AGENDA

Lecture 1: 3/29/21

Introduction and thermo refresher.

Lecture 2: 3/31/21

This introductory lecture was a refresher of Chem 2A and 2B material that is important for the first half of Chem 2C. Specifically, Free (Gibbs) energy and its connection to equilibrium. The concept of Spontaneity and how the signs and meanings of \(\Delta G\), \(\Delta S\), \(\Delta H\). Then reintroduction of oxidation number rules and ending with balancing redox reactions (in both acidic and basic aqueous solutions).

Lecture 3: 4/2/21

Please go over balancing redox reactions in basic conditions as this will not be discussed in lecture, but you are expected to know. We did an Overview of Syllabus and grading rubric. Libretexts is the course textbook.… If you cannot access it try requesting a password reset with your FULL email address as the username. Galvani likes to torture frogs, but identified electricity (which we now know is the flow of electrons, but they didn’t at that time). And electricity affects life (specifically nerves). A proper discussion why requires a discussion of how nerves work and that is beyond this class. Oxidation-Reduction Reactions are reactions in which oxidation numbers change. If Zinc solid were added to a solution of Copper (2+), then a displacement reaction (redox too) would occur with Zinc going into solution and Copper coming out. Introduced the activity series as a mechanisms to identify when a metal-metal redox reaction is spontaneous.

Lecture 4: 4/5/21

Visited how the curve works in this class; Grades are given at the END of the class only. Otherwise numerical scores are discussed. Absolute scores do not matter. Only relative to the mean (in terms of how many standard deviations away from mean).Set the grade to a C+ (perhaps strong or weak depending on actual performance). We went over the Activity series again as a metric to identify spontaneous redox reactions. Introduce the galvanic cell that separate the two half reactions of a redox cell. Discussed the need to “close the loop” by having spectator ions flow also. This is required to balance charge neutrality. This is done via a salt bridge (or semipermeable membrane). We introduced electrodes: (1) Anodes are the electrodes where oxidation occurs and (2) Cathodes are the electrodes where reduction occurs. Galvanic cells has cell potentials (\(E_{cell}\)) that dependent on (1) the materials that are involved and (2) the Cell Conditions. We reintroduced standard state (1 barr and 1 M concentration; often at 298 K, but that is no longer part of standard conditions). The cell potentials is related to Gibbs Energy difference of the underlying REDOX reaction in some (inverse) way. Introduced Cell Diagram (notation) as a shorthand method to describe a cell without having to draw the cell.

Lecture 5: 4/7/21

Electrodes do NOT have to be active in the REDOX chemistry. They can be “inert”: Platinum (remember on the bottom of the activity series) or Carbon (specifically graphite, not diamond) are common. We introduce inert electrodes into cells when they have homogeneous reactions (specifically, when solid is not part of the reaction): Liquid → Liquid, Gas → Gas, Solution → Solution, Gas → Solution. Inert electrodes are added in the cell notation (diagram) with a vertical line since they are a phase change. Introduced cell potentials and discussed how (standard) cell potentials can be decomposed into Standard Reduction Potentials (SRP) for each half reaction via \(E^o_{cell} = E^o_{SRP}(cathode) - E^o_{SRP}(anode)\). Since cell potential is related to ΔG (negatively correlated), a similar argument can be made about “Driving force” for reduction half reactions: The more negative SRP (more positive ΔG) will want to do the reverse reduction reaction (oxidation) and these are good reducing agents (e.g. Group 1 elements). The more positive SRP (more negative ΔG) will want to do the forward reduction reaction (reduction) and these are good oxidizing agents (e.g., Group 17 elements). The zero does not matter in the SRP, since the cell potential is the difference of them (so we pick the reduction fo protons as our zero). In the past, Standard Oxidation Reactions (SOP) used to be used, but they are the opposite of SRP and hold no additional information. ALWAYS USE SRP in cell calculations and DO NOT FLIP the sign in calculating cell potentials (that is “pre-chewed” for you with the negative sign).

Lecture 6: 4/9/21

We build the BIG TRIANGLE of chemistry: (1) We can connect standard \(\Delta G^o\) to \(E_{cell}^o\), (2) we can connect standard \(\Delta G^o\) to \(K_{eq}\) and (3) We can connect \(E_{cell}^o\) to \(K_{eq}\). This is expresed via \(\Delta G^o - RT\ln K_{eq} = - nFE_{cell}^o\). We went into non-standard conditions. We reviewed Reaction Quotients (\(Q\)) that are formulated via Law of Mass Actions like an equilibrium constants: \(Q=1\) for standard conditions, \(Q=K\) for equilibrium conditions, and \(Q\) is anything else for non-standard conditions. We CANNOT calculate Q without having a balanced REDOX reaction. Underlying the cell potential under non-standard conditions is a basic thermodynamic property: \(\Delta G^o -= \Delta G +RT \ln Q\), which connects the BIG TRIANGLE of equations to non-standard cell conditions to get the NERNST Equation: \(E_{cell} = E_{cell}^o - \dfrac{RT}{nF} \ln Q\). For room temperature calculations, this is often simplified to \(E_{cell} = E_{cell}^o - \dfrac{0.0592 \,V}{n} \log Q\). To get \(n\) and \(Q\), you need to balance your REDOX reaction; getting \(E_{cell}^o\) does not require balancing (but is not a bad idea).

Lecture 7: 4/12/21

Started with a quicky review of equilibrium constants: (1) We should use the thermodynamics equilibrium constant in our calculuatsion technically, which involves activities. These can be approximated in terms of concentrations and partial pressures. (2) This differs from K_c which is in terms of all concentrations or K_p which is in terms of all partial pressures. When we do Nernst Equation problems, we should always ask ourselves if the conclusion makes sense from a simple Le Chatelier's Principle’s perspective. Batteries are self Contained, portable electrochemical power sources (galvanic cells) comprised of one or more voltaic cells, often connected in series to get higher voltage. (1) Primary Batteries cannot be recharged and non-desired reactions will occur if we try to charge them (and they can explode). (2) Secondary Barriers can be recharged and non-desired reactions will occur weakly and build up to kill them eventually (the "die" on use eventually). (3) Tertiary Batteries are fuel cells were the material undergoing the redox reaction flow in to be consumed. This is not self-contained and probably should not be considered a battery as per our definition.

Lecture 8: 4/14/21

We reviewed primary, secondary, and tertiary (fuel cells) batteries again. Corrosion is a natural process, which converts a refined metal to a more chemically-stable form, such as its oxide, hydroxide, or sulfide. (Option 1): Prophylactic Protection – Keeping Oxygen away from the metal via paint, or another metal overlay; this may also be from self-passivation where the metal will form a impermeable oxide layer (Aluminum is the classic example). (Option 2): Cathodic protection – sacrificial anode. Use a more reactive metal that will be preferentially oxidize. This require replacing once the metal is “used up. Zinc is common for protecting iron since it is cheap and has a more negative SRP (i.e., higher on the activity series). An Electrolytic cell is one that uses an external voltage to drive a non-spontaneous reaction. e.g, (1) recharge a “dead” secondary battery, (2) reduce a metal from a higher oxidation state like sodium in NaCl, (3) split water to made hydrogen and oxygen (which can be burned or used in a fuel cell). If the reduction of a metal occurs over another metal, this is call electroplating. This process follows standard stoichiometry problems, but involves electrons and rates of electrons added.

Mid-term Exam #1: 4/16/21

• Nernst Equation (review)
• Exam Reviews (general)
• Concepts to Master for Midterm #1

Lecture 8: 4/14/21

Reviewed electrochemical cells in general and electroplating in particular. We emphasize that electroplating is the pushing of non-spontaneous reaction that reduces a metal out of solution on top of another metal (although it can be the same metal). The voltage necessary to do this is the cell potential of the opposite (spontaneous) reaction. The rate of reduction of the metal ions is related directly to the current that is pushed by the external voltage AND the stoichiometry. The amount of metal that has been reduced is proportional to the current (rate), the time that the current has been on and stoichiometry of electrons to metal ions. Electrochemistry can directly be used as a metric to evaluate if a REDOX reaction can happen. We started this discussion within the content of activity series of metals. If you can remember how to use this series things will make sense. “The solid metals above will displace the metals ions below out of solution!” This mean “The oxidation of a higher metal pushes the reduction of a lower metal ion from solution.” If you want to know if a reaction will occur, you can always just calculate the cell potential (it may be under non-standard conditions though = Nernst) and evaluate its sign. Simple! Introduce complex ion and coordination compounds including transition metals, oxidation states, and charges. –Ligands can be anions, cations or neutral. Ligands have a slightly different name when bound than when separate from the metal. Much of the discussion focused on the nomenclature of the complex ions and coordination compounds.

Lecture 9: 4/19/21

Introduced the concept of an inner sphere and outer sphere in complexes. Briefly concluded nomenclature of Transition Metal complexes; Complexes can be positively or negative charged or not at all. What are Transition Metals? IUPAC says "an element whose atom has a partially filled d sub-shell, or which can give rise to cations with an incomplete d sub-shell", but most Chemists consider the entire d-block set of elements to be transition metals (for short). The Lanthanides and Actinides are considered as “inner” transition metals. Went back to Quantum Mechanics of electrons in atoms (ions count too): (1) Electron configuration: Four quantum numbers and their ranges, including electron configuration: Degeneracy of shells (especially the d-block), (3) Electron configuration: Pauli Exclusion Principle, (4)Electron configuration: Hund’s Rule (technically the first one, since there are three, but that is more advanced). Electron configuration: Aufbau Principle. The Aufbau Principle relies on relative ordering of orbital energies, which in general depend on Nuclear charge, effective charge, shielding, electron-electron repulsions, electron exchange interactions and electron correlations. However, the relative energies of orbitals to change depending on the number of electrons (or atomic number in neutral atoms). Atomic radius (goes down and then goes up), but less so than the higher rows. Electon configuration of transition metal ATOMS. Fill up the d-orbitals, but have a glitch for preferring half filled (e.g., Cr) and fully filled (Cu) d-orbitals.

Lecture 10: 4/21/21 (Now 4/26/21)

Went over electronic configuration for transition metal atoms and went over atomic radius of transitions, including lanthanide contraction where the third row of transition metals are not as big as expected from the difference between the first and second row. We rehashed the flexibility of orbital energies where: (1) When building up electrons on atoms, the 4s electrons are lower in energy than the 3p and are filled first, but (2) when removing electrons on atoms to make ions, the 4s electrons are higher in energy than the 3p and are removed first. Hence, when one ionizes transition metals to make non-zero oxidation states, take from the 4s orbital first. All transition metals have +2 oxidation states corresponding to the loss of the two s electrons and the max oxidation state corresponds to the group number! We went back to discussing differences between inner and outer sphere ligands; the difference has consequences on chemistry since different species will exist in solution. Then focused on structure of complex ions including coordination numbers (CN), which are number of bonds to the transition metal, NOT number of ligands. CN = 6 -> Typically Octahedral Geometry, CN= 4 -> tetrahedral or square planar, CN=2 -> Linear. In practice coordination numbers can vary from 1 to 12. We introduced polydentate ligands that can bind (“bite”) in multiple spots to the transition metals: three common ones are: Ethylenediamine (“en”), Oxalate (“ox”): oxalato- and Ethylenediaminotetraacetat (EDTA)^4-, which are bi-, bi-, and hexadentate ligands. We introduce isomers (“Same components, Different Geometries“) that are separated into Structural and Stereoisomers. The former has three forms and we discussed Ionization & Coordination Isomers. The other types will be completed next lecture.

Lecture 11: 4/23/21 (Now 4/28/21)

There are two class of inorganic Coordination Isomers: Structural and Stereoisomers: (1) Structure Isomers have “Different Bonds” and “Different Orientation” and (2) Stereoisomers have “Same Bonds” and “Different Orientation”. Review: Ionization Isomers (a sub-class of Structural Isomers) result when the ions inside and outside of the coordination sphere interchange. Review: Coordination Isomers (a sub-class of Structural Isomers) result when there is a change in ligand between cation and anion coordination sphere in multi-coordination complex chemicals. We introduced Linkage Isomers (a sub-class of Structural Isomers) results when there are two or more coordination compounds in which the donor atom of at least one of the ligands is different. Stereoisomers differ in the 3-D orientation of ligands about the metal atom, but have the same bonding (number and type of bonds). CIS/TRANs Isomers: Metal complexes that differ only in which ligands are adjacent to one another (cis) or directly across from one another (trans) in the coordination sphere of the metal are called geometric isomers; They can be in square planar or octahedral complexes. If considering octahedal complexes with three of each MA₃B₃ then we can introduce the mer-fac system. (1) Mer have all B-M-B ligand angles at 90° and fac have all B-M-B ligand angles at 90° and 180°. Two geometric isomers are distinct if and only if, via translations and rotations, one isomer cannot be superimposable over the other!

Lecture 12: 4/26/21 (Now 4/30/21)

We completed the discussion of Stereoisomers with a discussion of Optical Isomers; Optical Isomers are Stereoisomers as are Geometric (e.g., CIS/TRANS or MER/FAC) and they are obviously not Structural. Physics: A photon has a polarization that describes the angle between the plane of the electric field with respect to the direction of propagation. Many photons can be unpolarized and can be plane polarized (there are other options not discussed). If unpolarized, there are photons with polarization at all 360° (like sun). If (plane) polarized, there are photons with polarization at 1° (or some small number). Polaroid sunglass are polarizers (a filter that removed light at all angles except one). Polarizer can unpolarized light and convert it to polarized light. Optically active material can rotate plan polarized light. Some optical isomers can rotate the polarization to the left (levorotatory or L isomer). Some optical isomers can rotate the polarization to the right (dextrorotatory or D isomer). An equal mixture of both is racemic and will not rotate the plane polarized light at all. Optical Isomers are Chiral. Chiral molecules are molecules that the mirror image of is non-superimposable on the original molecule!. The metal atom with the four different groups attached which causes this lack of symmetry is described as a chiral center. The tetrahedral complex with four different ligands M(A)(B)(C)(D) are always Chiral! A molecule which has no plane of symmetry (or center of inversion) is described as chiral.

Lecture 13: 4/28/21 (Now 5/3/21)

We introduced Ligand Exchange Reactions, which can be viewed as an equilibrium between a Lewis-Base/Lewis Acid complex and a different Lewis-Base/Lewis Acid complex. Hence, they have an associated equilibrium constant. Knocking out multiple ligands in a complex is a sequential process. Each step has a corresponding equilibrium constant (this is sometime called step-wise associated constants). The overall reaction involving multiple Ligand-exchange steps will have an equilibrium constant that is the product of the step-wise association constants (E.g., \(K = K_1K_2K_3...\)). Instead of making a massive table of possible ligand-exchange reactions for each metal (i.e., each possible outgoing ligand(s) with each possible incoming ligand(s), we use a “reference state” or more specifically a reference complex (the aqua-complex). These are call Formation Constants. We can then construct the relevant equilibrium constant for any ligand exchange reaction by a hypothetical two step process: Step 1: removing aqua ligands to make desired reactant complex. Step 2: removing aqua ligands to make desired product complex. Step 3: Take the product of the associated constants (after flipping reaction 2). From the big Triangle of Chemistry we can convert the K to \(\Delta G\) (big K is more negative \(\Delta G\)). For Ni, the ligand exchange reaction of 3 \(en\) for 6 \(NH_3\) is strongly favored. From the temperature dependence of K, we can identify that is both favored enthalpically and entropically (since there are more free molecules generated after the reaction); this is called the Chelate effect. EDTA is the Kraken of Chelating agents, with one EDTA ion knocking out 6 ligands.

Lecture 14: 4/30/21 (Now 5/5/21)

We reviewed the Chelate effect again, which argues there is a strong thermodynamic driving force for chelating ligands (polydentate ligands that bind in 5 or 6 member rings) to displace monodentate ligand (e.g., water). This is strongly entropically driven since more molecules exist after the ligand exchange reaction that before and entropy scales with the number of molecules. However, it can be also enthalpically driven, which was a missed for many decades by chemists. Then we transitioned to discussing d-electron and their orbitals. Each of the d-orbitals has a unique 3D geometry that the square of will give the probability of find an electron in that orbitals. There are regions that this probability is zero (node), which are mostly planes in the d-orbitals (the \(d_{z^2}\) orbital is a cone). And there are region that there is a high probability of finding an electron. The ligands are Lewis bases, so they bring electrons in to form the dative bond, so there is an electrostatic issues between the electrons on the ligand and the electrons in the d-orbitals. This, as described, is not a bonding situation like in Molecular Orbitals! It is just electrostatic repulsion. The \(t_{2g}\) orbitals in an octahedral field had nodes on the x-, y- and z- axis. These are the \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\) orbitals and the eg orbitals in an octahedral field had nodes on the x-, y- and z- axis; these are the \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals. Once an octahedral field comes in, it will stabilize the three \(t_{2g}\) orbitals (more negative energy) and destabilize the two eg orbitals. This splitting is described by the “crystal field splitting” parameter, \(\Delta_o\). The total energy of all electrons in the presplitting and splitting diagrams is the same.

Lecture 15: 5/3/21 (Now 5/7/21)

We focused on populating crystal field splitting diagrams with electrons of octahedral complexes:

• For d¹-d³ ions, there is only one configuration (t_2g)ⁿ(e_g)⁰ where n is 1,2, or 3.
• For d⁸-d¹⁰ ions, there is only one configuration (t_2g)⁶(e_g)ⁿ where n is 2, 3, or 4.
• For d⁴-d⁷ ions, we have some flexibility. They can have high spin or low spin configurations.

The relative amplitude of the spin pairing energy (P) and the \(\Delta_{o}\) decides: If \(P > \Delta_{o}\) then the more stable configuration is the high spin where electrons will be promoted to the eg orbitals before pairing up (for a high spin d5 ion: (t_2g)³(e_g)²). However, If \(P < \Delta_{o}\) then the more stable configuration is the low spin where electrons will be paired in the t_2g orbitals before being promoted (for a low spin d⁵ ion: (t_2g)⁵(e_g)⁰). It is all about the relative magnitude of P and \(\Delta_{o}\), not the absolute magnitude! Many factors contribute to determining the absolute magnitude of Do and the nature of the ligand is the more important. We introduced the spectrochemical series that ranks ligands based on how much they split the d-orbitals (i.e., \(\Delta_{o}\)): Big bulky halogens are weak fields ligand (small \(\Delta_{o}\)) and CO and CN ligand are strong field ligands (big \(\Delta_{o}\)). Strong field ligands are low spin inducing ligands and weak field ligands are high spin inducing ligands. The d-splitting diagrams is also a function of ligand geometry (we discussed square-planar and tetrahedral). You should memorize the tetrahedral splitting and corresponding stabilization energy! Also, the \(\Delta_{t}\) is lower than \(\Delta_{o}\): \[\Delta_{t} = 0.44\,\Delta_o \nonumber\] Three types of magnetism (for this class): ferromagnetism, paramagnetism, and diamagnetism: Ferromagnetism is a permanent magnet, while paramagnetism and diamagnetism are attracted or repelled by an external magnetic field. The more unpaired electrons a molecule has, the more paramagnetic it is. Then introduced spectroscopy as a mechanism to estimate the absolute \(\Delta_{o}\) values!

Lecture 16: 5/5/21 (Now 5/10/21)

We started the discussion with a quick review of how one can measure the paramagnetic nature of systems with unpaired electrons (via a Gouy balance). The rest of the lecture focused on the spectroscopy on what is commonly called d-to-d transitions. These are electronic transitions that are associated with the absorption of a photon and they involve promotion of an electron from a low energy orbital to a unfilled d-orbital.

• For octahedral complex, that would be a \(t_{2g} → e_g\) transition and hence the energy of the photon that is absorbed equated to \(\Delta_o\)
• For tetrahedral complex, that would be a \(e_g → t_{2g}\) transition and hence the energy of the photon that is absorbed equated to \(\Delta_t\)

In absorption spectroscopy, the color of a sample is the preferential enhancement of light at the specific color to the detector (eye). Something is blue to the eye, because of the light that scatters or is transmitted through will have more blue light. This is the same things as saying that if initially white light is exposed to the sample and then scatted or transmitted, then the other colors are preferentially absorbed. The complementary color wheel is how you can determine the color of a sample. A sample that does not absorb light because (for an octahedral complex):

• There are no d-electrons to promote or
• There are no free d-orbitals for d-electrons to be promoted into or
• \(\Delta_o\) is too big so the photon energy is greater than what our eyes can see (this d-d transition would be in the ultraviolet)
• \(\Delta_o\) is too small so the photon energy is lower than what our eyes can see (this d-d transition would be in the infrared)