Zumdahl Textbook Summaries (Lectures 13-36 Material)

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11.1 Galvanic Cells  Oxidation involves a loss of electrons (an increase in oxidation number) and reduction involves a gain of electrons (a decrease in oxidation number).  Overall reactions balance the transfer of electrons between species  The key to creating a galvanic cell is in separating the oxidising agent from the reducing agent, thus requiring the electron transfer to occur through a wire. The current produced can then be wired through a motor and harnessed.  Current stops flowing as charge builds up in the two apartment, requiring the introduction of a salt bridge or a porous disc to complete the circuit.  Electrons flow through the wire from the reducing agent to the oxidising agent, and ions between the compartments to keep the net charge zero.  Galvanic cell; a device in which electrical energy is changed to chemical energy.  Anode; where oxidation occurs and electrons are produced (-)  Cathode; where reduction occurs and electrons are consumed (+)  Cell potential is the driving force for the reaction to occur, measured through a voltmeter which draws current through a known resistance. 11.2 Standard Reduction Potentials  The overall reaction can be broken down into half-reactions assigned a potential to each measured against a hydrogen cell.  Overall reactions balance the electrons transferred between species.  In regards to standard reduction potentials, one of the half-reactions must be reversed, always the reaction with the lowest potential.  Half reactions much be multiplied by integers to achieve electron balance.  The cell will always run spontaneously in the direction that produces a positive cell potential.  Galvanic cell diagrams need the cell potential, balanced cell reaction, direction of electron flow, half reactions, designation of anode and cathode. 11.4 Dependence of the Cell Potential on Concentration  Cell potential depends on the concentration of species, and is variable under conditions which differ from standard 1M.  An increase in the concentration of a reactant will favour the forward reaction and increase the driving force on the electrons, increasing the cell potential. ( )  The Nernst Equation: ( )  The potential calculated from the Nernst Equation is the maximum potential before any current flow occurs. As the cell discharges and current flows from anode to cathode, the concentrations change, and cell potential changes.  The cell will spontaneously discharge until it reaches equilibrium at which E cell  At equilibrium the components in the two cell compartments have the same free energy; the cell no longer has the ability to do work.  A pH meter can measure the concentration from an observed potential, has 3 main components; a standard electrode of known potential, a special glass electrode and a potentiometer that measures the potential between two electrodes.  Electrodes that are sensitive to the concentration of a particular ion are called ion- selective electrodes (i.e. glass electrode in pH meter)  A cell in which both compartments have the same components but at different concentrations is called a concentration cell.  Because the measured potential of an electrochemical cell provides a very sensitive method for the experimental determination of equilibrium concentrations, the values of equilibrium constants are often determined from electrochemical measurements. 11.5 Batteries  A battery is a galvanic cell, or a group of galvanic cells connected in series where the potentials of individual cells add to give the total battery potential.  Lead storage battery: automobile manufacturing, can function for several years under temperature extremes. Typically 6 connected cells, total 12 volts. Continuously charged by alternator. Anode: lead Cathode: lead coated with lead dioxide. Electrolyte: sulphuric acid  Dry Cell batteries: used in calculators and watches. Potential of about 1.5V. Anode: zinc inner case Acid Cathode: carbon rod in contact with moist MnO , solid N2 Cl and 4 carbon. Alkaline Cathode: NH Cl4replaced with KOH or NaOH. Lasts longer.  Lithium ion batteries involve the migration of Li ions from the cathode to the anode, where they intercolate as the battery is charged. On discharge, the opposite occurs.  Fuel Cells: a galvanic cell in which the reactants are continuously supplied. Includes hydrogen fuel cells which are non-polluting. 11.6 Corrosion  Corrosin is the process of returning metals to their natural state, ores from which they were obtained. Involves oxidation.  Metals corrode because they oxidise easily, most having standard reduction potentials less than oxygen.  Most metals collect a thin oxide coating that protects their internal atoms against further oxidation e.g. aluminium.  Iron’s oxide coating is not an infallible shield, it tends to flake off.  Controlling the corrosion of steel is necessary to maintain the structure of buildings. Steel is vulnerable due to its non uniform surface where iron is more easily oxidised (anodic regions).  Moisture acts as a salt bridge between anodic and cathodic regions.  Corrosion is prevented by plating, with metals such as chromium and tin which react with oxygen to form a durable, effective oxide coating.  Galvanised zinc coating acts as a sacrificial material which is preferentially oxidised.  Alloying is also used to prevent corrosion, e.g. chromium and nickel, which form oxide coatings changing reduction potentials to one of noble metals.  Cathodic protection is most widely used to protect buried fuel tanks and pipelines, by attaching an active metal e.g. magnesium to steel. 11.7 Electrolysis  Electrolysis involves forcing a current through a cell to produce a chemical change for which the cell potential is negative that is electrical work causes an otherwise non- spontaneous reaction to occur.  Anode and cathode are reversed  Stoichiometry of electrolytic process: how much chemical change occurs with the flow of a given current for a specified time.  Plating means depositing the neutral metal on the electrode surface by reducing the metal ions in solution.  Step 1; calculate total charge in coloumb passed through cell  Step 2; calculate the number of moles of electrons required to carry this charge. I.e. divide by Faraday’s constant.  Step 3; account for electron: atom ratios  Step 4: calculate the mass of substance formed.  Water can be hydrolysed by electrolysis.  Electrolysis of a mixture of ions occurs in order of the most to least positive cell potential value.  NOTE: overvoltage can occur, meaning species are oxidised out of order. 12. 1 Electromagnetic Radiation  Energy travels through space by electromagnetic radiation- including visible light, x- rays and infrared which exhibit similar wavelike behaviour and travel at the speed of light in a vacuum.  They have different frequencies and wavelengths  Electromagnetic radiation is so-named as it has electrical and magnetic fields that oscillate in two dimensions.  Wavelength: distance between two consecutive peaks or troughs in a wave.  Frequency: the number of cycles per second that pass a given point in space.  Waves with shorter wavelengths have higher frequencies, and vice versa.  C= 2.9979 X 10 m/s  C=λv 12. 2 The Nature of Matter  Particles: had a mass and occupied space -34  Planck’s constant: 6.636 X 10 J s   Planck proved that energy is in fact quantized and can be transferred only in discrete units of size called a quantum.  Einstein proposed that electromagnetic radiation itself is quantized.  The Photoelectric effect: observations are explained by assuming that electromagnetic radiation is quantized (consists of photons) and that the threshold frequency represents the minimum energy required to remove the electron from the metal’s surface.  (energy of incident photon – energy required to remove electron from metal’s surface.  Greater intensity means that more photons are available to release electrons.  Photons do not exhibit mass in the same way as classical particles, only in a relativistic sense, however they have momentum and appear to be affected by gravity.  Diffraction results when light is scattered from a regular array of points or lines. Colours result as various wavelengths are not scattered in the same way, separating colours.  Light produces a diffraction pattern of constructive and destructive interference.  Significant as shows that matter and energy are not distinct; all matter exhibits both particulate and wave properties. 12.3 The Atomic Spectrum of Hydrogen  When a high energy discharge is passed through a sample of hydrogen has, the molecules absorb energy, causing some bonds to break and exciting the atoms. Excess energy is emitted in the form of light to produce an emission spectrum.  A continuous spectrum contains all the wavelengths of visible light ~ every energy level is allowed.  Hydrogen emission produces a line spectrum. Only certain energies are allowed for the electron in the hydrogen atom, in other words it is quantized. 12.4 The Bohr Model  Bohr’s model: electrons in a hydrogen atom move around the nucleus only in certain allowed circular orbits.  Electrons are made to travel in a circular orbit due to their attraction to the positive nucleus.  Hypothesized that as electrons constantly change direction and emit energy they are constantly accelerating.  The expression for the energy levels available to the electron in the hydrogen atom is: ( ) where n is an integer and Z is the atomic number.  The energy of the electron in any orbit is negative relative to this reference state.  Excited electrons have more energy than those in their ground state.  The negative sign for the change in energy indicates that the atom has lost energy and is now in a more stable state.  The Bohr model: 1. Correctly fits the quantized energy levels of the hydrogen atom as inferred from its emission spectrum. These energy levels correspond to certain allowed circular orbits for the electrons. 2. As the electron becomes more tightly bound, its energy becomes more negative relative to the zero-energy reference state; energy is released from the system.  NOTE: ELECTRONS DO NOT MOVE AROUND THE NUCLEUS IN CIRCLES, Bohr’s model is fundamentally flawed. 12.5 The Quantum Mechanical Description of the Atom  Wave mechanics and quantum mechanics were hypothesized by de Broglie and Schrodinger. To them the electron bound to the nucleus seemed similar to a standing wave.  As standing waves have a node at each end there is a left over half-wavelength in any allowed motion.  ̂ , where is called the wave function and tracks the electron’s position in 3D space, and H represents a series of mathematical instruments called an operator.  Heisenberg uncertainty principle: There is a fundamental limitation to just how precisely we can know both the position and the momentum of a particle at a given time. 12.6 The Particle in a Box  Only certain electron energies are allowed, meaning that the system is quantized.  An integral number of half wave lengths exactly equals the size of the box- others cannot exist because they would destructively interfere  Ambiguous and incomprehensible. 12.7 The Wave Equation for the Hydrogen Atom  The electron of the hydrogen atom moves in three dimension and has potential energy because of its attraction to the positive nucleus at the atom’s centre.  E =n-2.178 X 10 -18J (Z /n ) where z=atomic number and n is integer values 12.8 The Physical Meaning of a Wave Equation  The uncertainty principle indicates that there is no way of knowing the detailed movements of the electron in a hydrogen atom.  The square of the function evaluated at a particular point in space indicates the probability of finding an electron near that point.  The relative probability of finding the electron near positions 1 and 2 is determined by substituting the values of r, θ and φ for the two positions into the wave function, squaring the function value and computing the N1/N2 ration.  The square of the wave function is given as the probability distribution  If an electron visits a point more times the negative becomes darker, thus the intensity of a point indicates the probability of finding an electron there. = electron density.  Radial probability distribution: the total probability of finding the electron in each spherical shell plotted verses the distance from the nucleus. Maximum when electron is at ideal sphere volume and nucleus distance.  The normally accepted arbitrary definition of the size of the hydrogen 1s orbital is the radius of the sphere that encloses 90% of the total electron probability. 12.9 The Characteristics of Hydrogen Orbitals  Orbitals are characterised by a set of quantum numbers that arise when the boundary conditions are applied  N is related to the size and energy of the orbital.  L is the anguar momentum quantum number which has integral values from 0 to n-1.  M islthe magnetic quantum number which has values –l, 0, -l. Relates to the orientation in space of the angular momentum associated with the orbital.  Orbital diagrams show areas of high probability called nodal surfaces or nodes. The number of these increase as n increases  The functions for s orbitals are positive everywhere in three-dimensional space.  There are no d orbitals that correspond to principal quantum levels  All orbitals with the same value of n have the same energy- they are said to be degenerate. o The quantum mechanical model describes electrons as waves o This model cannot specify the details of electron motions o The size of the orbital is arbitrarily defined as the surface that contains 90% of the total electron probability. o Electrons can be excited to higher energy orbitals if the atom absorbs energy. 12.10 Electron Spin and the Pauli Principle  A fourth quantum number was necessary to account for the details of the emission spectra of atoms called the electron spin quantum number; -0.5 or +0.5  Pauli exclusion principle: In a given atom no two electrons can have the same set of four quantum numbers (n, l, m anl m ) s  An orbital can hold only two electrons, and they must have opposite spins. 12.11 Polyelectronic Atoms  Polyelectronic atoms are those with more than one electron.  Important factors include kinetic energy of electrons, potential energy of attraction between nucleus and electrons as well as the potential energy of repulsion between two electrons.  Electron correlation problem: we cannot rigorously account for the effect a given electron has on the motions of the other electrons in an atom.  Can be treated by assuming each electron moves in a field of charge that is the net result of the nuclear attraction and the average repulsions of all the other electrons.  The large differences in the energies required to remove one electron must arise from the electron-electron repulsions in the neutral atom. They can therefore be thought of as reducing the nuclear charge. 12.13 The Aufbau Principle and the Periodic Table  Aufbau Principle: s protons are added one by one to the nucleus to build up the elements, electrons are similarly added to these atomic orbitals.  Two electrons with opposite spins can occupy an orbital as in 1s subshell.  Hund’s rule: the lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals.  Valence electrons are those in the outermost principal quantum level of an atom. Elements in the same group have the same electron configuration. (1) The (n+1)s orbitals always fill before the nd orbitals (2) Lanthanide series fills seven 4f orbitals. (3) Actinide series fills seven 5f orbitals (4) Main group elements have the same electron configuration down a group.  Predicting the configurations of transition metals is more difficult 12.15 Periodic Trends in Atomic Properties  Ionisation energy is that require to remove an electron from a gaseous atom or ion that is assumed to be in its ground state.  Koopman’s theory: the ionisation energy of an electron is equal to the energy of the orbital from which it came  In a stepwise ionisation process it is always the highest-energy electron that is removed first. With each ionization more energy is required to move another electron, due to atomic charge and nuclear attraction.  As we go across a period from left to right, the first ionization energy increases. Down a group the first ionisation values decrease as electrons are farther away from the nucleus.  Shielding occurs when electrons repel one another.  Electron affinity is the energy change associated with the addition of an electron to a gaseous atom. Generally become more negative from left to right across a period since the electron is added at increasing distances from the nucleus  A
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