In the year 1864, chemists Cato Maximilian Guldberg and Peter Waage formulated the law of speed, which proposes that the speed of a chemical reaction is determined exclusively by the reactants of that reaction.
the law of speed is stated or represented by a mathematical expression that obtains the product of the concentrations in mol/L of the reactants, raised to their respective coefficients (a, b) stoichiometric (balancing values) with a constant (k).
v = k.[reagent 1]The.[reagent 2]B
To build the expression referring to law of speed, it is essential that we know whether the reaction is elementary (processed in one step) or non-elementary (which is processed in several steps).
Velocity Law for Elementary Reactions
For reactions that proceed in a single step, the expression of law of speed uses the components (reactants and their coefficients) of the equation. Example:
1 CH4(g) + 2 O2 → CO2 + 2 H2O
In this elemental reaction, we have the reactants methane (CH4, with coefficient 1) and oxygen (O2, with the coefficient 2). Thus, the expression of the law of speed will be:
v = k.[CH4]1.[O2]2
Velocity law for non-elementary reactions
As non-elementary reactions occur in several steps, determining the expression of law of speed it depends on the analysis of the influence of each reagent on the speed of each step. For this, the exercises or the texts provide a table containing concentration and speed values for each step, as in the example below:
a A + b B + c C → d D
As the table has four lines, therefore, it is a non-elemental reaction that is processed in four steps, and its reactants are A, B and C. Now, to know the coefficients they have, we must perform the following steps:
1st Step: determine the order of reagent A.
For that, we must choose two stages in which the concentration of A changes, and that of B and C do not change. Thus, the chosen steps are the first and second, in which we have the following changes:
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- Concentration of X: doubles in value, as it goes from 2 to 4;
- Speed: quadruples in value as it goes from 0.5 to 2.
Thus, the analysis should be:
2.[X] = 4.v
Putting the two values on the same base:
2.[X] = 22.v
We have that the difference is the exponent 2, so the order of A will be 2.
2nd Step: Determine order of reagent B.
For this, we must choose two stages in which the concentration of B changes, and that of A and C do not change. Thus, the chosen steps are the 2The and at 3The, in which we have the following changes:
- Y concentration: doubles in value, as it goes from 3 to 6;
- Speed: does not change its value, as it was 2 and remains 2.
Thus, the analysis should be:
2.[X] = 2.v
Since the two values are already on the same basis, and the change in concentration does not change the velocity, then the order of B will be 0.
3rd Step: Determine order of reagent C.
For this, we must choose two stages in which the concentration of C changes, and that of X does not change. The chosen steps are the 3The and at 4The, in which we have the following changes:
- Y concentration: doubles in value, as it goes from 1 to 2;
- Velocity: otfolds the value, as it goes from 2 to 16.
Thus, the analysis should be:
2.[X] = 16.v
Putting the two values on the same base:
2.[X] = 24.v
We have that the difference is the exponent 2, so the order of C will be 4.
Step 4: Assemble the velocity expression.
To assemble this velocity expression, just multiply the concentrations of the reactants, raised in their respective orders, by the constant (k):
v = k.[A]2.[B]0.[Ç]4
or
v = k.[A]2..1.[C]4
v = k.[A]2..[Ç]4
By Me. Diogo Lopes
Would you like to reference this text in a school or academic work? Look:
DAYS, Diogo Lopes. "What is the law of speed?"; Brazil School. Available in: https://brasilescola.uol.com.br/o-que-e/quimica/o-que-e-lei-da-velocidade.htm. Accessed on June 28, 2021.
