## 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 DOES NOT have a non-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.

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.

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!

## 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”!

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.

## Physical Chemistry Lesson of the Day – State Functions vs. Path Functions

Today’s lesson may seem mundane; despite its subtlety, it is actually quite important.  I needed to spend some time to learn it and digest it, and it was time well spent – these concepts are essential for understanding much of thermodynamics.  For brevity, I have not dove into the detailed mathematics of exact differentials, though I highly recommend you to learn it and review the necessary calculus.

Some thermodynamic properties of a system can be described by state variables, while others can be described by path variables.

A state variable is a variable that depends only on the final and initial states of a system and not on the path connecting these states.  Internal energy and enthalpy are examples of state functions.  For example, in a previous post on the First Law of Thermodynamics, I defined the change in internal energy, $latex \Delta U$, as

$\Delta U = \int_{i}^{f} dU = U_f - U_i$.

State variables can be calculated by exact differentials.

A path variable is a variable that depends on the sequence of steps that takes the system from the initial state to the final state.  This sequence of steps is called the path.  Heat and work are examples of path variables.  Path variables cannot be calculated by exact differentials.  In fact, the following quantities may seem to have plausible interpretations, but they actually do not exist:

• change in heat ($\Delta q$)
• initial heat ($q_i$)
• final heat ($q_f$)
• change in work ($\Delta w$)
• initial work ($w_i$)
• final work ($w_f$)

There is no such thing as heat or work being possessed by a system.  Heat and work can be transferred between the system and the surroundings, but the end result is an increase or decrease in internal energy; neither the system or the surroundings possesses heat or work.

A state/path variable is also often called a state/path function or a state/path quantity.

## Physical Chemistry Lesson of the Day – Standard Heats of Reaction

The change in enthalpy of a chemical reaction indicates how much heat is absorbed or released by the system.  This is valuable information in chemistry, because the exchange in heat affects the reaction conditions and the surroundings, and that needs to be managed and taken into account – in theory, in the laboratory, in industry or in nature in general.

Chemists often want to compare the changes in enthalpy between different reactions.  Since changes in enthalpy depend on both temperature and pressure, we need to control for these 2 confounding variables by using a reference set of temperature and pressure.  This set of conditions is called the standard conditions, and it sets the standard temperature at 298 degrees Kelvin and the standard pressure at 1 bar.  (IUPAC changed the definition of standard pressure from 1 atmosphere to 1 bar in 1982.  The actual difference in pressure between these 2 definitions is very small.)

The standard enthalpy of reaction (or standard heat of reaction) is the change in enthalpy of a chemical reaction under standard conditions; the actual number of moles are specified by the coefficients of the balanced chemical equation.  (Since enthalpy is an extensive property, the same reaction under standard conditions could have different changes in enthalpy with different amounts of the reactants and products.  Thus, the number of moles of the reaction must be standardized somehow when defining the standard enthalpy of reaction.)  The standard enthalpy of reaction has the symbol ΔHº; the º symbol indicates the standard conditions.

## Statistics and Chemistry Lesson of the Day – Illustrating Basic Concepts in Experimental Design with the Synthesis of Ammonia

To summarize what we have learned about experimental design in the past few Applied Statistics Lessons of the Day, let’s use an example from physical chemistry to illustrate these basic principles.

Ammonia (NH3) is widely used as a fertilizer in industry.  It is commonly synthesized by the Haber process, which involves a reaction between hydrogen gas and nitrogen gas.

N2 + 3 H2 → 2 NH3   (ΔH = −92.4 kJ·mol−1)

Recall that ΔH is the change in enthalpy.  Under constant pressure (which is the case for most chemical reactions), ΔH is the heat absorbed or released by the system.

## Physical Chemistry Lesson of the Day – The Difference Between Changes in Enthalpy and Changes Internal Energy

Let’s examine the difference between a change enthalpy and a change in internal energy.  It helps to think of the following 2 scenarios.

• If the chemical reaction releases a gas but occurs at constant volume, then there is no pressure-volume work.  The only way for energy to be transferred between the system and the surroundings is through heat.  An example of a system under constant volume is a bomb calorimeter.  In this case,

$\Delta H = \Delta U + P \Delta V = \Delta U + 0 = q - w + 0 = q - 0 + 0 = q$

This heat is denoted as $q_v$ to indicate that this is heat transferred under constant volume.  In this case, the change in enthalpy is the same as the change in internal energy.

• If the chemical reaction releases a gas and occurs at constant pressure, then energy can be transferred between the system and the surroundings through heat and/or work.  Thus,

$\Delta H = \Delta U + P \Delta V = q - w + P \Delta V = q$

This heat is denoted as $q_p$ to indicate that this is heat transferred under constant pressure.  Thus, as the gas forms inside the cylinder, the piston pushes against the constant pressure that the atmosphere exerts on it.  The total energy released by the chemical reaction allows some energy to be used for the pressure-volume work, with the remaining energy being released via heat.  (Recall that these are the 2 ways for internal energy to be changed according to the First Law of Thermodynamics.)  Thus, the difference between enthalpy and internal energy arises under constant pressure – the difference is the pressure-volume work.

Reactions under constant pressure are often illustrated by a reaction that releases a gas in cylinder with a movable piston, but they are actually quite common.  In fact, in chemistry, reactions under constant pressure are much more common than reactions under constant volume.  Chemical reactions often happen in beakers, flasks or any container open to the constant pressure of the atmosphere.

## Physical Chemistry Lesson of the Day – Heat Capacity

The heat capacity of a system is the amount of heat required to increase the temperature of the system by 1 degree.  Heat is measured in joules (J) in the SI system, and heat capacity is dependent on each substance.  To make heat capacities comparable between substances, molar heat capacity or specific heat capacity are often used.

• Molar heat capacity is the amount of heat required to increase the temperature of 1 mole of a substance by 1 degree.
• Specific heat capacity is the amount of heat required to increase the temperature of 1 gram of a substance by 1 degree.

For example, over the range 0 to 100 degrees Celsius (or 273.15 to 373.15 degrees Kelvin), 4.18 J of heat on average is required to increase the temperature of 1 gram of water by 1 degree Kelvin.  Thus, the average specific heat capacity of water in that temperature range is 4.18 J/(g·K).