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# 1.1 - Lab Background

matPurpose of Experiment

This experiment is designed to introduce you to the following:

1.    The synthesis of simple coordination compounds;
2.    IR and Visible spectroscopy;
3.    The kinetics of a chemical reaction by determining its rate and rate law;
4.    The determination of activation energy from kinetics data.

This experiment will contribute to improving your skills in the following lab techniques:
•    Volumetric and gravimetric measurements
•    Crystallization and isolation of metal complexes
•    Correct sample preparation and handling of the IR and UV-VIS instruments

Safety

1.     Concentrated acids, bases and hydrogen peroxide (30%) should be handled only while wearing gloves.
2.     Reaction waste should be placed in appropriately labeled bottles.
3.     Concentrated ammonia should be used in the hood to avoid breathing its fumes.

Introduction

A. Coordination Chemistry

In introductory chemistry, you learned that although transition metal salts(e.g., $$CoCl_3$$) can be obtained in amorphous anhydrous form, they are often obtained as a crystalline hexahydrate. Cobalt(II) nitrate hexahydrate is, in fact $$[Co(H_2O)_6](NO_3)_2$$; the six waters are coordinated to cobalt through an electron pair on water (a Lewis base) in an octahedral array around the metal (a cationic Lewis acid). Nitrates are relatively weak ligands and are not coordinated to the metal in this case, although they could coordinate in different circumstances. The coordination environment of the metal can be viewed most simply in electrostatic terms, which is the simplest theory of bonding in transition metal chemistry called Crystal Field Theory (CFT). The lowest energy orbitals in a cationic cobalt complex are the 3d orbitals, followed by the 4s and 4p orbitals. Cobalt is in group 9 in the periodic table, thus $$Co^{3+}$$ contains six electrons beyond the last inert gas configuration. In an octahedral environment, the 3d orbitals are split into two classes based on their energy. The $$d_{xz})$$, $$d_{yz})$$, and $$d_{xy})$$orbitals fall into a class that is called $$t_{2g}$$ while the$$d_{x2-y2}$$ and $$d_{z2}$$ orbitals fall into a class called $$e_g$$. (The symbols $$e_g$$ and $$t_{2g}$$ denote a doubly degenerate and triply degenerate set of orbitals, respectively, which are gerade, i.e., the sign of their wave function does not change upon inversion through the origin.) The orbitals pointing toward the six ligands are higher in energy because the ligands have electron pairs pointing toward the metal. The relative energies of the two classes of d orbitals are shown below:

If six electrons are added such that they are paired up in the $$t_{2g}$$ set of orbitals (the energy difference between the $$e_g$$and $$t_{2g}$$orbitals is large with respect to the energy required to pair up the electrons in the $$t_{2g}$$ orbitals), the metal is said (in CFT) to have the low spin d6 configuration, or more accurately, $$(t_{2g})^6(e_g)^0$$.

Many octahedral transition metal complexes can be transformed into others by ligand substitution reactions, which may be either associative or dissociative ("$$SN_1$$" or "$$SN_2$$", respectively, in terms, learned in organic chemistry), or sometimes complex and subtle variations of these basic reactions. The associative reaction would proceed through a seven-coordinate intermediate complex, while the dissociative reaction would proceed through a five-coordinate intermediate complex. In general low spin, octahedral complexes of $$Co(III)$$ are relatively slow to exchange ligands at the metal because the coordination number is relatively high (six), thereby discouraging formation of a seven-coordinate species for steric reasons. Also, the metal electrons are in orbitals that lie between the axes ($$d_{xy}$$, $$d_{yz}$$, $$d_{xz}$$), thereby minimizing repulsion between them and the electrons on the six ligands (bases). In contrast, a $$Co(II)$$ complex ($$d^7$$ therefore with electrons in the eg orbitals) is usually readily substituted. For this reason we begin the synthesis of a $$Co(III)$$ species with $$[Co(H_2O)_6](NO_3)_2$$, a high spin $$d^7$$ $$Co(II)$$ species.

B. IR and Visibility Spectroscopy

Infrared Spectroscopy is a powerful tool for simply and quickly learning something about many organic and inorganic species. IR spectroscopy measures the absorption of infrared radiation due to the vibrations of a molecule as a function of their energy. The specific number of vibrations can be determined through a normal coordinate analysis of the possible vibrations in the molecule (for example, a nonlinear molecule has 3N-6 vibrational modes where N is the number of atoms in the molecule). An IR spectrum can be acquired on a gaseous, liquid, or solid sample. For inorganic samples where only a qualitative spectrum is desired it is often easiest to grind the sample in a relatively non-IR- absorbing material such as solid KBr crystals which are subsequently placed under high pressure to form a thin window, or an oil such as Nujol® (a mineral oil that consists of $$C_{20}$$-$$C_{30}$$ alkanes) or Krytox® (fluorolube, a grease made from polytetrafluoroethylene) to yield a paste, which is either applied to a microporous polymeric film (such as polytetrafluoroethylene or polyethylene) in a thin layer or squeezed gently between two solid salt plates(typically single crystals of NaCl). It is important that these materials do not absorb IR radiation in the regions of interest. This technique effectively provides a spectrum of a solid, unless the sample happens to dissolve in the grinding material. In the often complex IR spectrum there are frequently strong vibrational modes that are relatively characteristic of a given type of bond, e.g., the C=O stretch in a ketone, or in carbonate ($$CO_3^{2-}$$) or the N=O stretch in nitrate ($$NO_3^{-}$$). Visible spectroscopy employs visible light, which is higher energy than infra-red light. Absorption of visible light by a sample (again in the gas, solution, or solid phase) promotes electronic transitions. Absorption of visible light gives rise to the colors of many transition metal complexes and some organic compounds (most organic compounds are colorless or nearly so). According to the Lambert-Beer law (or sometimes simply "Beer's Law"), the amount of light transmitted (T) by an absorbing sample ($$I/I_o$$ = intensity) is given by

$\% T = I/I_o = e^{-A} = e^{- \varepsilon cl}$

where the absorbance A is proportional to the concentration (c, in mol/L) of the solute, the length of the path the light travels through the sample (l, in cm), and the constant of proportionality, ε , called molar absorptivity coefficient (units M-1 cm-1) or molar extinction coefficient, which is characteristic of the sample and the electronic transition (vibrational if using infra-red radiation) in question. Therefore A = ε cl. Since the absorbance is directly proportional to concentration, both IR and visible spectroscopy can be employed to follow changes in the concentration of an absorbing species involved in a reaction.

C. Kinetic Studies

In this experiment you will follow the conversion of one compound into another by measuring the visible spectrum of the compound being consumed at a specified temperature as a function of time. The reaction rate can be measured as the change in concentration of a reactant (x) per unit of time $$\Delta t$$. The change in concentration of a reactant (or alternatively a product) is followed. Therefore

$Rate = \frac{[x]_{t2}-[x]_{t1}}{t_2-t_1} = \frac{\Delta [x]}{\Delta t}$

As a differential, the rate would be written as $$d[x]/dt$$. Therefore in a reaction in which reagent x is consumed, we might find that the rate depends upon the concentration of x, as shown in equation 3, where k is the observed rate constant for the reaction in question under the conditions employed. In general, however, the rate might depend in a more complex fashion upon [x], and also upon the concentration of other species, such as a catalyst y, which is not consumed in the reaction (equation 3). If a = 1, then the reaction is said to be first order in [x].

$\frac{d[x]}{dt} = =k[x]$

$\frac{d[x]}{dt} = =k[x]^a[y]^b ...$

If b = -1/2, then the reaction is inverse 1/2 order in [y], and so forth. The observed rate law will be consistent with the mechanism of the reaction, i.e., a series of elementary reactions. (An example of an elementary reaction is a simple collision between two species.) It is often possible to think of several elementary reactions (each with its own "absolute" rate constant) that taken together would yield the observed rate law with the observed rate constant. The units of the rate of a reaction in solution are mol $$l^{-1}$$, $$s^{-1}$$ or $$Ms^{-1}) . The rate of a reaction generally is limited by a relatively slow elementary reaction. Relatively fast elementary reactions that occur before or after a relatively slow reaction are not observable, i.e., are not part of the observed law. In a given solvent (e.g., water) generally, it cannot be determined to what extent the solvent itself is involved in the reaction since its concentration is constant. Therefore a rate constant is given for a specific solvent at a specific temperature. The Nobel Prize in chemistry in 1903 was awarded to Svante Arrhenius, who proposed that the rate constant for a reaction depended upon temperature according to equation 5, $k = Ae^{-( \frac{E_a}{RT})}$ the Arrhenius equation, where k is the rate constant, A is the "pre-exponential factor", R is the universal gas constant (1.99 cal \(deg^{-1} mol^{-1}$$ or 8.31 joules $$deg^{-1} mol^{-1}$$, T is the temperature in Kelvin, and $$E_a$$ (in kcal $$mol^{-1}$$ or kJ $$mol^{-1}$$) is the activation energy for the reaction (units must fully agree to cancel). The activation energy is the energy required by molecules reacting with one another to pass through a transition state and yield a product or products. If a reaction is well behaved in a given temperature range a plot of $$ln(k)$$ versus 1/T will produce a straight line with slope $$-E_a/R$$ and intercept ln(A). Rate constants (and therefore reaction rates) usually are found to increase by a factor of 2 - 3 with every 10-degree increase in temperature. Later and more advanced treatments in physical chemistry courses will reveal more details about A, but the simple treatment shown in equation 5 is still correct and will suffice for now.

References:

General Spectroscopy: Skoog, D.A. et al. Fundamentals of Analytical Chemistry 8th Ed. Part V Spectrochemical Methods: Chapter 24 Introduction to Spectrochemical Methods and Chapter 25 Instruments for Optical Spectrometry.

UV-VIS Spectroscopy: Skoog, D.A. et al. Fundamentals of Analytical Chemistry 8th Ed. Part V Spectrochemical Methods: Chapter 26 Molecular Absorption Spectrometry.

IR Spectroscopy: Mohrig J.R. et al. Techniques in Organic Chemistry 2nd Ed. Technique 18.

Kinetics: Skoog, D.A. et al. Fundamentals of Analytical Chemistry 8th Ed. Chapter 29 Kinetic Methods of Analysis. (See also your general chemistry textbookʼs section on kinetics)

Coordination Chemistry: See your general chemistry textbookʼs section on coordination compounds/transition metal chemistry. (For more advanced treatments of coordination chemistry see Miessler, Gary and Tarr, Donald. Inorganic Chemistry 2nd Edition)

Footnotes:

$$^1$$ The synthesis and kinetic procedures in this experiment have been adapted from: Angelici, R.J. Synthesis and Techniques in Inorganic Chemistry, 2nd Ed.; University Science Books: Mill Valley, 1986; Chapters 1 and 2.

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