Rate Law Equation: Constant & Reaction Order

What is the Rate Law Equation?

Whether someone is studying a chemical reaction in chemistry, molecular biology, or biochemistry, it is important to understand not just what the starting reactants and ending products are, but how the reaction is advancing over time. Simply knowing that a reaction is occurring is often not very useful for solving problems involving chemical reactions.

For instance, one reaction might be quick and occur in seconds while another could be slower and take hours, days, or months to occur. What if the chemical reaction had some impact on the environment? Knowing how quickly the reaction occurs over time would provide extremely valuable data. In any chemical reaction, rate means how fast the reaction is moving over time. The rate of a reaction will differ based on factors like the identity of the reactants, the concentration of each reactant, and the temperature at which the reaction is occurring.

There is a mathematical formula called the rate law equation which allows the rate of a reaction to be calculated. An example of how to write the rate law equation (with reactants A and B) is as follows: {eq}r = k[A]^x[B]^y {/eq} where the equation components are:

• Rate law, which is the entire equation, with rate represented by r
• Rate law constant, represented by k
• Order of reaction, represented by exponents x and y
• Molar concentration of the reactants, represented by the letters A, B, etc., in brackets.

Rate Law

The terms rate law and rate law equation are synonymous and interchangeable with each other. Rate law, with rate represented by the symbol r, represents the speed of a reaction per a set unit of time. The rate of reaction definition is always expressed as some concentration (e.g., molarity, or M, which is mol/L) over a unit of time (e.g., seconds, or s), with the rate of reaction units written as concentration/time, e.g., M/s. How to determine rate law requires knowledge of the identity of the reactants, the order of reactants, and the rate law constant.

Order of Reaction

In rate law, the order of reaction or reaction order refers to the concentration of reactants, expressed as exponents (e.g., x and y). How does the order of a reaction impact rate? The concentration for each reactant, A and B, is multiplied by the power of the reaction order.

• For reactants A and B, where x = 1 and y = 1, the rate law is expressed as {eq}r = k[A][B] {/eq}

• For reactants A and B, where x = 2 and y = 1, the rate law is expressed as {eq}r = k[A]^2[B] {/eq}

• For reactants A and B, where x = 1 and y = 2, the rate law is expressed as {eq}r = k[A][B]^2 {/eq}

How to Determine Order of Reaction:

The reaction order for a chemical equation is the sum of exponents for every reactant in the chemical equation. So, for {eq}r = k[A][B]^2 {/eq} the reaction order is 3, because x = 1 and y = 2, with x + y = 3. In this case, reactant A is first-order, reactant B is second-order, and the entire reaction is third-order. The types of order reactions and their definitions include:

• First-order reactions: happens when the sum of all exponents of the reactants equals 1, e.g., {eq}r = k[A] {/eq}

• Second-order reactions: happens when the sum of all exponents of the reactants equals 2, e.g., {eq}r = k[A][B] {/eq}

• Third-order reactions: Happens when the sum of all exponents of the reactants equals 3, e.g., {eq}r = k[A][B]^2 {/eq}

• Zero-order reactions: This happens only when the concentration of the reactants does not have any impact on the rate of the reaction.
• Pseudo-order reactions: This happens when the concentration of one of the reactants is not included in the reaction order for the equation. Pseudo-order reactions can be pseudo-zero or pseudo-first-order, e.g., where a second-order reaction acts as a first-order reaction, or a first-order reaction acts like a zero-order reaction.
• Complex reactions: Complex reactions are reactions with multiple steps.

How to Find Rate Constant?

Rate constant is a number that represents the relationship between reactant concentration and reaction rate in a particular chemical reaction at a set temperature. To find the value of the rate constant, k, which differs for each chemical reaction, experimental data is required. How to find rate constants for each reaction involves solving for k in the rate law equation and then plugging in values from experimental data.

An example of how to find the rate constant equation, where {eq}r = k[A][B]^2 {/eq}, for instance, is to solve for k, which gives {eq}k = \frac{r}{[A][B]^2} {/eq} as the rate constant equation. Because the concentrations of A and B are expressed in units of M and the units of k are expressed as M/s, the rate constant units for k is {eq}\frac{1}{M^2s} {/eq}. An example of how to find values for the order of a reaction, the rate constant, and rate law using experimental data is covered in the next section of this lesson.