# Differential Rate Laws

Just a summary of the differential rate law

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Helena Bonici Chemistry 04/07/2011
12EA2Kinetics
DIFFERENTIAL RATE LAWS
A rate law is a mathematical equation that describes the progress of the reaction.
It is not possible to predict the rate law from the overall chemical equation.
There are two forms of a rate law for chemical kinetics: the differential rate law and the integrated
rate law.
The differential rate law relates the rate of reaction to the concentrations of the various species in the
system.
Differential rate laws can take on many different forms, especially for complicated chemical reactions.
However, most chemical reactions obey one of three differential rate laws. Each rate law contains a
constant, k, called the rate constant.
For a zero-order reaction, the rate of reaction is a constant. When the limiting reactant is completely
consumed, the reaction abruptly stops.
Differential Rate Law: r=k
The rate constant, k, has units of mole L-1 sec-1.
For a first-order reaction, the rate of reaction is directly proportional to the concentration of one of
the reactants.
Differential Rate Law: r = k [A]
The rate constant, k, has units of sec-1.
For a second-order reaction, the rate of reaction is directly proportional to the square of the
concentration of one of the reactants.
Differential Rate Law: r = k [A]2
The rate constant, k, has units of L mole-1 sec-1.
For a zero-order reaction (red line), the rate of reaction is constant as the reaction progresses.
For a first-order reaction (green line), the rate of reaction is directly proportional to the
concentration. As the reactant is consumed during the reaction, the concentration drops and so
does the rate of reaction.
For a second-order reaction (blue line), the rate of reaction increases with the square of the
concentration, producing an upward curving line in the rate-concentration plot. For this type of

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Helena Bonici Chemistry 04/07/2011
12EA2Kinetics
reaction, the rate of reaction decreases rapidly (faster than linearly) as the concentration of the