RRKM theory

Key takeaways

RRKM theory belongs to chemistry; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect RRKM theory to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of RRKM theory from memory before moving on to harder problems.

Reference excerpt

The Rice–Ramsperger–Kassel–Marcus (RRKM) theory is a theory of chemical reactivity. It was developed by Rice and Ramsperger in 1927 and Kassel in 1928 (RRK theory) and generalized (into the RRKM theory) in 1952 by Marcus who took the transition state theory developed by Eyring in 1935 into account. These methods enable the computation of simple estimates of the unimolecular reaction rates from a few characteristics of the potential energy surface.

Assumption Assume that the molecule consists of harmonic oscillators, which are connected and can exchange energy with each other.

Assume the possible excitation energy of the molecule to be E, which enables the reaction to occur. The rate of intra-molecular energy distribution is much faster than that of reaction itself. As a corollary to the above, the potential energy surface does not have any "bottlenecks" for which certain vibrational modes may be trapped for longer than the average time of the reaction

Derivation Assume that A* is an excited molecule:

A ∗ → k ( E ) A ‡ → P {\displaystyle A^{*}{\xrightarrow {k(E)}}A^{\ddagger }\rightarrow P}

where P stands for product, and A‡ for the critical atomic configuration with the maximum energy E0 along the reaction coordinate. The unimolecular rate constant k u n i {\displaystyle k_{\mathrm {uni} }} is obtained as follows:

k u n i = 1 h Q r Q v ∫ E 0 ∞ d E ∑ J = 0 ∞ ( 2 J + 1 ) G ‡ ( E , J ) exp ( − E k b T ) 1 + k ( E , J ) ω , {\displaystyle k_{\mathrm {uni} }={\frac {1}{hQ_{r}Q_{v}}}\int \limits _{E_{0}}^{\infty }\mathrm {d} E\sum _{J=0}^{\infty }{\frac {(2J+1)G^{\ddagger }(E,J)\exp \!\left({\frac {-E}{k_{b}T}}\right)}{1+{\frac {k(E,J)}{\omega }}}},}

where k ( E , J ) {\displaystyle k(E,J)} is the microcanonical transition state theory rate constant, G ‡ {\displaystyle G^{\ddagger }} is the sum of states for the active degrees of freedom in the transition state, J {\displaystyle J} is the quantum number of angular momentum, ω {\displaystyle \omega } is the collision frequency between A ∗ {\displaystyle A^{*}} molecule and bath molecules, Q r {\displaystyle Q_{r}} and Q v {\displaystyle Q_{v}} are the molecular vibrational and external rotational partition functions.

Worked examples

Example 1 — a first encounter with RRKM theory

Start with the simplest possible case. Write down what RRKM theory claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In chemistry, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to RRKM theory before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about RRKM theory ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of RRKM theory

In research: RRKM theory appears in chemistry research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses RRKM theory in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: RRKM theory is common in secondary-school and first-year university syllabi. It links to neighbouring topics Chemical kinetics, Chemical physics, Molecular physics, so understanding it makes those chapters shorter.
In everyday life: Look for RRKM theory outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study RRKM theory in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what RRKM theory means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain RRKM theory out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is RRKM theory in simple terms?

The Rice–Ramsperger–Kassel–Marcus (RRKM) theory is a theory of chemical reactivity. It was developed by Rice and Ramsperger in 1927 and Kassel in 1928 (RRK theory) and generalized (into the RRKM theory) in 1952 by Marcus who took the transition state theory developed by Eyring in 1935 into account.

Why does RRKM theory matter?

Because it connects several chemistry ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study RRKM theory?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on RRKM theory.