Eyring Equation

The Eyring equation is a kinetics equation that relates a reaction’s rate constant to temperature, activation enthalpy, and activation entropy. In Organic Chemistry, it is used to describe how reactions pass through a transition state.

What is the Eyring Equation?

The Eyring equation is the Organic Chemistry way to connect reaction speed to the transition state. Instead of treating rate as just a number, it shows how temperature and the properties of the activated complex affect the rate constant, k.

At its core, the equation comes from transition state theory. Reactants do not jump straight to products, they pass through a high-energy arrangement of atoms called the transition state. The Eyring equation describes how often molecules reach that point and how favorable that passage is.

A common form is k = (kB T / h) e^(-ΔG‡ / RT), where kB is the Boltzmann constant, h is Planck’s constant, T is temperature, R is the gas constant, and ΔG‡ is the Gibbs free energy of activation. That free-energy term can also be split into activation enthalpy and activation entropy, so you may see the equation written in a form that highlights ΔH‡ and ΔS‡ instead.

That split is useful because it tells you two different things about the barrier. ΔH‡ reflects the energy cost of reaching the transition state, while ΔS‡ reflects how organized or disorganized the system becomes on the way there. A reaction with a very negative activation entropy may need a more ordered collision pattern, even if the enthalpy barrier is not huge.

In practice, the Eyring equation gives you a way to interpret experimental rate data instead of just memorizing that one reaction is faster than another. If a reaction speeds up as temperature rises, the equation helps you reason about the size of the activation barrier and the nature of the transition state. It also connects nicely to NMR line-shape and exchange problems, where you estimate how fast molecules interconvert on the timescale of the instrument.

Why the Eyring Equation matters in Organic Chemistry

Organic Chemistry uses the Eyring equation to make reaction kinetics feel less mysterious. When you compare two mechanisms, you are not just asking which one has products that look more stable. You are asking which pathway gets through its transition state more easily, and the Eyring equation gives you the language for that.

This is especially useful when a reaction rate changes with temperature, concentration conditions, or molecular shape. If a mechanism requires two molecules to line up in a very specific way, the activation entropy can slow it down even if the energy barrier seems manageable. That kind of reasoning shows up in substitution reactions, conformational changes, and other steps where molecular order matters.

The equation also bridges structure and dynamics. A mechanism drawing gives you the sequence of bond breaking and bond making, but the Eyring equation connects that picture to measurable rates. That makes it a good tool for interpreting experimental data, especially when you are asked why one pathway is faster or why a compound exchanges too quickly or too slowly to see clean NMR signals.

How the Eyring Equation connects across the course

Transition State Theory

The Eyring equation is built on transition state theory, so the two are tightly linked. Transition state theory gives the idea of a short-lived activated complex at the top of the barrier, while the Eyring equation turns that idea into a rate expression you can use with temperature data. If you understand one, the other stops feeling abstract.

Activation Energy

Activation energy is the older, more simplified way many students describe the barrier to reaction. The Eyring equation goes further by separating the barrier into enthalpy and entropy terms. That means you can explain not only how high the barrier is, but also whether the transition state requires a more ordered or less ordered arrangement.

Rate Constant

The whole point of the Eyring equation is to describe the rate constant, k, as temperature changes. In Organic Chemistry, that matters when you compare reaction speeds across different conditions or different mechanisms. If k increases a lot with temperature, the equation helps you connect that change to the underlying transition state.

Arrhenius Plot

An Arrhenius plot and the Eyring equation are both ways to analyze how rate depends on temperature. The Arrhenius approach emphasizes activation energy and a frequency factor, while the Eyring approach emphasizes ΔH‡ and ΔS‡. They often describe the same data, but they give slightly different mechanistic insight.

Is the Eyring Equation on the Organic Chemistry exam?

A lab question or problem set might give you rate constants at different temperatures and ask you to extract activation parameters from an Eyring plot. You may need to recognize that a linear plot of ln(k/T) versus 1/T points to the Eyring relationship, then read the slope and intercept for ΔH‡ and ΔS‡. In mechanism questions, the term shows up when you explain why one pathway is faster, especially if the transition state is more ordered or less ordered than the reactants. In NMR-based questions, it can appear when you are interpreting why a signal broadens, sharpens, or averages out as a molecule exchanges between conformations on a certain timescale.

The Eyring Equation vs Arrhenius Plot

Students often mix these up because both connect temperature and rate. An Arrhenius plot emphasizes activation energy and the frequency factor, while an Eyring plot comes from transition state theory and uses ΔH‡ and ΔS‡. If the question mentions enthalpy or entropy of activation, you are probably in Eyring territory.

Key things to remember about the Eyring Equation

• The Eyring equation links a reaction’s rate constant to temperature and the properties of the transition state.

• It comes from transition state theory, which treats the activated complex as the peak between reactants and products.

• The equation can separate activation enthalpy from activation entropy, so you can tell whether a barrier is mainly energetic or mainly due to molecular order.

• In Organic Chemistry, it is useful for comparing mechanisms, interpreting rate data, and making sense of fast exchange in NMR.

• If you see ln(k/T) versus 1/T, think Eyring plot and look for transition state information rather than just a simple energy barrier.

Frequently asked questions about the Eyring Equation

What is the Eyring equation in Organic Chemistry?

It is the kinetics equation that relates a reaction’s rate constant to temperature and transition state properties. In Organic Chemistry, it is used to describe how reactants cross the activation barrier to form products. The equation is especially useful when you want more detail than a simple activation energy picture gives you.

How is the Eyring equation different from the Arrhenius equation?

Both describe how rate changes with temperature, but they frame the barrier differently. The Arrhenius equation uses activation energy and a frequency factor, while the Eyring equation uses activation enthalpy and activation entropy from transition state theory. They can fit similar data, but Eyring gives more mechanistic insight.

Why does entropy appear in the Eyring equation?

Because getting to the transition state is not just about energy, it is also about how much order the molecules need. If reactants must line up in a very specific way, the activation entropy can be negative, which lowers the rate. That is common in reactions where orientation or association matters.

How do you use the Eyring equation in a problem?

You usually use temperature-dependent rate data to build an Eyring plot and then pull out activation parameters from the slope and intercept. In some questions, you also use the equation qualitatively to explain why one mechanism is faster or slower. The main move is connecting the measured rate to the transition state, not just memorizing symbols.