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Lecture 1: 4/3/17 (Unit I: Electrochemistry - REDOX Chemistry and Thermodynamics)

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).

Required Supplementary

Lecture 2: 4/5/17 (Unit I: Electrochemistry)

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 is add to a solution of Copper (2+) a displacement reaction (redox too) occurs 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.

Required Supplementary
 

Lecture 3: 4/7/17 (Unit I: Electrochemistry)

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.

Required Supplementary

Lecture 4: 4/10/17 (Unit I: Electrochemistry)

•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).

Required Supplementary

Lecture 5: 4/12/17 (Unit I: Electrochemistry - The Big Triangle of Chemistry)

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 \(E_{cell} = E_{cell}^o - \dfrac{0.0592 \,V}{n} \ln Q\). 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).

Required Supplementary
 

Lecture 6: 4/14/17 (Unit I: Electrochemistry - Non-standard Cell = Nernst Equation)

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 Kc which is in terms of all concentrations or Kp 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 Châtelier'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.

Required Supplementary
 
End-of-Chapter_Material (optional problems)

Lecture 7: 4/17/17 (Unit I: Electrochemistry - Corrosion and Resistance)

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.

Required Supplementary

Lecture 8: 4/19/17 (Unit II: Inorganic Chemistry - Electrolytic Cells and Electroplating)

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.

Required Supplementary

Lecture 9: 4/21/17 (Unit II: Inorganic Chemistry - Electrons, d-Block and Configurations)

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.

Required Supplementary
 

Lecture 10: 4/24/17 (Unit II: Inorganic Chemistry)

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.

Required Supplementary

Lecture 11: 4/26/17 (Unit II: Inorganic Chemistry - Geometric Isomers)

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!

Required Supplementary

Mid-term Exam #1: 4/28/17 (Friday)

Lecture 12: 5/1/17 (Unit II: Inorganic Chemistry - Optical Isomers)

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. 

Required Supplementary

Lecture 13: 5/3/17 (Unit II: Inorganic Chemistry - Complex Stability)

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.

Required Supplementary

Lecture 14: 5/5/17 (Unit II: Inorganic Chemistry - Crystal Field Splitting)

•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.

Required Supplementary
Exercises Week 5 (optional)

Lecture 15: 5/8/17 (Unit II: Inorganic Chemistry - Magnetism)

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

  • For d1-d3 ions, there is only one configuration (t2g)n(eg)0 where n is 1,2, or 3.
  • For d8-d10 ions, there is only one configuration (t2g)6(eg)n where n is 2, 3, or 4.
  • For d8-d10 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: (t2g)3(eg)2). However, If \(P < \Delta_{o}\) then the more stable configuration is the low spin where electrons will be paired in the t2g orbitals before being promoted (for a low spin d5 ion: (t2g)5(eg)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 \(\Delta_{o}\): \[\Delta_{t} = 0.44\,\Delta_o\] 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!

Required Supplementary

Lecture 16: 5/10/17 (Unit II: Color)

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)
Required Supplementary

​​​​​Lecture 17: 5/12/17 (Unit III: Descriptive Chemistry I)

We gave an introduction to descriptive chemistry, which primarily involves connecting basic properties of elements to describe observed chemical and physical behavior. There are four trends things that students must master for this section of the class

  1. Atomic Radius: decreases from left to right across a period increase as you go down a group
  2. Electronegativity: increases from left to right across a period decreases as you go down a group
  3. Ionization Energy: Increases from left to right across a period decreases as you go down a group
  4. Metallic Character: Decreased from left to right across a period increases as you go down a group

For each Group (8), you want to master

  1. Know at least one General Physical or chemical Property that is characteristic.
  2. Origin of the name of group
  3. Allotropes of key elements

A key aspect of descriptive chemistry is to connect electronic structure to chemistry.

  • Group 1 (Alkali metals) – name comes from what happens to water when they are added. This elements have low ionization energy and like to explode with water since so reactive.
  • Group 2 (Alkali earth metals) – name comes from what happens to water when they are added. These elements are like group I, but a bit weaker. They are also less soluble in water.
  • Group 3 (Boron group) – name is obvious. Nonmetal at top and poor metals below.
  • Group 4 (Carbon family) - name is obvious. Nonmetal at top, metalloids in middle, and poor metals below. Carbon has three allotropes (graphite, diamond, and fullerenes). Tin has two (gray and white).
  • Group 5 (Nitrogen family) - name is obvious. Nonmetal at top, metalloids in middle, and poor metals below. Phosphorous has many allotropes (black, white, red, violet).
  • Group 6 (oxygen family) - name is obvious (also called chalcogens). Oxygen has two allotropes: \(O_2\) and \(O_3\) (ozone).
Required (don't get stuck in details) Supplementary

Lecture 18: 5/15/17 (Unit III: Descriptive Chemistry II and Chemical Kinetics)

We completed our very brief interlude into descriptive chemistry.

  • Group 16 (oxygen family) - name is obvious (also called chalcogens meaning “ore formers”). Oxygen has two allotropes: \(O_2\) and \(O_3\) (ozone).
  • Group 17 (halogens) - name means “salt formers”). They are good oxidizers since they are great non-metals (prefer to be reduced to get octet so they oxidize): no allotropes to be concerned with. They have a set of odd molecules called interhalogens which are made up of mixed halogen atoms.
  • Group 18 (noble gas) - name means special; they used to be call the “inert gases”). Very weak intermolecular forces, so they are gases at STP. Xenon and Krypton can be made into ionic compounds, when mixed with high electrogenativity atoms (\(F^-\) and \(O^{2-}\)).

Introduced Kinetics: The flip side of thermodynamics, which is a driving force for a reaction, but tells nothing about timescales. Discusses Mechanism as a “black box” between reactants and products. Thermodynamics does not tell you about the mechanism (only cares about beginning end) and as we will see kinetics tells us about mechanisms (but not definitely as we will see). The balanced reaction tells us NOTHING about the mechanism! For a reaction to occur species much collide with sufficient kinetic energy and proper orientation. Most collisions do not induce a reaction (only the lucky ones). The instantaneous rate of a reaction can be defined in terms of the balanced reaction and rates of decay of reactants and rates of growth for products. For a general reaction of the form

\[aA + bB \rightarrow cC + dD \label{gen}\]

we will define

\[ \text{rate} = - \dfrac{Δ[A]}{a Δt} = - \dfrac{Δ[B]}{b Δt} = + \dfrac{Δ[C]}{c Δt} = + \dfrac{Δ[D]}{d Δt} \]

Required (don't get stuck in details, except for kinetics) Supplementary

 Lecture 19: 5/17/17 (Unit IV: Chemical Kinetics - Differential Rate Laws)

The instantaneous rate of a reaction can be defined in terms of the balanced reaction and rates of decay of reactants and rates of growth for products. We separate average and instantaneous rates by a differential or with ratio of differences. We can use experimental data to calculate average rate and if time interval is small, the approximate it to instantaneous rate. There are different methods to measure reaction rates depending on nature of reactants or products. Color is a common example (if possible). Often in such experiments we monitor the concentration of species (all of them is ideal, but not needed) as a function of time. From this we can extract rate as a function of time. We can postulate a rate law that relates how the rate at a specific point in evolution changes as a function of concentrations of species at that point.\[\text{rate} \propto [A]^x[B]^b…\] where x and y are called the reaction order with respect to A and B, respectively. The sum of x and y is called the overall reaction order. The reaction order can be zero, an integer or even a non-integer! The rate law and the reaction order can NOT be derived from the stoichiometric equation! There is in general NO connection between the stoichiometric coefficient and the reaction order! The reaction order(s) for a reaction can be determined from inspection (or calculation) of the initial (or at any time) rates as a function of concentration.

Required Supplementary

Mid-term Exam #2: 5/19/17 (Friday)

Lecture 20: 5/22/17 (Unit IV: Chemical Kinetics - Integrated Rate Laws)

The three differential rates laws we discussed before (0th, 1st and 2nd) were in the differential form (there are others of course); these formulations describe how the instantaneous rate changes as a function of concentration (which in turn changed as a function of time). To identify how the concentrations changes a function of time, requires solving the appropriate differential equation (i.e., the differential rate law).

  • The zero-order rate law predicts in a linear decay of concentration with time: \([A]= [A]_o  -kt\)
  • The 1st-order rate law predicts in an exponential decay of concentration with time: \([A]= [A]_o e^{-kt}\)
  • The 2nd-order rate law predicts in an reciprocal decay of concentration with time: \(\dfrac{1}{[A]}= kt + \dfrac{1}{[A]_o}\)

The half-life of a reaction is defined as the time it takes for the concentration of the reactant to decrease to half its original value. This is a phenomenological metric based off of observation.

  • For 0th order, the half life is: \(t_{1/2} =  \dfrac{[A]_o}{2k}\)
  • For 1th order, the half life is: \(t_{1/2} = \dfrac{\ln 2}{k} \approx \dfrac{0.693}{k}\)
  • For 2nd order, the half life: \(t_{1/2} = \dfrac{1}{k [A]_o}\)

You can tell which order a reaction is by identifying which plot vs. time will be linear.  

Required Supplementary

Lecture 21: 5/24/17 (Unit IV: Chemical Kinetics - Temperature Dependence)

The lecture started the discussion arguing how you can determine the rate law by plotting up a certain function vs. time.

  • If concentration vs. time is linear -> zeroth order
  • If ln (concentration) vs. time is linear -> first order
  • If 1/(concentration) vs. time is linear -> second order

All you have to do is plot these up and inspect (this is for simple reactions BTW). We reintroduced to collision theory which requires a collision to react. Three aspects are involved in the rate then.

  1. The collisional frequency (function of temperature)
  2. The ration of collision with sufficient “Activation Energy” (function of temperature)
  3. The orientation effects (also called steric factor and is not a function of temp)

Then introduces Arrhenius theory to predict temperature dependence of reaction rate constant

\[k=Ae^{-E_a/RT}\]

This introduces two constants: The activation energy (\(E_a\)) and the pre-exponential constant (\(A\)). The activation energy is the energy needed to initiate the reaction (E.g., breaking a bond) and the pre-exponential constant is related to the frequency of collisions. From knowledge of rate constant at two temperatures, both \(A\) and \(E_a\) can be extracted (i.e., two equations and two unknowns). The lecture concluded with a brief introducion to reaction mechanisms and molecularity (unimolecular, bimoleculatar, termolecular; the latter is very very very rare!)

Required Supplementary

Lecture 22: 5/26/17 (Unit IV: Chemical Kinetics - Mechanisms)

Reintroduced molecularity (unimolecular, bimoleculatar, termolecular). The latter is very very very rare. The Molecularity of a reaction is not the Order of the reaction (determined by experiment). We can construct reaction profiles to represent mechanisms

  • We can identify ΔG (or ΔH if written in terms of enthalpy)
  • We can identify Ea (or sometimes called ΔG‡) values
  • We can identify the number of steps
  • We can identify the intermediates
  • We can identify the rate determining step (if existing)

We reiterated that the rate law must be expressed in terms of reaction and products only! So no intermediates! Rate determining step is the slowest step (Not all mechanisms have a rate determining step, by the way). Each mechanism has a characteristic rate law. However, each rate law may have multiple mechanisms that produce it. Kinetics (and Science in general) can propose mechanisms and disprove them based on comparing characteristic rate law to experimental rate law, but never can prove the “correct” mechanism.

Required Supplementary

​​​​​Memorial Day: No Lecture (5/29/17)

Lecture 23: 5/31/17 (Unit IV: Chemical Kinetics - Mechanisms and Catalysis)

Reiterated similarities between science and kinetics (w.r.t. rate laws)

  • Each mechanism (with specific rate constants) predicts a rate law for a reaction
  • Experiments are used to determine the rate law for the reaction
  • If predicted rate law does not agree with experiment, the mechanism is false
  • If predicted rate law does agree with experiment, the mechanism is may be true
  • Just like science, we cannot prove the mechanism, just disprove it.

Again, rate determining step is slowest step and has highest energy barrier. If mechanism has rate determining step as first elementary step, then the corresponding rate law for that step (from the molecularity) is the rate law for the mechanism. If mechanism has rate determining step as second elementary step, then the corresponding rate law for that step (from the molecularity) typically involves an intermediate is NOT rate law for the mechanism. This requires approximations (or more advanced math) to solve for predicted rate law in terms of reactants and product ONLY. Rapid Equilibrium and Steady-State Approximation. Only the former is expected to use on the final.

  1. This involves assuming the first step is reversible and the next step is the rate determining step (slower). This is needed to establish the equilibrium.
  2. We can construct an equilibrium constant (\(K\)) from law of mass action and connect to rate constants (\(k\)).
  3. This is then is used to express the concentration of an intermediate in terms of the reactants and then is used to predict a proper rate law for the mechanism.

Catalysis involve a species that participates in the reaction, but does not get consumed or generated (overall). It operates by generating a different mechanism for the reaction that has multiple energy barriers lower than the uncatalyzed reaction. But, since the mechanism is different and more complicated, the reaction profile is more complex involving intermediates. Two general classes of catalyst: Homogeneous and Heterogeneous (terms discussed in electrochemistry). The catalyst does NOT affect the ΔG, ΔH, ΔS for the reaction (based on endpoints of the reaction). It affects the kinetics and mechanisms only (the stuff in the middle). Similarly, the catalyst does not affect an equilibrium constant for a reversible reaction (since \(ΔG = -RT \ln K\)).

Required Supplementary
14.9: Catalysis

Lecture 24: 6/2/17 (Unit V: Nuclear Chemistry - Radioactivity)

“Regular chemistry” involves the electrons – configurations, bondings, ionization, electron affinity, valence, orbitals, shielding, penetration, crystal field theory. These reasonably small energy issues. “Nuclear chemistry” is concerned with the nucleus and involves much, much higher energy issues. Both types of chemistries have spontaneous (not-induced) and non-spontaneous  (induced) Radioactivity is the emission of ionizing radiation or particles caused by the spontaneous disintegration of atomic nuclei. Three types of fundamental particles: electrons (-1 charge, negligible mass), protons (+1 charge, 1 amu mass), and neutrons (no charge, 1 amu mass). We can introduce a “nuclear nomenclature” for a specific nucleus that gives: (1) The number of protons (atomic number, Z). Well, twice actually and (2) The number of nucleons (mass number A). The number of neutrons can be calculated A-Z. In chemical reactions, mass is conserved. In nuclear reactions, A and Z are conserved (“nuclear accounting”). Three general types of reactivity: alpha particles, beta particles and gamma rays.

  • Alpha particles have a higher mass (4 amu) and are positively charged (+2) = helium nucleus.
  • Beta particle have much smaller mass (1/1800 amu) and are negatively charged (-1).
  • Gamma rays have no mass and are not charged = EM radiation (like light)
Required Supplementary

Lecture 25: 6/5/17 (Unit V: Nuclear Chemistry - Transmutation and Energetics)

Natural Radioactivity involves the emission of alpha, beta and/or gamma rays.

Emission by Alpha particles - \(\ce{^{4}_{2}He}\):

  • Emitting a alpha particle decreases neutron number by two
  • Emitting a alpha particle decreases proton number by two
  • Emitting a alpha particle decreases mass number by four

Emission by beta particles (negative time = electron) - \(\ce{^{0}_{-1}\beta ^-}\):

  • Emitting a negative beta particle decreases neutron number by one
  • Emitting a negative beta particle increased proton number by one
  • Emitting a negative beta particle does not change mass number
  • Also results in emission of an antineutrino

Emission by beta particles (positive time = positron) - \(\ce{^{0}_{1}\beta ^+}\)::

  • Emitting a positive beta particle increases neutron number by one
  • Emitting a positive beta particle decreases proton number by one
  • Emitting a positive beta particle does not change mass number
  • Also results in emission of an neutrino

Emission by gamma ray particles - \(\gamma\)

  • Does not affect “nucleus accounting” .

Each emission has different penetration depths: alpha < beta < gamma. Species are stable when on the belt of stability and unstable when off. They give off natural (spontaneous) radiation when unstable to get back on. This often involves multiple steps forming a “decay chain”. There are magic numbers associated with neutron and proton numbers to describe why a nucleus is state vs. unstable. I do not expect you to memorize those numbers. Law of Conservation of Mass that works oh so well in “regular” Chemistry does not work so well in nuclear chemistry. Energy can be convert to mass (hard to do actually), but mass can be converted to energy much easier to do). This is controlled by Einstein’s \(E=mc^2\) formula in any nuclear reaction. That energy released is converted to thermal energy => things get hot very quickly. This is good for nuclear power and for nuclear weapons. Energy can be convert to mass (hard to do actually), but mass can be converted to energy much easier to do). This is demonstrated via a “defect mass” between a mass of a nucleus and the mass of the constituent nucleons (protons and neutrons). Convert this to energy via Einstein’s formula and this is called a “binding energy”

Required Supplementary

Lecture 26: 6/7/17 (Unit V: Nuclear Kinetics - Fusion and Fission)

Natural radioactivity is everywhere and can be measured with a Geiger counter. Artificial radioactivity can be induced (non-spontaneous) by collisions of nuclei with other species (e.g., neutrons). Whether natural or artificial, "nuclear accounting" still holds (conserving A and Z). This is how we make new elements (transmutation). Natural radioactivity kinetics is govern by first-order kinetics. \[A = \lambda N \] or \[N = N_oe^{-\lambda t}.\] We can construct half lives \(t_{1/2} = \ln 2/ \lambda\) and used to identify timescales if a initial time is set ("radioisotope dating"). Unlike chemical kinetics, nuclear kinetics are temperature independent (poor Arrhenius). Each isotope has a binding energy  and the most stable is often ascribed to iron (although technically it is Ni-62). Fission and fusion reactions may be induced occur to increase stability (per nucleon) of daughter isotopes. Fission involve fusing two nuclei together and releasing energy. Fission involved breaking a nucleus into (typically) two nuclei with release of energy. Both can be sustained in a chain reaction if conditions permit (high density of nuclei is critical in both).

Required Supplementary

Final Exam: 6/13/17 at 6:00 p.m. - 8:00 p.m. (Comprehensive)