For the other species, 3 molecules of hydrogen are used for every molecule of nitrogen, and two molecules of ammonia are produced.
rate = -D[N2]/DT = -D[H2]/3DT = D[NH3]/2DT =0.100 mol/L*min
Therefore, the change in concentration for each species is
  • -D[H2]/3DT = 0.100 mol/L*min ---> D[H2]/DT = -0.300 mol/L*min
  • D[NH3]/2DT = 0.100 mol/L*min ---> D[NH3]/DT = 0.200 mol/L*min


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