Core Concepts
In this article, we learn all about order of reaction, including its importance, its effect on the rate constant and rate law, and how to calculate it using kinetic data.
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What is Order of Reaction?
In chemistry, reactions can occur fast, slow, or anywhere in between. Chemists tend to characterize the kinetics of a reaction through a rate law. This rate law tends to depend on the concentrations of one or more reactants. The reaction rate equals the rate of product formation or reactant consumption, adjusted by stoichiometric coefficients.
aA + bB → cC + dD
Rate = k[A]n[B]m = ∆[C]/ct = ∆[D]/dt = -∆[A]/at = -∆[B]/bt
In rate laws, the reactant concentrations are raised to some power (n and m). Chemists call these values the reaction order, with respect to each reactant.
The sum of the two order reactant reaction orders yields the overall reaction order. The overall order of reaction has a lot of importance to chemists since it determines the reaction’s rate law and integrated rate law.
Notice that these reaction orders have no dependence on the stoichiometry of the reaction. As we explore in the next section, reaction order instead depends on the mechanism of the reaction. For instance, we can imagine that the above reaction is first-order with respect to reactant A and second-order with respect to reactant B, yielding a third-order reaction.
Rate=k[A]1[B]2
We can also imagine reactions that have a zeroth-order reactant. In such cases, the overall rate completely depends on the concentration of the other reactant or no reactant.
Rate1=k[A]1[B]0=k[A]1
Rate2=k[A]0[B]2=k[B]2
Rate3=k[A]0[B]0=k
In truth, reactions with an overall order of zero tend to be rare. However, chemists have found some examples, which tend to involve a catalyst or enzyme in much lower concentrations than the reactants. In these cases, the steady state approximation often applies. For instance, for all intents and purposes, the enzymatic degradation of ethanol to acetaldehyde has zeroth-order kinetics.
Reaction Order and Rate Constants
As you may have noticed, each rate law involves some constant “k”. Chemists call this value the rate constant, which serves to adjust reactant concentration values to equal the reaction rate. Most importantly, the rate constant adjusts the rate law’s units in order to yield a rate in molar per second (Ms-1).
To fulfill this, the units of the rate constant can vary depending on the overall order of reaction. For zeroth-order reactions, the rate constant has units of molar per second (Ms-1). In first-order reactions, the rate constant has units of “per second” (s-1). For second-order reactions, the rate constant has units of “per molar per second” (M-1s-1). For each successive reaction order, the power of the molar decreases by one.
Zeroth-Order: k → Units: (Ms-1) = Ms-1
First-Order: k[A] →Units: (s-1)(M) = Ms-1
Second-Order: k[A][B] →Units: (M-1s-1(M)(M) = Ms-1
Third-Order: k[A][B]2 → Units: (M-2s-1)(M)(M2) = Ms-1
How to find Order of Reaction
The methods for finding reaction order, overall and for given reactants, are the same for finding the rate law. This is because you need to know reaction order to write a rate law.
Rate Determining Step Method
As mentioned before, the order of reaction depends on the specific mechanism of the reaction, rather than the stoichiometry. Many reaction mechanisms involve multiple elementary steps. For instance, the SN1 reaction from organic chemistry involves two steps:
(H3C)3CBr + OH– → (H3C)3COH + Br–
- Step 1: (H3C)3CBr ⇌ (H3C)3C+ + Br–
- Step 2: (H3C)3C+ + OH– → (H3C)3COH
Importantly, Step 1 occurs at a much slower rate than Step 2. As a result, Step 1 serves as the rate-determining step, which means that it equals the overall rate of reaction. Therefore, our rate-determining step yields our rate law, depending on the stoichiometry of the reactants in that step:
Rate = k[(H3C)3CBr]
To be clear, only the stoichiometry of the rate-determining step influences the rate law not the stoichiometry of the overall reaction.
Since only one molecule of reactant participates in the rate-determining step, the SN1 must therefore be first-order overall. Further, since tert-butyl bromide ((H3C)3CBr) has a stoichiometric coefficient of 1, the reaction must be first-order with respect to tert-butyl bromide. Hydroxide (OH–) does not participate in the rate-determining step, thus making the reaction zeroth-order with respect to hydroxide.
Empirical Data Method
However, if you don’t know the mechanism and rate-determining step of a reaction, you can instead determine reaction orders through empirical data. Specifically, you need to perform multiple trials of a reaction, adjusting the concentration of reactants. The concentrations of reactants thus affect the reaction rate depending on their reaction orders, which you can measure using spectrophotometry. The Iodine Clock Reaction provides a good example of a reaction whose kinetics can be determined through this method.
The Iodine Clock Reaction proceeds by the following reaction:
2S2O32- + 6H+ + 3H2O2 + 6I– → 2I3– + 6H2O + S4O62-
Triiodide forms a complex that absorbs blue light (590nm), which means that a spectrophotometer can therefore measure its rate of formation. To find the reaction order, you run this reaction five times, varying the initial concentrations of each reactant:
By comparing specific trials, we find that disulfur trioxide and aqueous protons do not affect reaction rate, while iodide and hydrogen peroxide have a one-to-one effect. This therefore means that the reaction is first-order with respect to iodide and hydrogen peroxide and zeroth-order for the others. Overall, the reaction is second-order.
Rate = k[H2O2][I–]
If you’d like to see an in-depth analysis of kinetic data to yield reaction order and rate law, check out this article.