Category: Science Poetry

“A molecule’s turning rotations;
Its stretching and bending vibrations—
To calculate, heed them:
The degrees of freedom.
(Forget not three types of translation!)”

The 10 April 2022 limerick addressed a concept related to molecular motions and energetics.  The main idea here is that a molecule can undergo 3N types of motion, where N is the number of atoms in a molecule.  The types of motion are more precisely termed “degrees of freedom” in chemistry analyses.  

“A molecule’s turning rotations; /
Its stretching and bending vibrations…”

We can consider water as a sample molecule.  Water, with its V-shape, has the formula H₂O: thus, three atoms and nine (3N) degrees of freedom.  

We can think of the ways that a water molecule could move.  It could “translate” (move in space) in three dimensions: the x, y, and z axes in a Cartesian system.  As we look at a water molecule, we see that it could also “rotate” in three ways: first, so that the H atoms spin to the “left and right” around the O atom; second, in the direction perpendicular to the first direction (so the H atoms spin “over and under” relative to the O atom); third, within the plane of the screen itself.  

The possible “vibrations” correspond to the remaining number of degrees of freedom possible for water as a non-linear molecule.  These can be calculated via the equation 3N-6 (since six degrees of freedom are already occupied: three translations and three rotations).

From that equation, we can confirm that water has three vibrational modes: a symmetric stretch, in which both O-H bonds stretch and compress at once; an asymmetric stretch, in which the O-H bonds alternate their motion; and a bending mode, in which the molecule’s H-O-H bond angle changes.  

“To calculate, heed them: /
The degrees of freedom. /
(Forget not three types of translation!)”

The concept of degrees of freedom facilitates many calculations in chemistry, such as those related to infrared spectroscopy. 

Interestingly, this essay is slightly misaligned with the poem: the “three types of translations” provide the poetic punchline, but it doesn’t work to omit that prose-based explanation until the end.  

“A solute plus solvent: solution.  
We quantify its constitution:
Numeric relation;
Expressed concentration,
Decreasing upon its dilution.”

The 9 April 2022 Twitter limerick returned to far less dense material than the mechanistic deciphering of the last few verses and posts!  As the title suggests, this post (composition) translates a poem related to solution chemistry.

“A solute plus solvent: solution…”

A solution is a homogeneous (uniform) mixture of two substances: the substance present in the lesser amount is the solute, and the substance present in the greater amount is the solvent.  

If we take one gram of table salt (sodium chloride, NaCl) and dissolve it in enough water to form exactly 150 mL of the solution, we generate an aqueous solution of sodium chloride: the salt is the solute and the water is the solvent.  

“We quantify its constitution: /
Numeric relation; /
Expressed concentration…”

Chemists have several ways to quantify the constitution of a solution (to answer the question of how much solute and how much solvent will be present in the solution) and find its concentration.  Concentrations are calculated through “numeric relations,” or equations. The most common concentration expression is molarity: moles of solute divided by liters of solution (M = mol / L).  

In the solution described above, 1.00 g of sodium chloride (NaCl) is equal to 0.0171 moles of NaCl, due to its molar mass of 58.4 g/mol. By taking 0.0171 mol NaCl divided by 0.150 L of solution, we obtain a molarity of 0.114 M here.  

“Decreasing upon its dilution.”

If a solution is diluted, more solvent is added, while the amount of the solute stays the same.  

For instance, in our example, if enough water is subsequently added to generate exactly 300 mL total, then the solution’s volume is doubled, and the molarity becomes half what it was: the solution’s concentration “decrease[s] upon its dilution.”  

Some analogy likely applies here about how the clarity of this simpler post, compared to the last few, benefits from its succinctness (its “smaller volume”)!

“A simplified rhyming summation:
Chem concept of hybridization.  
Geometry-fixing 
From orbitals’ mixing;
Molecular bonding formation.”

The 3 April 2022 Twitter limerick addressed some key topics related to molecular geometries: the shapes molecules adopt, which impact their reactivities.  Molecular geometries are explained by chemists via several different theories and concepts, depending on which lens is most useful for the situation at hand.    

“A simplified rhyming summation: / 
Chem concept of hybridization.” 

The first two lines state that this poem will summarize the chemical concept called hybridization, acknowledging that this will be a simplification!  

“Geometry-fixing /
From orbitals’ mixing: / 
Molecular bonding formation.” 

VSEPR Theory is the simplest explanation of three-dimensional molecular geometries, via concepts of “valence-shell electron-pair repulsion.”  Via VSEPR Theory, a methane molecule (CH₄) would be predicted to have its geometry (shape) because of four regions of electron density (the four C-H bonds) around the central carbon; this shape would be called tetrahedral. 

However, that geometry does not make sense with carbon’s electron configuration: the way in which a carbon atom has its electrons distributed among its orbitals, via its subshells and shells.  Carbon’s electron configuration as an individual neutral atom is represented as [He] 2s² 2p² (an arrangement suggesting that carbon will form only two bonds).    

The concept of orbital hybridization is introduced via a different approach called valence bond (VB) theory.  Via hybridization, orbitals mix together to generate what are called “hybrid orbitals,” capable of forming bonds of equal energy.  Methane’s orbitals undergo “sp³ hybridization,” which means the one s orbital and the three p orbitals in the n=2 shell are averaged together to yield four sp³ orbitals of equivalent energy, rationalizing why methane can form the four equivalent bonds necessary for the tetrahedral shape.  

This can be summarized poetically as “geometry-fixing from orbitals’ mixing,” resulting in “molecular bonding formation.”  The last lines can be read in two reasonable ways: either as “a given geometry (formation) is rationalized via hybridization” or as “hybridization results in the formation of several molecular bonding interactions” (i.e., the chemical bonds of interest).  

“To rank-classify chem collections,
Note elements’ relative directions;
Sort kaleidoscopic
With chart Periodic.
(Beware, though, of trending exceptions!)”

The 2 April 2022 Twitter limerick described the concept of periodic trends, or periodic properties: qualitative information that can be inferred from the relative location of elements on the Periodic Table of Elements (PTE).

“To rank-classify chem collections, /
Note elements’ relative directions…”

The first two lines provide an overview of some ways in which the Periodic Table of Elements (PTE) provides an enormous amount of information. Collectively, sets of elements can be “rank-classif[ied]” with respect to many of their properties: for instance, it can be discerned which of a given pair of elements has the larger atomic radius (atomic size) or first ionization energy, based on their relative placement (“relative directions”) on the PTE. Similar analyses can be completed for many other periodic properties; the practice of doing so is called analyzing periodic trends.

For instance, iodine (I) is lower than bromine (Br) in the column for the halogens (Group 7A) on the PTE. Without looking up any specific data, we can predict from our knowledge of periodic trends that an atom of iodine is larger than an atom of bromine and that iodine has a lower first ionization energy (a lower energetic cost for forming a singly-positively-charged ion) than bromine.

“Sort kaleidoscopic /
With chart Periodic. /
(Beware, though, of trending exceptions!)“

One of the most amazing aspects of the PTE (the “chart Periodic”) is the way that it allows chemists to arrange a wide array of chemical information in a meaningful way: to “sort [the data] kaleidoscopic,” in this limerick’s phrasing.

However, not every trend described is a perfectly linear one, as nuances in elements’ electron configurations can lead to exceptions from the trends in question. Often, the question I ask of my General Chemistry class is not to “predict this trend” but rather to “rationalize the exception to this trend.” This can be a complex topic to encounter, meriting an accentuating “beware”!

“To month of light verses, returning;
Fourth year of this fourth month’s discerning. 
Attempt quaternary:
Chem rhymes ancillary,
With goal of supporting STEM learning.”  

This post returns to the more familiar routine of translating past Twitter chemistry poems.  This particular limerick was posted on 1 April 2022 and marked the beginning of National Poetry Writing Month (NaPoWriMo) 2022.  

“To month of light verses, returning; /
Fourth year of this fourth month’s discerning.” 

April 2022 was the fourth NaPoWriMo for me (which is difficult to believe).  My first year of April poems fell in 2019 during the overlap of National Poetry Writing Month and the International Year of the Periodic Table.  The subsequent April routines have marked various stages of progress through the COVID-19 pandemic and thus provided stability during some strange times.

The combination of the fourth attempt at this routine and the theme of passing time (with time as the fourth dimension) together gave rise to this post’s title.  In these poems, I use the forms of light verse as structures through which to communicate chemistry concepts; most commonly, these forms are limericks or double dactyls.  This April routine provides a “fourth month’s discerning”: a way to practice understanding and communicating chemistry concepts in a different way. 

“Attempt quaternary: /
Chem rhymes ancillary, /
With goal of supporting STEM learning.”  

This month was my fourth attempt (“attempt quaternary”) at this routine, in which “chem rhymes ancillary” were a useful addition to my academic routine.  As can be seen throughout this website, my goal is to use this approach to scientific content to “support STEM learning.”  

I suspect I’m primarily writing to the student I once was: interested in the unusual vocabulary and etymologies of chemistry… to a sometimes-distracting extent! However, I hope these essays might be more generally interesting to others as well. 

Astronomer, learnéd… expounding
Through proofs, figures: dense and confounding.  
The student, receptive
To nature’s perspective,
Will exit the lecture resounding.  

This week’s poem is a non-Twitter one; I had initially drafted it during the summer, when I was focused on a series of posts inspired from lines from works of literature, as a limerick-framed restatement of some of the images and themes of Walt Whitman’s “When I Heard the Learn’d Astronomer.”  However, as this poem is primarily a paraphrase, it did not seem to fit as well with the others, which used direct quotes or allusions to initiate the new verses and essays, so I tabled it for a few weeks.

Astronomer, learnéd… expounding
Through proofs, figures: dense and confounding.  

Walt Whitman’s “When I Heard the Learn’d Astronomer” famously describes a speaker’s encounter with a lecture from a renowned scientist.  The speaker first notes the overwhelming amount of data presented in the auditorium: “When the proofs, the figures, were ranged in columns before me, / When I was shown the charts and diagrams, to add, divide, and measure them…”

I teach many content-heavy chemistry courses.  I appreciate their roles in various disciplinary curricula, but I am also aware that the first presentations undoubtedly seem “dense and confounding” to new students.    

The student, receptive
To nature’s perspective,
Will exit the lecture resounding.  

Whitman’s poem concludes with lines describing how the speaker seeks refuge from the information-dense presentation in a primary encounter with astronomical observation: “[R]ising and gliding out I wander’d off by myself, / In the mystical moist night-air, and from time to time, / Look’d up in perfect silence at the stars.”  

The student is clearly open to appreciating the subject matter at hand (in the limerick phrasing: “receptive / [t]o nature’s perspective”), but via a direct, self-initiated study: the truest example of active learning. 

I expect that the limerick form might seem trivializing here, but I had intended this verse as a tribute.  Whitman’s poem is one I remember when teaching, where my goal is primarily that students progress toward becoming independent life-long learners, regardless of their responses to the chemistry content presented.  In reading, I find the effect of the speaker’s shift from the passive voice (“When I was shown”) to the active observation (“I… [l]ook’d up in perfect silence at the stars”) to be unfailingly moving.   

“A simplified Chem situation,
Analysis by isolation:
One species in excess 
So rate law is expressed 
In pseudo-nth-order notation.”

The 22 October 2021 Twitter limerick was the last in the poetic series for National Chemistry Week 2021.  It summarized a technique called the isolation method, which (as with other approaches highlighted in the last few poems) is a technique used by chemists to simplify a complicated rate law.  

“A simplified Chem situation, /
Analysis by isolation…”

The first two lines note that this is another simplifying scenario in the discipline of chemistry, pertaining to kinetics.  

“Isolation method” is a phrase that came to mind often in 2020’s early days of the pandemic, as the terms “social distancing” and “isolation guidelines” suddenly were added to everyone’s lexicon.  In the chemistry setting, though, the approach allows an investigator to examine the kinetic role of one reactant at a time as it affects a rate law.

“One species in excess /
So rate law is expressed /
In pseudo-nth-order notation.”

The last three lines summarize a typical example.  One experiment I cite often in class involves the fading of a pink-colored solution over time, where the solution takes on a vibrant color because excess base is present (a case of “one species in excess”) with a chemical indicator (phenolphthalein).  By monitoring the fading of the pink color, students determine information about how the reaction depends specifically on the presence of the phenolphthalein.  

Rate laws are typically classified as first-order, second-order, etc. with respect to a given reactant.  When the isolation method is used, the phrasing changes to pseudo-first-order, etc., acknowledging that this is a finding that has yet to be fully clarified to explore the role of the excess reactant.  “Pseudo-nth-order” means the value of n is under investigation (and is a phrase that fits neatly into a metric rhythm!).

In the case of the experiment described above, the experimental finding is that the rate law is pseudo-first-order with respect to phenolphthalein.  When the entire rate law is determined, it is first-order with respect to both phenolphthalein and the base, so second-order overall. 

“Reactant and product, by
Way of transition state…
Progress reactive in
Graph summarized:  
Ornate coordinate,
Diagrammatical;
Relative energies,
Here analyzed.”  

To my chagrin, I realized last week that I had accidentally set two essays to post at the exact same time!  That means that I am suddenly a bit less ahead of the writing process here than I like to be.  However, I also cannot help but find it fitting that this misstep happened in the midst of a set of poems devoted to kinetics, given how concepts of timing and (at the molecular level!) collisions are so pertinent to this theme.   

In any event, the next Twitter poem was posted on 21 October 2021, and it described the concept of a reaction energy diagram; this is an efficient way for chemists to communicate information related to both the thermodynamics and kinetics of a chemical reaction of interest.      

“Reactant and product, by /
Way of transition state… /
Progress reactive in /
Graph summarized…”

A reaction energy diagram is a graphical depiction of the relative energies of the distinct species involved in a chemical mechanism.  I’ve highlighted such chemical communication here before, noting another common title of potential energy surface (when such a PES is considered in two dimensions).  

The reaction energy diagram described here cites “reactant and product, by way of transition state.”  This essentially will look like a hill, with the transition state at the peak in the middle.  The height of the hill is called the activation energy, or activation barrier, of the chemical reaction: the higher it is, the greater the barrier that must be overcome, and the longer this process takes.  These concepts are related through the Arrhenius equation, which states:

k  = A * e ^[-Ea/(RT)]

The rate constant (k) depends on a “pre-exponential factor” (A), which can be dissected into information about the mechanism, multiplied by an exponential term in which the activation energy (represented here as E_a), the gas constant (R), and the temperature (T) are all involved.  

Equations can look complex, but again, the two big ideas communicated here are that: first, the greater the activation energy is, the longer the reaction will take; second, the lower the temperature is, the longer the reaction will take.  The former concept is discussed by this poem.                

“Ornate coordinate, /
Diagrammatical; /
Relative energies, /
Here analyzed.”  

The last lines acknowledge that a reaction energy diagram is sometimes called a reaction coordinate.  This “ornate coordinate” is a diagram that provides an efficient analysis of the relative energies of the reactant, transition state, and product of a chemical reaction.   

“Consider a scheme mechanistic; 
Apply explanation simplistic:
The rate of step slowest
Determines how ‘goest’
The rate of whole process logistic.”  

The 19 October 2021 Twitter limerick expressed the concept of the “rate-determining step,” a common approach used by chemists to simplify analyses and determine kinetic information.   

“Consider a scheme mechanistic; / 
Apply explanation simplistic…”

In chemistry, a mechanism is a description of how a starting chemical species (reactant) is transformed into a different one (product).  Often, a “scheme mechanistic” takes multiple steps, so its kinetic rate law would be tricky to monitor precisely.  Simplifying approaches provide more efficient determinations of rate laws; this poem will describe one such “explanation simplistic.”  

“The rate of step slowest /
Determines how ‘goest’ /
The rate of whole process logistic.” 

One simplifying approach assumes that the rate of the slowest step of a multi-step chemical process is roughly equivalent to the rate of the process overall. 

For instance, if a commute takes ten minutes, and nine of them are devoted to waiting for an infuriatingly slow stoplight that cannot be bypassed, then the stoplight step would be considered “rate-determining.”  The  rate of the commute could be approximated as the rate of that step: the rate of the “step slowest,” here caused by the unavoidable stoplight, determines how “goest” (adjusting vocabulary slightly to fit the rhyme!) the rate of the commute.     

For a chemical example, in a reaction called a unimolecular nucleophilic substitution (abbreviated as S_N1), two main steps occur.  First, a bond breaks and a “leaving group” originally on the reactant molecule departs, creating a space on the main part of the reactant in which a new bond can form.  Second, an incoming nucleophile (electron donor) forms that new bond: the net result is that the nucleophile substitutes where the leaving group had been.  The bond-breaking step is far slower than the nucleophilic-attack step, so the rate of the entire S_N1 reaction is approximated as the rate of the bond-breaking step. 

“Ready?  State steady-state
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.  

“Ready?  State steady-state /
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.)