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Approximation (the
Famous, eponymous
Calc step involved):
Key intermediate’s
Change over time shows a
Negligibility;
Rate law resolves.”

The 20 October 2021 Twitter poem was another posted in National Chemistry Week 2021.  This poem highlighted another simplifying technique commonly used in chemical kinetic analyses, called the steady-state approximation, and it did so via a pseudo-double-dactyl structure.

Approximation (the /
Famous, eponymous /
Calc step involved)…”

The biggest challenge with this week of poems was identifying potential rhymes related to these often-math-centric concepts!  The first line here grew out of considering the phrase “steady state.”  The steady-state approximation takes its name from the “eponymous calc step involved”: a mathematical simplification relying on the idea that the concentration of a given reaction mechanism’s intermediate remains relatively consistent (steady).

“Key intermediate’s /
Change over time shows a /
Negligibility; /
Rate law resolves.”

In this simplified mechanism, a reactant forms an intermediate, which forms a product:

Reactant → Intermediate → Product

To monitor this reaction’s rate, we consider the appearance of the product over time. Without going too equation-heavily into the details, we can look at the big ideas.

The intermediate is typically in what is called a steady state: once the reactant forms an intermediate, that intermediate forms the product.  The intermediate’s concentration stays relatively steady: relatively constant.  Stepping briefly into calculus, the derivative of a mathematical function represents the change of that function over time.  For a constant function, the derivative is zero.

Thus, the steady-state approximation is that the change in concentration of this intermediate over time is roughly equal to zero.  Chemists use this approach and the steps that ensue to derive a rate law, finding the rate of the appearance of the product over time.  The change in concentration of the intermediate over time is approximated as zero (it “shows a negligibility”), so the rate law is more easily calculated.

(This poem and essay obviously approximate several mathematical steps of their own; however, ideally, they provide an introduction to another kinetic concept useful to chemists.)