Rates of reaction: what speeds a reaction up or slows it down
What a rate of reaction is, how to calculate it, what changes it, how zero-, first- and second-order reactions differ, and how to work out a half-life.
By Zachery Casey · Published · Reviewed · Editorial policy
The rate of reaction is how quickly a reactant is used up or a product is formed, measured as a change in amount or concentration per unit of time. Some reactions are over in a fraction of a second; others take years. The study of rates is called chemical kinetics. This guide explains how to calculate a rate, what changes it, what a rate constant is, how chemists describe the way a reaction slows as it goes, and how to work out a half-life. It is the background to why stored samples break down at the speed they do.
Terms are defined in the glossary.
What is a rate of reaction?
The rate of reaction is how much the amount of a substance changes in a given time. For a reaction in solution it is usually given as a change in concentration per unit of time, such as moles per litre per second (mol/L/s).
A reaction's rate isn't fixed. It is usually fastest at the start, when there is most starting material, and slows as the reactants are used up. That is why chemists describe a rate at a particular moment, or describe the whole course of a reaction with a rate constant and an order (both below).
How to calculate the rate of reaction
The mean rate over a period is the change in the amount of a reactant or product divided by the time taken (Cognito, calculating rate from graphs):
mean rate = change in amount ÷ time taken
The amount can be a mass in grams, a gas volume in cm³ or a concentration in mol/L.
Worked example. Marble chips react with hydrochloric acid and give off carbon dioxide. In the first 30 seconds, 60 cm³ of gas is collected. The mean rate over that time is 60 ÷ 30 = 2 cm³/s.
To find the rate at one moment, plot the amount against time and draw a tangent to the curve at that time. The rate at that moment is the gradient of the tangent: its rise divided by its run (Cognito, calculating rate from graphs). If the tangent at 60 seconds rises 30 cm³ over 40 seconds, the rate at 60 seconds is 30 ÷ 40 = 0.75 cm³/s. The curve flattens as the acid is used up, so the rate falls over time.
Collision theory
Molecules can only react when they meet. Collision theory says a reaction happens when molecules collide:
- often enough,
- with enough energy to get over the activation energy, and
- the right way round, so the reacting parts actually touch.
Every factor that changes a rate works through one of these three.
Factors affecting rate of reaction
| Factor | Effect | Why |
|---|---|---|
| Concentration | Higher concentration, faster | More molecules in the same space collide more often |
| Temperature | Higher temperature, faster | Molecules move faster and more collisions have enough energy |
| Surface area | Smaller particles or more surface, faster | More of a solid is exposed to react or dissolve |
| Catalyst | Faster | Provides a route with a lower activation energy |
| Pressure (gases) | Higher pressure, faster | Same as concentration for gases |
| Light | Can start or speed reactions | Light supplies energy to break bonds |
| pH | Varies | Many reactions, including hydrolysis, are catalysed by acid or base |
Some lab examples:
- Temperature. For many reactions near room temperature, a 10 °C rise roughly doubles or triples the rate. This is why samples are stored cold. The Arrhenius equation puts numbers on it.
- Surface area. A freeze-dried cake is a porous solid with a very large surface, which is one reason it dissolves quickly. See what lyophilisation is.
- Catalysts. Enzymes called proteases cut peptide bonds far faster than water alone. Trace metal ions catalyse oxidation, which is why some buffers contain EDTA. See EDTA and chelating agents.
- Light. Ultraviolet light can drive oxidation of some amino acid residues, so light-sensitive materials are kept in the dark. See how to store freeze-dried peptides.
- pH. Peptide bond hydrolysis is slowest near neutral pH and speeds up in strong acid or base (Smith & Hansen, 1998). See hydrolysis.
The rate equation and the rate constant
For many reactions, the rate depends on concentration in a simple way that can be written as a rate equation:
rate = k [A]ⁿ
- [A] is the concentration of reactant A.
- n is the order of the reaction with respect to A. It is found by experiment, not from the balanced equation.
- k is the rate constant. It is fixed for a given reaction at a given temperature, and larger k means a faster reaction.
The rate constant changes with temperature, which is exactly what the Arrhenius equation describes. It doesn't change with concentration. That is what makes it useful: two experiments started at different concentrations give the same k.
Zero-, first- and second-order reactions
The order describes how the rate responds to concentration.
| Order | Rate equation | Concentration over time | Units of k | Half-life |
|---|---|---|---|---|
| Zero | rate = k | Falls in a straight line | mol L⁻¹ s⁻¹ | [A]₀ ÷ 2k, shorter as the reaction goes on |
| First | rate = k[A] | Falls exponentially | s⁻¹ | 0.693 ÷ k, the same throughout |
| Second | rate = k[A]² or k[A][B] | Falls steeply, then slowly | L mol⁻¹ s⁻¹ | 1 ÷ k[A]₀, longer as the reaction goes on |
Zero-order reactions
In a zero-order reaction the rate doesn't depend on how much reactant is left. The same amount reacts in each minute until it runs out. This happens when something other than the reactant limits the speed: for example, when a catalyst's surface is fully occupied, or when a reaction only happens on the surface of a solid.
First-order reactions
In a first-order reaction the rate is proportional to how much reactant is left. Double the concentration and the rate doubles. The same fraction reacts in each period of time, so the amount falls exponentially:
[A] = [A]₀ × e^(−kt)
Radioactive decay is the classic example. Many breakdown reactions in solution behave this way too.
Pseudo-first-order reactions
Hydrolysis needs a peptide and a water molecule, so strictly it involves two reactants. But in a dilute solution there is so much water that its concentration barely changes. The rate then depends only on the peptide, and the reaction behaves as first order. This is called pseudo-first-order, and it is why many breakdown reactions in solution can be treated as first order.
Half-life in chemistry
The half-life (t½) of a reaction is the time it takes for half of a reactant in a sample to be used up.
For a first-order reaction the half-life is constant:
t½ = ln 2 ÷ k ≈ 0.693 ÷ k
So it takes the same time to go from 100% to 50% as from 50% to 25%.
A worked example
Suppose a compound in solution breaks down by first-order kinetics with k = 0.01 per day.
- Half-life: 0.693 ÷ 0.01 = about 69 days.
- After two half-lives (about 139 days), 25% remains. After three, 12.5%.
- Time to lose 10%: ln(100 ÷ 90) ÷ k = 0.105 ÷ 0.01 = about 10.5 days. This "t₉₀", the time until 90% remains, is often more useful than the half-life, because a sample is usually out of specification long before half of it has gone.
These numbers are an illustration of the arithmetic, not a figure for any product.
Measuring a rate
To find a rate, chemists measure how a concentration changes over time:
- Take samples at set times, or watch the reaction continuously.
- Measure the amount left by a suitable method. For peptides this is usually HPLC, which tracks the main peak shrinking and new peaks growing.
- Plot the results. If concentration against time gives a straight line, the reaction is zero order. If the natural log of concentration against time gives a straight line, it is first order. The slope gives k.
Small changes are hard to measure precisely. A rate based on a fall of a fraction of a percent may sit within the method's normal spread. See accuracy, precision and significant figures and confidence intervals, standard error and error bars.
Rates and stored samples
Kinetics explains the usual advice on keeping samples stable:
- Keep them cold to lower k.
- Keep them dry, because water is a reactant in hydrolysis. In a freeze-dried solid there is very little.
- Keep them dark to avoid light-driven reactions.
- Keep solutions near a suitable pH and free of catalysts such as proteases and metal ions.
For how stability is studied over months and years, see shelf life and stability.
Related guides
For why a reaction can be allowed by energy and still be slow, see energy in reactions. For temperature in detail, see the Arrhenius equation and accelerated stability testing. For the breakdown reaction most relevant to peptides, see hydrolysis, and for electron-transfer reactions, see oxidation and reduction.
More on peptide chemistry
- Moles, Avogadro's number and percentage yieldPercentage yield and theoretical yield with worked examples, plus what a mole is, what Avogadro's number means and how to calculate moles from mass.
- GHK-Cu: the chemistry of a peptide–copper complexGHK-Cu structure and chemistry: how the GHK peptide binds copper(II), why the complex is blue, how pH affects it, and how its identity is confirmed.
- NAD+: structure, stability and handling of a coenzymeNAD+ chemistry: why it is a coenzyme, not a peptide, how NAD+ and NADH differ, how pH affects its stability, and how to measure and store it.