Tag: chemistry

“The stories of STEM can seem hidden
Under layers of vocab; forbidden.
Brave the terms and march on
Through the daunting jargon
To your narratives now to be written.”   

I will post my discussion of the 28 April 2019 limerick a bit early, before I backtrack to the 25 April 2019 poem and complete this project over the next few weeks.  This poem was written for Graduation Day 2019, and, were this a regular spring semester, Graduation Day 2020 would be soon underway.  This is, of course, not a regular spring semester, and so this essay is a good chance to commemorate this year’s class as well. (Given that I’m focusing on two years, I’ll give myself twice my normal word limit!) 

“The stories of STEM can seem hidden/
Under layers of vocab; forbidden…” 
I encounter most of my students in General Chemistry coursework, which are the largest lecture sections I teach.  General Chemistry (and indeed, any introductory course) can be difficult, as students simultaneously learn and apply a challenging disciplinary vocabulary.  I often regret that I cannot spend more time on what I was fascinated by as a student myself: the stories underlying science.  However, these courses must cover a wide range of concepts and calculations, allowing students to demonstrate the efficient mastery of challenging technical material.  These first two lines attempt to balance that tension: the stories are not a focus of introductory courses, but they are there.  

“Brave the terms and march on/
Through the daunting jargon/
To your narratives now to be written.”  
I am reminded again of the difference between state and path functions.  A state function is one that we can fully analyze by knowing the initial and final states of a system: what were the conditions at the start, and what are the conditions at the end?  A path function is one for which we must know more about the intervening steps, to complete our analysis. 

“Imagine a mountain climber,” I’ve told countless students.  “They’re starting at the base of the mountain and climbing to the top.  Altitude is the state function: you can easily determine the height to which they’ve climbed and thus find the altitude.  Distance is the path function: they could climb directly up the mountain; they could take a winding route.  Until you know more about their path, you can’t report the distance they traveled.”   

After teaching students in their first-year General Chemistry courses, I rarely see most of them again before their senior-year events and commencement ceremonies.  These initially seem like chances to celebrate “state functions,” in many senses of that phrase!  We contrast the end of a campus journey with the beginning; we discuss the end of one chapter and the start of another.  The pomp and circumstance of graduation are themselves associated with occasions (functions, if you will…) of state.   

The last three lines of this poem, though, commemorate the path.  Over their four undergraduate years, students “brave the terms” of their disciplinary vocabularies to proceed to their own independent research and creative work.  The combined potential of the new stories that lie ahead, “the narratives now to be written,” is phenomenal: graduation ceremonies are dramatic to witness, but their substance and meaning are no less moving to consider this spring.  I shift in those lines to speaking directly to my former students, and I’ll close this essay the same way. 

“Look at where you are; look at where you started.”  These lines are from the musical Hamilton, and they always remind me of the concept of… a state function!  This is certainly a day to remember your initial few moments on campus, and to celebrate your status now as graduates.  But I would add one more exhortation in 2020, on this unusual graduation day.  Please take some time to look back at these last seven weeks and to appreciate the significance of your accomplishment: the steepness of the slope you just scaled; your historic, remarkable path.  

“A task that invokes fearful symmetry: 
Form point groups from elements’ litanies. 
Planes and axes, inversions; 
These abstract immersions 
Unpack complex structures‘ consistencies.”

Continuing the week of poetic homages, the 24 April 2019 limerick used as its central theme a memorable phrase–“fearful symmetry”— from William Blake’s “The Tyger.”  

Symmetry is an important concept in chemistry, as many of the properties that molecules exhibit can be predicted from the types of symmetry displayed in their three-dimensional shapes.  (For this highly visual topic, I have relied on several outstanding resources constructed and written by many others, and I have provided several pertinent links to their much more detailed information.)     

“A task that invokes fearful symmetry:/
Form point groups from elements’ litanies.”
Molecular symmetry is typically presented in advanced chemistry coursework.  It is complex, challenging, and rewarding; characterizing its associated tasks via Blake’s phrasing of “fearful symmetry,” in the first line, seems apt!     

The second line introduces pertinent vocabulary.  A molecule can contain different types of symmetry elements (separate from the periodic table’s definition!), which in turn represent particular symmetry operations.  For instance, a square has “four-fold rotational symmetry”: we can imagine repeatedly turning a perfect square 90 degrees clockwise; we’d achieve four equivalent, indistinguishable square shapes, in total.  We would denote this set of symmetry operations (the four rotations) with a symmetry element called a C₄ proper axis; this is the axis around which the rotations occur.         

A list of all the elements exhibited by a given molecule (i.e., the “litany” of its symmetry elements) constitutes its symmetric designation: the point group of that molecule.    

“Planes and axes, inversions; / These abstract immersions /
Unpack complex structures‘ consistencies.”            
Along with axes of rotation, internal mirror planes and centers of inversion are also types of symmetry elements.  Considering the symmetry of a molecule is a rigorous exercise and often requires a complex thought process: an “abstract immersion.”  For instance, an analysis of the molecule benzene, discussed previously, involves characterizing two dozen symmetry operations.  

Understanding a molecule’s symmetry provides a valuable introduction to its spectroscopic and geometric properties.  If two molecules are in the same point group, then even though they may be made up of completely different atoms, they will display similar behaviors in some respects; understanding their symmetries can help “unpack [these] consistencies.”         

“The salt of the earth, role emergent;
Strong electrolytes, their traits observant.
Compounds’ crystals dissolve
In pure water. Resolved:
Now the water will conduct a current.”

Aqueous chemistry– the chemistry that occurs in water– constitutes yet another common topic in introductory textbooks.  Species that are ionized in water are called electrolytes: these ions can go on to a variety of reactions, such as precipitations, redox, and neutralizations (acid-base reactions).  The 21 April 2019 limerick explains the characteristic properties of electrolytes in aqueous solutions. Characterizing compounds as strong, weak, or non electrolytes is a useful skill to learn in introductory chemistry coursework.   

“The salt of the earth, role emergent; /
Strong electrolytes, their traits observant.”  
Ionic compounds are commonly called salts.  If an ionic compound is water-soluble (dissolving in water rather than remaining a solid), it ionizes completely: dissociating completely into its component ions.  This behavior characterizes it as a strong electrolyte.  

The most famous salt is table salt: sodium chloride, a compound referenced in a wide range of contexts throughout history!  It is useful to consider as a representative strong electrolyte. Table salt exists as the neutral (uncharged) chemical compound NaCl.  When dissolved in water, it ionizes completely into sodium ions (represented as Na⁺) and chloride ions (represented as Cl^–).    

A weak electrolyte ionizes partially in water.  Keeping our focus on the kitchen: one component of vinegar is acetic acid, a weak electrolyte with the molecular formula CH₃COOH.  When dissolved in water, acetic acid ionizes only partially to its component ions (CH₃COO^– and H⁺).  Most of the acetic acid molecules stay in their neutral forms (as CH₃COOH).

Finally, a non-electrolyte does not ionize in water.  Table sugar (sucrose, C₁₂H₂₂O₁₁), for instance, is a non-electrolyte.  It dissolves in water, but if we looked at the compound at the molecular level, we would see that the sugar molecules all stay intact in their neutral forms.       

“Compounds’ crystals dissolve/
In pure water. Resolved: /
Now the water will conduct a current.”
Where does the name “electrolyte” come from?  When an electrolyte dissolves in water, the resulting solution can conduct an electric current.  This is more pronounced with a strong electrolyte than a weak one, a fact which is the substance of many chemistry demonstrations!  An aqueous solution of a non-electrolyte does not conduct any electric current.

“Covalent bonds: electrons’ sharing, 
In two orbitals’ overlap, pairing. 
H2’s bond length can be 
Found via minimized E 
As a function of H atoms’ bearings.”

Chemical compounds form when their component elements can stabilize one another via energetic interactions.  The 20 April 2019 limerick summarizes several important pieces of information related to one such type of interaction: a covalent bond.  In particular, the poem describes a hydrogen molecule and how its geometry is related to the energy of its covalent bond.  

“Covalent bonds: electrons’ sharing,/
In two orbitals’ overlap, pairing.” 
Chemical compounds bond in two main ways: ionic bonds, in which oppositely charged ions attract, and covalent bonds, in which atoms share their valence electrons.  This poem focuses on the latter case.  

To share electrons to form a covalent bond, two atoms’ orbitals (regions of space in which electrons are likely to be found) must overlap.  This is the substance of valence bond theory: as these orbitals overlap, the electron of one atom pairs with the electron of another in a covalent bond, stabilizing the molecule overall.  

“H2’s bond length can be/ Found via minimized E/
As a function of H atoms’ bearings.”
The simplest molecule is the hydrogen molecule, written as H₂ and containing two hydrogen atoms covalently bonded together (again, my Twitter notation fails to subscript the numeral two!).  

These last three lines of the poem narrate the potential energy surface of a hydrogen molecule, with energy as a function of internuclear distance (bond length).  As we look at the graph, we can find the bond length of H₂ by finding the minimum energy (the minimum point on the y-axis) and looking at what bond length corresponds (on the x-axis).  In other words, we look for “minimized E as a function of H atoms’ bearings”: minimized energy as a function of the hydrogen atoms’ distance from one another.  

Such a graph can be found in any introductory chemistry textbook and gives us two important pieces of information: the bond dissociation energy of H₂ (how much energy is required to break the bond?), which is 432 kJ/mol, and the bond length of H₂, which is 74 picometers (pm).     

“The forward momenta of Thermo,
Through progress from Physics and Chem, show
Laws named One, Two, and Three,
Then seek to define T,
So backtrack to a fourth law deemed Zero.”

In learning chemistry, I was often distracted by the etymologies of some of the terms of interest presented in my courses.  The 19 April 2019 limerick addresses one such linguistic oddity, one of the topics I now teach each year: the “zeroth” law of thermodynamics.  

“The forward momenta of Thermo,
Through progress from Physics and Chem, show…”
Thermodynamics is a field that generally examines heat energy and thus is of interest to many types of scientists.  This particular poem highlights the field’s development by physicists and chemists as commemorated in the four laws of thermodynamics, which were articulated during the mid-nineteenth to early-twentieth centuries.  

“Laws named One, Two, and Three,
Then seek to define T,
So backtrack to a fourth law deemed Zero.” 
The fundamental principles of thermodynamics are collected in the four laws of thermodynamics.  The first law explains the conservation of energy: energy cannot be created or destroyed; it can only change forms.  For chemists, this is generally presented as: ΔU = q + w. This equation states that a system exchanges its energy (ΔU) with its surroundings via two energetic “currencies”: heat (q) and work (w).  The second law contextualizes a property called entropy, which has been poetically dubbed “time’s arrow”; in terms of processes, entropy governs their spontaneity: the direction in which these processes naturally occur.  The third law states that as temperature approaches absolute zero (0 K), the entropy of a system approaches zero.   

The meaning of this limerick hinges on the unusual fact that the law of thermodynamics that was fourth to be formulated is named the zeroth law!  This is because the first, second, and third laws all rely on the property of temperature (T)… but to use temperature, it’s necessary to first define it.  The zeroth law defines temperature; when it was formulated, scientists decided it would be simpler to denote it as zeroth rather than renumber the existing three laws.      

“A puzzle-like problem: expunction
Of like terms from reactions’ adjunction
Towards a target process…
Keep in mind: Law of Hess! 
Find solution since H is state function.”  

The April 17 limerick is the third of three limericks focused on enthalpy.  So far we’ve seen both enthalpy’s empirical implications (what does it mean for a chemical reaction run in the lab?) and its mathematical relationships.  This third limerick examines one of the most common applications of enthalpy-related concepts: a calculation called Hess’s Law. It is named after chemist Germain Hess, who was the first to publish this mathematical approach in 1840.  

“A puzzle-like problem: expunction/
Of like terms from reactions’ adjunction/
Towards a target process…/”
The essence of Hess’s Law is that if we want to know the Delta H (𝛥H, or change in enthalpy) for a reaction for which that quantity isn’t yet known, we can manipulate other, related reactions for which the Delta H values ARE known and then add those values to obtain the Delta H of the target reaction (“target process”).  

Much more detailed explanations are available, but the paragraph above gives the gist of the limerick’s wording: when we add up the manipulated, related reactions (and thus examine their “adjunction”), we end up “expunging” terms that are identical on either side of the reaction arrow until we reach the target reaction.       

I tend to present this type of problem as a puzzle when I lecture on it: we know the picture on the front of the jigsaw puzzle box (the target reaction) and we fit together the pieces (the given reactions) to get there.    

“Keep in mind: Law of Hess!/
Find solution since H is state function.”   
The last two lines reveal the name of this specific type of calculation and point to the mathematical properties of enthalpy (H) as key to facilitating this type of solution.  

Since enthalpy is a state function, all that matters is the final state of the reaction (having the correct products) and the initial state (having the correct reactants).  Once we have them, we can determine the Delta H of the target reaction. It doesn’t matter how we got to that target (that is, the order in which we put the puzzle pieces together is irrelevant), because enthalpy is a state function. 

“Delta H represents change in enthalpy,
A chemic’lly convenient quantity.
Vessel’s open to air?
Find the Delta T there,
And thus heat transferred in pressure’s constancy.” 

The April 16 limerick likely comes the closest of these April 2019 poems to a lecture explanation; I cover all these points “in prose” when I teach chapters on thermochemistry (the chemical bookkeeping of the quantities via which reactions absorb or release heat energy).  

“Delta H represents change in enthalpy.”
The Greek letter delta represents a change in a type of function called a state function.  We can subtract the initial value (state) of a function from the final value (state) of that function to obtain the change in that function; altitude is a simple example.  The letter H represents the state function of enthalpy.   

“A chemically convenient quantity.”
When I introduce enthalpy to my students, it is with a direct acknowledgement that many functions (as well as symbols and units more generally, as discussed in Andy Weir’s excellent book The Martian) throughout history were derived to provide convenient shorthands for a group of chemists working at a given time.  Generations later, students are tasked with making sense of this polyglot science!  

Here, enthalpy is the heat energy transferred at constant pressure. Most chemistry lab work is done at constant (atmospheric) pressure; heat energy is particularly convenient to monitor, via temperature changes. Enthalpy is itself a state function, while heat energy is a path function (involving different types of calculations).  Equating the two under constant-pressure conditions opens the door to many useful concepts and calculations.  

“Vessel’s open to air?/  Find the Delta T there./ 
And thus heat transferred in pressure’s constancy.”
Are we running an experiment in glassware (also called a “reaction vessel”) that is open to the air?   We almost always are, when in a chemistry lab, and so the reaction in question is at constant pressure. 

We can infer the change in heat energy for the reaction from the temperature change (Delta T) in the solution in which it occurs… and thus the change in enthalpy, our “convenient quantity.”