Themes > Science > Chemistry > Miscellenous > Help file Index > kinetics > Rate constants and order of a reaction

The rate of a reaction can be expressed in terms of the concentrations of the various species. In general, the higher the concentrations of the reactants, the faster the reaction. For a general chemical reaction of the form

aA + bB -> products
the rate expression has the form
rate = k[A]m[B]n
• k is the rate constant for the reaction
• [A] is the concentration of A, [B] the concentration of B
• m is the order of the reaction with respect to A, n is the order of the reaction with respect to B
The overall order of the reaction is the sum of m and n.

If the power m or n is zero, then the reaction is 0th order in that species. m or n = 1 means the reaction is first order, 2 means 2nd order, and so on.

Example: a reaction has the rate expression rate = k[A]2[B]1. The reaction is 2nd order in A, 1st order in B and overall the reaction is third order.

To determine the order of a reaction from experimental data, simply vary the concentration of a species while holding everything else constant and look at the change in rate. If you double the concentration of A and the reaction rate doubles, then the reaction is first order; if the rate quadruples, then the reaction is 2nd order and so on. To see this, consider a general reaction of the form above and vary the concentration of [A] while keeping [B] constant

rate1 = k[A]12[B]1
rate2 = k[A]22[B]1
Divide the 2nd rate expression by the first: [B] doesn't change so it will cancel
rate2/rate1 = ([A]2/[A]1)m
The same method can be used to find the order of B by varying [B] and holding [A] constant.

Example: Given the following data, what is the rate expression for the reaction between hydroxide ion and chlorine dioxide?

2ClO2(aq) + 2OH-(aq) -> ClO3-(aq) + ClO2-(aq) + H2O

 [ClO2] (M) [OH-] (M) Rate (mol/L*s) 0.010 0.030 6.00*10-4 0.010 0.075 1.50*10-3 0.055 0.030 1.82*10-2

Solution: In the first and third reactions, the concentration of chlorine dioxide is varied while holding the concentration of hydroxide constant. In the first and second, hydroxide is varied while holding chlorine dioxide constant. To determine the order of the reaction in chlorine dioxide, divide the rate expression for the third experiment by the first.
• rate3/rate1 = ([ClO2]3/[ClO2]1)m
• 1.82*10-2/6.00*10-4 = (0.055/0.010)m
• 30.3 = (5.5)m
By inspection, m = 2. The reaction is 2nd order in ClO2

For hydroxide, do the same thing with the first and second reactions

• rate2/rate1 = ([OH-]2/[OH-]1)n
• 1.50*10-3/6.00*10-4 = (0.075/0.030)n
• 2.5 = (2.5)n
By inspection, n = 1

The overall rate expression is therefore

rate = k[ClO2]2[OH-]

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