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Complete Guide: How to Determine Rate Law and Rate Law Constant Using Experimental Data?

Rate Law is an equation that shows how the rate of the reaction is affected by the concentration of reactants


Rate Law Expression
Rate Law Expression

Overall order of the reaction is equal to the sum of the powers of the reactants in the rate law.


Let's take a look at an example of a rate law.




The reaction is second order with respect to NO2 and first order with respect to H2. The overall order of reaction is third (2+1 = 3).


How to determine the rate law from experimental data.


Problem: Determine the rate law for the following reaction

F2(g)+2ClO2(g) -> 2FClO2(g)




  1. Choose two experiments where the concentration of one of the reactants changes and the concentration of the other one stays the same.

  2. Write out the rate law equation for each experiment plugging the values from the table in.

  3. Divide one experiment over the other to find the power (order) of the reactant.

  4. Repeat with the other reactants until all orders are known


How to determine the rate law from experimental data
How to determine the rate law from experimental data

The rate is first order with respect to F2 and first order with respect to ClO2. The overall rate is second order (1+1).


Alternatively, if the numbers in the chart are easy, we can determine the orders without plugging numbers into the rate law.

For example, looking at the experiment 1 and 3, we notice that as the concentration of F2 doubles, the rate double as well. This means F2 must be to the first power.

Similarly, looking at the experiment 1 and 2, as the concentration of ClO2 quadruples, the rate quadruples as well. ClO2 must be to the first power.


Notes:

  • If the concentration changes but the rate stays the same, the power/order for that reactant must be zero (it doesn't affect the rate).

  • If the concentration doubles, but the rate quadruples, the power/order for the reactant must be 2. The order may also be other numbers including fractions and could be positive or negative.


How to determine the rate law constant (k)

After you found the rate law, you can use on the experiments given (you may choose any experiment) to plug in the values for the reactants and rate to solve for k. Let's find the rate constant for the problem above.


How to determine the rate law constant (k)
How to determine the rate law constant (k)

Note: Some professors ask students to find the rate constant for every experiment given and take their average.


How to determine the correct units for the rate constant k


rate constant (k) units for first, second, third and fourth order reactions
rate constant (k) units for first, second, third and fourth order reactions

Alternatively, you can plug in the units yourself and cancel to determine the units of the rate constant. The units for rate are M/s and the units for the concentrations of reactants are M.



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