Organic and Inorganic Chemistry Lesson of the Day – Optical Rotation is a Bulk Property

It is important to note that optical rotation is usually discussed as a bulk property, because it’s usually measured as a bulk property by a polarimeter.  Any individual enantiomeric molecule can almost certainly rotate linearly polarized light.  However, in a bulk sample of a chiral substance, there is usually another molecule that can rotate light in the opposite direction.  This is due to the uniform distribution of the stereochemistry of a random sample of the molecules of one compound.  (In other words, the substance consists of different stereoisomers of one compound, and the proportions of the different stereoisomers are roughly equal.)  Because one molecule’s rotation of the light can be cancelled by another molecule’s optical rotation in the opposite direction, such a random sample of the compound would have no net optical rotation.  This type of cancellation will definitely occur in a racemic mixture.  However, if a substance is enantiomerically pure, then all of the molecules in that substance will rotate linearly polarized light in the same direction – this substance is optically active.

Organic and Inorganic Chemistry Lesson of the Day – The Difference Between (+)/(-) and (R)/(S) in Stereochemical Notation

In a previous Chemistry Lesson of the Day, I introduced the concept of optical rotation (a.k.a. optical activity).  You may also be familiar with the Cahn-Ingold-Prelog priority rules for designating stereogenic centres as either (R) or (S).   There is no direct association between the (+)/(-) designation and the (R)/(S) designation.  In other words, an (R)-enantiomer can be dextrorotary or levorotary – it must be determined on a case-by-case basis.  The same holds true for an (S)-enantiomer.

(R)/(S) can be used to distinguish between enantiomers in one exception: If the stereoisomer has only 1 stereogenic centre, then this designation can also serve as a way to distinguish between 2 enantiomers.

Furthermore, note that the designation of optical rotation applies to a molecule, whereas the R/S designation applies to a particular stereogenic centre within a molecule.  Thus, a molecule with 2 stereogenic centres may have one (R) stereogenic centre and one (S) stereogenic centre.  However, a chiral compound consisting purely of one enantiomer can rotate linearly polarized light in only one direction, and that direction must be determined on a case-by-case basis by a polarimeter.

Organic and Inorganic Chemistry Lesson of the Day – DO NOT USE THE PREFIXES (d-) and (l-) TO CLASSIFY ENANTIOMERS

In a recent Chemistry Lesson of the Day, I introduced the concept of optical rotation, and I mentioned the use of (+) and (-) to denote dextrorotary and levorotary compounds, respectively.

Some people use d- and l- instead of (+) and (-), respectively.  I strongly discourage this, because there is an old system of classifying stereogenic centres that uses the prefixes D- and L-, and the obvious similarity between the prefixes of the 2 systems causes much confusion.

This old system classifies stereogenic centres based on the similarities of their configurations to the 2 enantiomers of glyceraldehyde.  It is confusing, non-intuitive, and outdated, so I will not discuss its rationale or details on my blog.  (If you are interested, here is a good explanation from the University of Maine’s chemistry department.)

Also, note that D- and L- classify stereogenic centres, whereas d- and l- classify enantiomers - this just adds more confusion.

In short,

  • DO NOT use d- and l- to classify enantiomers; use (+) and (-) instead.
  • DO NOT use D- and L- to classify stereogenic centres; use the Cahn-Ingold-Prelog priority rules (R/S) instead.

Organic and Inorganic Chemistry Lesson of the Day – Optical Rotation (a.k.a. Optical Activity)

A substance consisting of a chiral compound can rotate linearly polarized light – this property is known as optical rotation (more commonly called optical activity).  The direction in which the light is rotated is one way to distinguish between a pair of enantiomers, as they rotate linearly polarized light in opposite directions.

Imagine if you are an enantiomer, and linearly polarized light approaches you.

  • If the light is rotated clockwise from your perspective, then you are a dextrorotary enantiomer.
  • Otherwise, if the light is rotated counterclockwise from your perspective, then you are a levorotary enantiomer.

In a previous Chemistry Lesson of the Day, I introduced the concept of diastereomers, and I used threose as an example.  Let’s use threose to illustrate some notation about optical activity.

D-threose.svg 2

(-)-Threose

  • Levorotary compounds are denoted by the prefix (-), followed by a hyphen, then followed by the name of the compound.  The above molecule is (-)-threose.
  • Dextrorotary compounds are denoted by the prefix (+), followed by a hyphen, then followed by the name of the compound.  The enantiomer of (-)-threose is (+)-threose.

A compound’s optical rotation is determined by a polarimeter.

I strongly discourage the use of the prefixes (d)- and (l-) to distinguish between enantiomers.  Use (+) and (-) instead.

Beware of the difference between designating enantiomers as (+) or (-) and designating stereogenic centres as either (R) or (S).

It is important to note that optical rotation is usually referred to as a bulk property.

Organic and Inorganic Chemistry Lesson of the Day – Cis/Trans Isomers Are Diastereomers

Recall that the definition of diastereomers is simply 2 molecules that are NOT enantiomers.  Diastereomers often have at least 2 stereogenic centres, and my previous lesson showed an example of how such diastereomers can arise.

However, while an enantiomer must have at least 1 stereogenic centre, there is nothing in the definition of a diastereomer that requires it to have any stereogenic centres.  In fact, a diastereomer does not have to be chiral.  A pair of cis/trans isomers are also diastereomers.  Recall the example of trans-1,2-dibromoethylene and cis-1,2-dibromoethylene:

dibromoethylene

 

Image courtesy of Roland1952 on Wikimedia.

These 2 molecules are stereoisomers – they have the same atoms and sequence/connectivity of bonds, but they differ in their spatial orientations.  They are NOT mirror images of each other, let alone non-superimposable mirror images.  Thus, by definition, they are diastereomers, even though they are not chiral.

Organic and Inorganic Chemistry Lesson of the Day – Racemic Mixtures

A racemic mixture is a mixture that contains equal amounts of both enantiomers of a chiral molecule.  (By amount, I mean the usual unit of quantity in chemistry – the mole.  Of course, since enantiomers are isomers, their molar masses are equal, so a racemic mixture would contain equal masses of both enantiomers, too.)

In synthesizing enantiomers, if a set of reactants combine to form a racemic mixture, then the reactants are called non-stereoselective or non-stereospecific.

in 1895, Otto Wallach proposed that a racemic crystal is more dense than a crystal with purely one of the enantiomers; this is known as Wallach’s rule.  Brock et al. (1991) substantiated this with crystallograhpic data.

 

Reference:

Brock, C. P., Schweizer, W. B., & Dunitz, J. D. (1991). On the validity of Wallach’s rule: on the density and stability of racemic crystals compared with their chiral counterparts. Journal of the American Chemical Society, 113(26), 9811-9820.

Organic and Inorganic Chemistry Lesson of the Day – Stereogenic Centre

A stereogenic centre (often called a stereocentre) is an atom that satisfies 2 conditions:

  1. it is bonded to at least 3 substituents.
  2. interchanging any 2 of the substituents would result in a stereoisomer.

If a molecule has only 1 stereogenic centre, then it definitely has a non-superimposable mirror image (i.e. this molecule is chiral and is an enantiomer).  However, depending on its stereochemistry, it is possible for a molecule with 2 or more stereogenic centres to be achiral; such molecules are called meso isomers (or meso compounds), and I will discuss them in a later lesson.

In organic chemistry, the stereogenic centre is usually a carbon atom that is attached to 4 substituents in a tetrahedral geometry.  In inorganic chemistry, the stereogenic centre is usually the metal centre of a coordination complex.

In organic chemistry, stereogenic centres with substituents in a tetrahedral geometry are common.  Inorganic coordination complexes can also have a tetrahedral geometry.  A stereoisomer with n tetrahedral stereogenic centres can have at most 2^n stereoisomers.  The “at most” caveat is important; as mentioned above, it is possible for a molecule with 2 or more stereogenic centres to have a spatial arrangement that results in having a superimposable mirror image; such isomers are meso isomers.   I will discuss meso isomers in more detail in a later lesson.

 

Inorganic Chemistry Lesson of the Day – 2 Different Ways for Chirality to Arise in Coordination Complexes

In a previous Chemistry Lesson of the Day, I introduced chirality and enantiomers in organic chemistry; recall that chirality in organic chemistry often arises from an asymmetric carbon that is attached to 4 different substituents.  Chirality is also observed in coordination complexes in inorganic chemistry.  There are 2 ways for chirality to be observed in coordination complexes:

1.   The metal centre has an asymmetric arrangement of ligands around it.

  • This type of chirality can be observed in octahedral complexes and tetrahedral complexes, but not square planar complexes.  (Recall that square planar complexes have a plane formed by the metal and its 4 ligands.  This plane can serve as a plane of reflection, and any mirror image of a square planar complex across this plane is clearly superimposable onto itself, so it cannot have chirality just by having 4 different ligands alone.)

2.   The metal centre has a chiral ligand (i.e. the ligand itself has a non-superimposable mirror image).

  • Following the sub-bullet under Point #1, a square planar complex can be chiral if it has a chiral ligand.

 

Organic and Inorganic Chemistry Lesson of the Day – Chirality and Enantiomers

In chemistry, chirality is a property of a molecule such that the molecule has a non-superimposable mirror image.  In other words, a molecule is chiral if, upon reflection by any plane, it cannot be superimposed onto itself.

Chirality is a property of the 3-dimensional orientation of a molecule, and molecules exhibiting chirality are stereoisomers.  Specifically, two molecules are enantiomers of each other if they are non-superimposable mirror images of each other.  In organic chemistry, chirality commonly arises out of an asymmetric carbon atom, which is a carbon that is attached to 4 different substituents.  Chirality in inorganic chemistry is more complicated, and I will discuss this in a later lesson.

It is important to note that enantiomers are defined as pairs.  This will be later emphasized in the lesson on diastereomers.

Organic and Inorganic Chemistry Lesson of the Day – Cis/Trans Isomers

Cis/Trans isomerism is a type of stereoisomerism in which the relative positions of 2 functional groups differ between the isomers.  An isomer is cis if the 2 functional groups of interest are closer to each other, and trans if they are farther from each other.  You may find these definitions to be non-rigorous based on the subjectivity of “closer” and “farther”, but cis/trans isomers have only 2 possible relative positions for these functional groups, so “closer” and “farther” are actually obvious to identify.  It’s easier to illustrate this with some examples.

Let’s start with an organic molecule.

dibromoethylene

Image courtesy of Roland1952 on Wikimedia.

The molecule on the left is trans-1,2-dibromoethylene, and the molecule on the right is cis-1,2-dibromoethylene.  The 2 functional groups of interest are the 2 bromides, and the isomerism arises from the 2 different ways that these bromides can be positioned relative to each other.  (Notice that the 2 bromides are bonded to different carbon atoms, thus the “1,2-” designation in its name.)  Relative to the other bromide, one bromide can either be on the same of the double bond (“closer”) or on the opposite side of the double bond (“farther”).  To view the isomerism from another perspective, the double bond serves as the plane of separation, and the bromides can be on different sides of that plane (trans) or the same sides of the plane (cis).  Cis/Trans isomerism often arises in organic chemistry because of a bond with restricted rotation, and such restriction is often due to a double bond or a ring structure.  Such a bond often serves as the plane of separation on which the relative positions of the 2 functional groups can be established.

 

Let’s now consider a coordination complex in inorganic chemistry.

cisplatin and transplatin

Image courtesy of Anypodetos on Wikimedia.

Cisplatin and transplatin are both 4-coordinated complexes with a square planar geometry.  Their ligands are 2 chlorides and 2 ammonias.  When looking at the pictures above, it’s obvious that there are only 2 relative positions for one chloride to take compared to the other chloride – they can be either closer to each other (cis) or farther apart (trans).

Cis/Trans isomerism can also arise in 6-coordinated octahedral complexes in inorganic chemistry.

Inorganic Chemistry Lesson of the Day: 5-Coordinated Complexes

There are 2 common geometries for 5-coordinated complexes:

  • Square pyramid: The metal centre is coordinated to 4 ligands in a plane and a 5th ligand above the plane.
  • Trigonal bipyramid: The metal centre is coordinated to 3 ligands in a plane and 2 lignads above and below the plane.

Inorganic Chemistry Lesson of the Day: 2-Coordinated Complexes

Some coordination complexes have just 2 ligands attached to the metal centre.  These complexes have a linear geometry; this allows the greatest separation of the electron clouds in the metal-ligand bonds, which minimizes electron repulsion.

Inorganic Chemistry Lesson of the Day: 4-Coordinated Complexes

My last lesson stated that the most common coordination number for coordination complexes is 6.  The next most common coordination number is 4, and complexes with this type of coordination adopt either the tetrahedral or the square planar geometry.  The tetrahedron is far more common than the square plane for 4-coordinated complexes, and the type of geometry depends a lot on the size and bonding strength of the ligands.  If the ligands are too big, then a tetrahedral geometry provides greater separation between ligands and minimizes electron repulsion.  If the ligands are too small, then there is room for 2 extra ligands to bond to the metal centre to form a 6-coordinated complex, and an octahedral geometry is adopted instead.

The square planar geometry is usually adopted by 4-coordinated complexes with metal ions that have a d8 electronic configuration.  Examples of such ions include Ni2+, Pd2+, Pt2+, and Au3+.

Determining chemical concentration with standard addition: An application of linear regression in JMP – A Guest Blog Post for the JMP Blog

I am very excited to announce that I have been invited by JMP to be a guest blogger for its official blog!  My thanks to Arati Mejdal, Global Social Media Manager for the JMP Division of SAS, for welcoming me into the JMP blogging community with so much support and encouragement, and I am pleased to publish my first post on the JMP Blog!  Mark Bailey and Byron Wingerd from JMP provided some valuable feedback to this blog post, and I am fortunate to get the chance to work with and learn from them!

Following the tradition of The Chemical Statistician, this post combines my passions for statistics and chemistry by illustrating how simple linear regression can be used for the method of standard addition in analytical chemistry.  In particular, I highlight the useful capability of the “Inverse Prediction” function under “Fit Model” platform in JMP to estimate the predictor given an observed response value (i.e. estimate the value of x_i given y_i).  Check it out!

JMP blog post - standard addition

SFU/UBC/UVic Chemistry Alumni Reception – Monday, June 2, 2014 @ Vancouver Convention Centre

I am excited to attend an alumni reception on next Monday for chemistry graduates from Simon Fraser University (SFU), the University of British Columbia (UBC), and the University of Victoria (UVic).  This event will be held as part of the 97th Canadian Chemistry Conference (CSC-2014), which will be hosted by SFU’s Department of Chemistry.  If you will attend this event, please feel free to come up and say “Hello”!

Eric Cai - Official Head Shot

I look forward to catching up with my old professors and learn about the research that chemists across Canada are conducting!  The coordinates of this event are below; no RSVP is necessary, and the attire is business casual.

SFU/UBC/UVic Alumni Reception
Date: Monday June 2nd, 2014
Time: 6:00 to 8:00pm

Location: Room 306, Vancouver Convention Centre

Inorganic Chemistry Lesson of the Day – Coordination Complexes

A coordination complex is a compound that consists of Lewis bases bonded to a Lewis acid in its centre.  The charge of the complex can be neutral, positive, or negative; if the complex has a positive or a negative charge, then it is called a complex ion.  The Lewis acid is almost always a metal atom or a metal ion.  The Lewis bases are called ligands, and they are often covalently bonded to the Lewis acid.  Common ligands include carbon monoxide, water, and ammonia; what unifies them is the existence of at least one lone pair of electrons in their outermost energy level, and this lone pair of electrons is donated to the Lewis acid.

Some key terminology:

  • The donor atom is the atom within the ligand that is attached to the Lewis acid centre.
  • The coordination number is the number of donor atoms in the coordination complex.
  • The denticity of a ligand is the number of bonds that it forms with the Lewis acid centre.
    • If a ligand forms 1 bond with the Lewis acid centre, then it is monodentate (sometimes called unidentate).
    • If a ligand forms multiple bonds with the Lewis acid centre, then the coordination complex is polydentate.  For example, a bidentate ligand forms 2 bonds with the Lewis acid centre.

In later Inorganic Chemistry Lessons of the Day, I will only refer to coordination complexes with metal atoms or metal ions as the Lewis acid centres.

Physical Chemistry Lesson of the Day – Effective Nuclear Charge

Much of chemistry concerns the interactions of the outermost electrons between different chemical species, whether they are atoms or molecules.  The properties of these outermost electrons depends in large part to the charge that the protons in the nucleus exerts on them.  Generally speaking, an atom with more protons exerts a larger positive charge.  However, with the exception of hydrogen, this positive charge is always less than the full nuclear charge.  This is due to the negative charge of the electrons in the inner shells, which partially offsets the positive charge from the nucleus.  Thus, the net charge that the nucleus exerts on the outermost electrons – the effective nuclear charge – is less than the charge that the nucleus would exert if there were no inner electrons between them.

Physical Chemistry Lesson of the Day – Standard Heats of Formation

The standard heat of formation, ΔHfº, of a chemical is the amount of heat absorbed or released from the formation of 1 mole of that chemical at 25 degrees Celsius and 1 bar from its elements in their standard states.  An element is in its standard state if it is in its most stable form and physical state (solid, liquid or gas) at 25 degrees Celsius and 1 bar.

For example, the standard heat of formation for carbon dioxide involves oxygen and carbon as the reactants.  Oxygen is most stable as O2 gas molecules, whereas carbon is most stable as solid graphite.  (Graphite is more stable than diamond under standard conditions.)

To phrase the definition in another way, the standard heat of formation is a special type of standard heat of reaction; the reaction is the formation of 1 mole of a chemical from its elements in their standard states under standard conditions.  The standard heat of formation is also called the standard enthalpy of formation (even though it really is a change in enthalpy).

By definition, the formation of an element from itself would yield no change in enthalpy, so the standard heat of reaction for all elements is zero.

 

Physical Chemistry Lesson of the Day – Hess’s Law

Hess’s law states that the change in enthalpy of a multi-stage chemical reaction is just the sum of the changes of enthalpy of the individual stages.  Thus, if a chemical reaction can be written as a sum of multiple intermediate reactions, then its change in enthalpy can be easily calculated.  This is especially helpful for a reaction whose change in enthalpy is difficult to measure experimentally.

Hess’s law is a consequence of the fact that enthalpy is a state function; the path between the reactants and the products is irrelevant to the change in enthalpy – only the initial and final values matter.  Thus, if there is a path for which the intermediate values of \Delta H are easy to obtain experimentally, then their sum equal the \Delta H for the overall reaction.

 

Physical Chemistry Lesson of the Day – The Perpetual Motion Machine

A thermochemical equation is a chemical equation that also shows the standard heat of reaction.  Recall that the value given by ΔHº is only true when the coefficients of the reactants and the products represent the number of moles of the corresponding substances.

The law of conservation of energy ensures that the standard heat of reaction for the reverse reaction of a thermochemical equation is just the forward reaction’s ΔHº multiplied by -1.  Let’s consider a thought experiment to show why this must be the case.

Imagine if a forward reaction is exothermic and has a ΔHº = -150 kJ, and its endothermic reverse reaction has a ΔHº = 100 kJ.  Then, by carrying out the exothermic forward reaction, 150 kJ is released from the reaction.  Out of that released heat, 100 kJ can be used to fuel the reverse reaction, and 50 kJ can be saved as a “profit” for doing something else, such as moving a machine.  This can be done perpetually, and energy can be created forever – of course, this has never been observed to happen, and the law of conservation of energy prevents such a perpetual motion machine from being made.  Thus, the standard heats of reaction for the forward and reverse reactions of the same thermochemical equation have the same magnitudes but opposite signs.

Regardless of how hard the reverse reaction may be to carry out, its ΔHº can still be written.

 

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