“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”)!
“Rivaling SN, An elimination will Lead to formation of Newfound alkene. (E2 results from build Anticoplanar; Abstraction and leaving, Coincident, seen.)”
This post is from 8 April 2022 and marks the last of the mechanism-themed poems from NaPoWriMo2022. These verses were fun to write but, as with both the kinetics and enthalpy “series” in previous months, the resulting essays deal with themes that can seem remarkably abstract! Next week marks a return to some less involved topics, for the remainder of the semester.
This last poem addresses two new types of reaction mechanisms that often compete with the nucleophilic substitution reactions seen in previous posts (SN1 and SN2). These two new types of reaction pathways are called eliminations, wherein a base reacts with (often) an alkyl halide to “eliminate” a hydrogen atom and the leaving group, ultimately yielding the formation of an alkene, a compound with a double bond. As with the nucleophilic substitutions, eliminations (represented generally as E) can occur via a two-step process (E1, for unimolecular elimination) or a single-step, concerted process (E2, for bimolecular elimination). Both are shown in the diagram below, using conventions of electron-pushing mechanisms.
Via E1, the bond to the leaving group breaks first, yielding a carbocation as the bromide ion leaves. As shown here, a neutral base with a lone electron pair then abstracts (removes) a proton, so that the electrons originally in that C-H bond form a new pi bond between two carbon atoms. Besides the bromide ion, which departed in Step 1, the other side product is the now-protonated generic base, from Step 2.
Via E2, the negatively-charged bulky base doesn’t have enough room to attack the alkyl halide as a nucleophile. Instead, it abstracts a proton, and the subsequent formation of a pi bond then causes the departure of the bromide ion as the leaving group, all in one reaction step. The leftover side products here are the now neutral tert-butanol and the bromide ion, both from the single reaction step.
As with the other poems from this month, before launching into the essay, it’s worth acknowledging the motivation: the “why do we care about this in the first place?” aspect of such complicated topics. These four reaction patterns (SN1, SN2, E1, and E2) are evident in a tremendous number of settings. Chemistry students traditionally begin their extensive training in chemical and biochemical mechanisms by learning these four options and learning how to predict which of the four is likely to predominate given a set of reaction conditions. The reactions have massive implications for organic synthesis, biochemistry, and many other branches of chemistry. However, trying to learn them in the first place can be imposing. This poem takes several aspects of the elimination mechanisms and presents them in a rhymed format, which ideally might be memorable for students learning the material.
“Rivaling SN, / An elimination will / Lead to formation of / Newfound alkene…”
Nucleophilic substitution reactions and elimination reactions “rival” one another: they involve comparable reactants that can accomplish multiple mechanistic steps, competing for the most likely pathway in a given situation. The reactant molecules in the reactions shown here could also theoretically undergo SN1 or SN2 reactions, respectively.
Why is this? Both bases and nucleophiles use electron pairs to achieve mechanistic ends: many molecules act as one or the other interchangeably. How a negatively charged species will act comes down to its own bulkiness and other reaction conditions. Does it have enough room to attack as a nucleophile, or is the organic molecule crowded (sterically hindered), so that abstraction of a proton is more feasible? Is it neutral or negatively charged? Many such questions help students make the “call” of whether SN2, SN1, E2, or E1 is occurring in a given scenario.
An elimination pathway yields a “newfound alkene”: a molecule containing a double bond.
“(E2 results from build / Anticoplanar; / Abstraction and leaving, / Coincident, seen.)”
Discerning between E1 and E2 mechanisms means considering characteristics of the reactant molecules, the base, the solvent, and other factors, in processes reminiscent of discerning between SN1 and SN2.
The new consideration for eliminations is that E2 has a geometric constraint (required 3-D arrangement) in the organic substrate. The proton that is abstracted from the alkyl halide and the leaving group must be “anticoplanar” to one another: in the same plane, on opposite sides of the molecule. “Abstraction and leaving [are] coincident”: these two steps happen in a concerted fashion, via E2.
Thus, this particular reaction is another early one from the curriculum of Organic Chemistry. As with the past three posts, this post is intended to help summarize some of the most pertinent material for students learning the reaction. Likewise, as with the other organic mechanisms cited in this series, it is probably useful to include a diagram.
This drawing uses the convention of the skeletal structure for simplicity’s sake: that is, only the “carbon skeletons” of the molecules are shown. Each vertex or terminus represents a carbon atom bonded to a number of hydrogen atoms appropriate to achieve its desired number of four bonds total (so it can obey the octet rule). For instance, the “dienophile” above, ethene in this case, is depicted as a short set of parallel lines. In a chemist’s reading, this translates instantly to H2C=CH2. Each of the two carbon atoms must be bonded to two hydrogen atoms, along with participating in the double bond. Moreover, electron movement in the reactants (left-hand side of the reaction arrow) is depicted via red curved arrows. The new bonds formed by these electron movements are shown in red in the product (right-hand side of the reaction arrow).
Covalent bonds in organic molecules are represented with lines; a single line represents a single bond (also known as a sigma bond), and a double line represents a double bond, consisting of one sigma bond and one pi bond. As the diagram shows, the two reactants that participate in a Diels-Alder reaction are classified as a diene (a molecule with two double bonds) and a dienophile (a molecule that wants to react with a diene). Here, the simplest diene is 1,3-butadiene, and the simplest dienophile is ethene; they yield the simplest Diels-Alder product of cyclohexene.
As with the last few weeks, we have much build-up and context here, given all of the shorthand and jargon inherent in a chemical mechanism. Ideally, this background will help the next 280 words or so make more sense.
“Diene and a dienophile / In movement, concerted, beguile…”
The Diels-Alder reaction involves the interaction of a diene and a dienophile. The mechanism is generally postulated to occur all at once (“movement concerted”), as shown with three red arrows of electron movement in the single reaction step. The electrons in each of the pi bonds here (a pi bond is often thought of as the “second” bond in a double bond) participate in what is called a cycloaddition. This means that two new bonds form between the diene and dienophile to yield a six-membered ring, as the single product takes on a hexagonal shape. Additionally, the electrons from a third pi bond shift their location.
“Diels-Alder reaction / Results in compaction…”
The reaction is named for Otto Diels and Kurt Alder, who published their findings in 1928 and received the Nobel Prize in Chemistry in 1950. The reaction results in the “compaction” of the molecular geometry of interest: it is smaller, since two reactant molecules have reacted to form a single product molecule.
“Route cyclohexenic in style.”
The reaction shown above, with the simplest possible dienophile and diene, yields a molecule named cyclohexene. The name gives us several clues about its structure: “cyclo” (the molecule is cyclic; it is a ring); “hex” (six carbon atoms are involved); and “ene” (the structure includes a double bond).
This closing line was my favorite from the mechanism poems, as I appreciated the wordplay possible with “scenic route” and “cyclohexenic route.” I also find the “scenic route” title fitting for this post, given the extensive background, since that phrase is often a euphemistic shorthand used to explain that something will take much more time!
“Lesson on SN1: Two-step-long journey Begins with the leaving group’s breaking away. Nucleophilic attack racemizes. (Activity, optical: lost in the fray.)”
The third mechanism poem from NaPoWriMo2022 was posted on 6 April 2022 and looks specifically at the process of unimolecular nucleophilic substitution, which is abbreviated as SN1. This is again a step-by-step depiction in which electron movement is represented by curved arrows; the poem again seeks primarily to communicate several attributes of the mechanism to an audience trying to learn them.
Here, the same net effect occurs as in the previous discussion of the SN2 process: an incoming nucleophile (Nuc) replaces a leaving group (LG) on a molecule. However, SN1 is a stepwise process that requires two distinct steps, rather than the concerted single step of SN2. (To reiterate from a few weeks ago: you’re not wrong. It’s confusing that the two-step process has the number one in its abbreviation! This is because the rate-determining step in an SN1 mechanism is the first step, which only involves one species.)
Shown above is a generalized depiction of this molecular process. Because this poem will discuss the three-dimensional structures of the molecules a bit more, the scene is much busier than for the SN2 poem/essay. The gist of this mechanism is as follows:
Step One) Reactant loses leaving group to form Intermediate. Step Two) Intermediate reacts with Nucleophile to form Products.
Before I launch into the discussion of the poem itself, it is worth remembering that several shibboleths accompany the vocabulary of organic chemistry, and a few will be cited here. A chemist pronounces the word “carbocation” as “car-bo-cat-ion”; a non-chemist would likely pronounce it as rhyming with “vacation.” “Racemization” is likewise pronounced in a non-intuitive way. Those are the two main terms seen in this entry (but as I think about it, the general topic might make for many more interesting poems for the next NaPoWriMo).
With all this buildup, the poem itself might well seem anticlimactic… but I will resolutely start the official 280-word count here.
“Lesson on SN1: / Two-step-long journey / Begins with the leaving group’s breaking away…”
In contrast to the SN2 mechanism’s single step, the SN1 mechanism is a two-step process. In Step 1, the reactant forms an intermediate, also called a carbocation: the bond between the leaving group and the rest of the molecule is broken, yielding the positively charged intermediate.
“Nucleophilic attack racemizes. / (Activity, optical: lost in the fray.)”
In Step 2, the carbocation intermediate reacts with an incoming nucleophile. Depending on the structure of the reacting molecule, a property called “optical activity” can sometimes be monitored during the SN1 process.
Above, the “Reactant” depicted (where X, Y, and Z all represent distinct substituents) is optically active. When placed into an instrument called a polarimeter, the “Reactant” would rotate the polarimeter’s light in a certain direction: dextrorotatory (d) for right; or levorotatory (l) for left, a behavior which is quantified as the sample’s “optical activity.” (Other notations for structural differences are often used, as well; rationalizing those would take this poem-explanation over its word limit!)
In Step 2, as shown, the nucleophile reacts with the “Intermediate” to form the “Products.” Why are there two? When the incoming nucleophile attacks, it can do so from the front or the back, relative to the planar (flat) intermediate. Each option happens 50% of the time, leading to what is called a racemate or racemic mixture: “[n]ucleophilic attack racemizes.” The final product mixture would NOT rotate the polarimeter’s plane-polarized light anymore: the optical activity has been lost.
Many aspects of mechanisms are framed in bellicose vocabulary (e.g., “nucleophilic attack”), as highlighted here by the closing descriptor for the optical activity: “lost in the fray.”
“A creative process, wall-stationed, With paintings long-lasting, emblazoned; The technique, pervasive On surface abrasive, Forms fresco through carbonatation.”
The second mechanism poem from NaPoWriMo2022 was the most general of the verses from that week, posted on 5 April 2022. It concerns the chemistry behind frescoes, an artistic medium seen widely throughout history and cultures, thus justifying to a reasonable extent (I hope) the pun in the post title.
The topic of fresco chemistry involves much fascinating science, art, and history. As with last week’s entry, the chemical reactions of interest here deserve some preliminary framing and additional words. Unlike the SN2 mechanism and others that will be described in future posts, this is a process reflecting general inorganic chemistry steps, rather than the specific electron pushing of organic molecule depictions. However, it still seemed to fit reasonably well in this week. Here, the abbreviations in parentheses denote the phases of the chemicals of interest: (s) for solid; (l) for liquid; (g) for gas; and (aq) for aqueous solution.
Step One: CaCO3 (s) → CaO (s) + CO2 (g) Step Two: CaO (s) + H2O (l) → Ca(OH)2 (aq) Step Three: Ca(OH)2 (aq) + CO2 (g) → CaCO3 (s)
The fresco cycle shown here is a three-step process. The first two steps prepare an artist’s materials for this artistic medium. The first is called calcination: calcium carbonate (CaCO3) is heated to yield calcium oxide (CaO) and carbon dioxide (CO2). The second is called slaking: calcium oxide is mixed with water (H2O) to form calcium hydroxide [Ca(OH)2], known to fresco artists as lime plaster.
The third step is the chemistry behind the fresco formation itself and the focus of the poem.
“A creative process, wall-stationed, / With paintings long-lasting, emblazoned…”
Frescoes consist of two layers of lime plaster used to coat a wall and create a painting surface (“wall-stationed”). In the rougher layer, the arriccio, plaster is mixed with coarse sand and applied directly to the wall. The intonacolayer (lime plaster and fine sand) is then applied over the arriccio layer to become the actual painting surface.
In fresco chemistry, pigments are painted directly on a surface consisting of calcium hydroxide [Ca(OH)2]. As the fresco dries, the calcium hydroxide reacts with the carbon dioxide (CO2) in the air and forms the stable and long-lived compound calcium carbonate (CaCO3): trapping the pigments, leading to an image that will be “long-lasting [and] emblazoned” on the wall.
A fresco artist ideally applies an intonaco layer only to an amount of wall feasible to finish before the plaster dries. The corresponding term is giornata, for “a day’s work.”
“The technique, pervasive / On surface abrasive…”
The technique is “pervasive”: seen in many eras and locations throughout history. Calcium hydroxide is a basic compound, bases are caustic; lime plaster is a “surface abrasive.”
“…Forms fresco through carbonatation.”
The last reaction in the sequence shown is called carbonatation, as it forms calcium carbonate. It is sometimes called carbonation, but the first term is less ambiguous (multiple processes are denoted as carbonation)… and scans more readily in this limerick!
This reaction is key to the buon fresco(“good fresco”) technique, in which the artist is painting on fresh lime plaster, aiming to cover their giornata. A related technique is called fresco a secco (“dry fresco”), in which the artist uses paints on an already-dried surface.
I remember my introduction to chemical mechanisms as involving a tremendous amount of specialized vocabulary: with exams perpetually on the near horizon, it seemed like I needed to memorize several complicated terms long before I could process what each of them truly meant. This poem and the ones that follow are intended to put some of the key trends and words together in a memorable way for someone trying to learn the basics.
In a first for these essays, I think it will be useful to have a small illustration for a few of these, over the next five weeks. Some additional introductory words are likely useful here, too, since one of the few things I suspect of being even more off-putting than unexpected chemistry jargon would be an unexpected chemistry diagram!
In these diagrams, curved arrows show electron flow, which is the underlying impetus for all of these processes. The curved arrow starts where the excess electrons are and points to where they end up, in a given reaction step; electrons typically move in pairs (two at a time). Lines represent covalent bonds. Dash-wedge notation shows three-dimensional (3-D) arrangements of these bonds. A “wedged” triangle shows that the bond is coming towards the viewer, and a “dashed” triangle shows that the bond is behind the screen.
(This illustration is brought to you courtesy of the whiteboard setup still present in my kitchen, which has never quite recovered from being a Spring 2020 classroom.)
Finally, to turn back to today’s mechanism and limerick: one of the simplest mechanisms of interest in Organic Chemistry is the SN2 process, depicted above. Overall, it is a depiction of how Molecule A turns into Molecule B: how a negatively charged nucleophile (abbreviated generically as Nuc above) replaces the bromine atom in the original molecule; as part of the same process, the bromine atom “leaves” the original molecule, becoming a negatively charged bromide ion, also characterized as the leaving group.
“A nucleophilic incursion / In polar aprotic submersion…”
Two mechanisms commonly taught to organic chemistry students are SN1 and SN2: two types of nucleophilic substitution (abbreviated as SN) that were both celebrated during NaPoWriMo2022. Both involve a nucleophilic attack, or “incursion.” SN1 reactions occur via a two-step process; SN2 reactions occur via a single, concerted step. (This non-intuitive naming is because one species is involved in the rate-determining step of an SN1 mechanism, whereas two species are involved in the rate-determining step of an SN2 mechanism… since its single step is the only one!)
A perennial, early challenge for students is discerning via which mechanism a nucleophilic substitution occurs. One clue is the solvent (the reaction medium). SN2 reactions are favored by polar aprotic solvents (polar solvents that lack a proton; acetone is a common choice), while SN1 reactions are favored by polar protic solvents (such as water). “Polar aprotic submersion” denotes that the reaction occurs in polar aprotic solvent, hinting at SN2.
“With leaving group egress / As synchronous process…”
As shown above, in an SN2 process, the nucleophile attacks simultaneously with the departure of the leaving group (“leaving group egress”), since everything happens at once (a “synchronous process”).
“It’s SN2 (Walden inversion).”
The closing line reveals the SN2 label and a corresponding inversion of stereochemistry: the 3-D arrangement of the atoms. The inversion is named for Paul Walden, the chemist who studied the process in 1896, and can be detected when the reaction occurs at a chiral center (which is not the case shown above).
“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).
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.