Can Order of Reaction Be Negative?

For students learning chemistry, reaction kinetics is often one of the more challenging topics. Understanding how chemical reactions proceed, and what factors affect the rate at which they occur, requires grasping some complex concepts. One idea that frequently puzzles beginners is whether the order of a reaction can ever be negative. This article will provide a plain English explainer on reaction orders, with a particular focus on illuminating the intriguing phenomenon of negative reaction orders.

What Does Reaction Order Mean?

In chemistry, the order of a reaction refers to how the reaction rate mathematically relates to the concentration of a reactant. Essentially, it describes the dependence of a reaction on the amount of a given reactant present.

For example, if doubling the concentration of a reactant doubles the reaction rate, the order with respect to that reactant is 2. If doubling the concentration instead quadruples the rate, the order would be 4. On the other hand, if changing the concentration has no effect on the rate, the order is 0.

The overall order of a reaction is determined by the sum of the orders with respect to each reactant. So for a hypothetical reaction:

A + 2B → Products

If A has an order of 1 and B has an order of 2, the overall order for the reaction would be 1 + 2 = 3.

Note that reaction orders do not need to be whole numbers. Orders can also be fractions or negative numbers in some cases, which is where things get interesting!

How Is Reaction Order Determined?

Experimental methods are used to determine the order of a reaction with respect to each reactant. The most common approach is the method of initial rates.

This involves running the reaction multiple times, each time with a different initial concentration of the reactant being analyzed. For each run, the initial reaction rate is measured. The order can then be derived by examining the mathematical relationship between the initial reactant concentrations and the corresponding reaction rates.

For example, if doubling the initial concentration doubled the initial rate, a first-order dependence would be indicated. If doubling the concentration instead quadrupled the rate, a second-order dependence would be shown. Mathematical analysis of the full data set allows the reaction order to be quantified.

Can Reaction Order Be Negative?

Now to address the main question at hand: Yes, the order of a reaction can be negative. But what does this counterintuitive possibility actually mean?

A negative order indicates that the reaction rate decreases as the concentration of that reactant is increased. In other words, adding more of that reactant actually slows the reaction down. This is the opposite of the much more common situation where increasing concentration speeds up the reaction.

How can this be possible? In certain complex reaction mechanisms, a reactant might participate in an intermediate step that inhibits the overall reaction rate. Some examples where negative orders have been observed are:

Decomposition of nitrous oxide: N2O → N2 + O (-1 order with respect to N2O)
Hydrolysis of esters: RCOOR' + H2O → RCOOH + R'OH (-1 order with respect to ester)
Oxidation of oxalic acid by bromine: C2O4H2 + Br2 → 2CO2 + 2HBr (-1 order with respect to oxalic acid)

In each case, the negative order indicates that having more reactant present hinders the reaction rate through involvement in a rate-determining intermediate step.

A Closer Look at Negative Reaction Orders

To really cement understanding of this non-standard reaction order, let's go through a more detailed example.

Say we have the generic reaction:

A + B → Products

And experiments determine the order with respect to A is +1, while the order with respect to B is -2.

What does this tell us?

The +1 order for A means:

Doubling [A] doubles the initial reaction rate
Tripling [A] triples the initial rate
And so on…

This is normal behavior – increasing the amount of A speeds up the reaction.

But the -2 order for B means:

Doubling [B] decreases the initial rate to 1/4 its original value
Tripling [B] decreases the initial rate to 1/9 its original value
And so on…

Here we see the bizarre but possible scenario where adding more B actually slows down the reaction rate significantly.

This implies that reactant B must be involved in a rate-determining intermediate step that inhibits the overall reaction. Thus, even though B is required for the reaction, having more of it present hinders the rate.

Real-World Examples of Negative Order Reactions

While negative orders may seem abstract or improbable, they do turn up in real chemistry research and have practical implications. Here are two examples:

1. Cobalt-Catalyzed Hydroformylation of Olefins

Hydroformylation is an important industrial process that adds carbon monoxide and hydrogen (syn gas) across an alkene double bond to produce aldehydes. It utilizes cobalt catalysts modified with phosphine ligands.

In a 2015 study, researchers investigated how altering the sterics of the phosphine ligands impacted the reaction order with respect to the olefin.[1] They found that increasing the ligand bulk changed the order from positive to negative.

This demonstrates the capacity of ligand tuning to fundamentally alter reaction kinetics. The ability to switch from positive to negative order enables finer control over hydroformylation rate and selectivity.

2. Cellular Metabolism of Sugars

In living cells, the metabolism of glucose and other sugars follows kinetic patterns including negative orders. Specifically, the phosphofructokinase step that converts fructose-6-phosphate to fructose-1,6-bisphosphate as part of glycolysis displays a negative order dependence on fructose-6-phosphate concentration.[2]

This indicates that buildup of this intermediate compound actually inhibits the rate of its own conversion to the downstream product. This kinetic control mechanism allows the cell to finely regulate its sugar metabolism pathways in response to nutritional conditions.

Key Takeaways on Negative Reaction Orders

To summarize the key points on this topic:

Reaction order describes the mathematical relationship between reactant concentration and reaction rate.
Orders can be positive or negative integers, fractions, or zero.
A negative order means that increasing the concentration slows down the reaction rate.
Negative orders imply that the reactant is involved in an inhibitory rate-determining step.
Real examples show that negative orders allow fine-tuned kinetic control in complex reaction systems.

So while counterintuitive, negative reaction orders are quite real and illustrative of the intricate mechanistic possibilities of chemical reactions. Understanding this concept provides deeper insight into the kinetics of both man-made and biological reaction systems.

References

[1] Leitner, Walter, et al. “A Highly Active Phosphite Ligand for the Cobalt‐Catalyzed Hydroformylation of 1‐Octene: Correlation of Steric and Electronic Properties with Catalytic Activity.” ChemCatChem, vol. 7, no. 1, 2015, pp. 15-18., https://doi.org/10.1002/cctc.201402668.

[2] Kohn, Lawrence, et al. “The Kinetic Order of the Phosphofructokinase Reaction in Muscle Extracts and Highly Purified Preparations.” The Journal of Biological Chemistry, vol. 242, no. 20, 1967, pp. 4815-4819., https://www.jbc.org/article/S0021-9258(18)97344-7/pdf.

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