102 Chem Notes Exam 3 Solubility Products Consider the equilibrium that exists in a saturated solution of BaSO 4 in water BaSO4(s) Ba2+(aq)+SO42-(aq) Equilibrium expression: Ksp=[Ba2+][SO42-] where the equilibrium constant , Ksp, is called the solubility constant Ksp is not the same as solubility Solubility is generally expressed as the mass of solute dissolved in 1 L (g/L) or 100 mL (g/mL) of solution, or in mol/L (M) Factors Affecting Solubility The Common-Ion Effect o If one of the ions in a solution equilibrium is already dissolved in the solution, the equilibrium will shift to the left and the solubility of the salt will decrease BaSO4(s) Ba2+(aq)+SO42-(aq pH o If a substance has a basic anion, it will be more soluble in an acidic solution o Substances with acidic cations are more soluble in basic solutions Complex ions o Metal ions can act as Lewis acids and form complex ions with Lewis bases in the solvent o The formation of these complex ions increases the solubility of the salts Amphoterism o Amphoteric metal oxides and hydroxides are soluble in strong acid or base, because they can act either as acids or bases o Examples of such cations are Al3+, Zn2+, Sn2+ Will a precipitate form? In a solution o If Q=Ksp, the system is at equilibrium and the solution is saturated o If Q>Ksp, more solid with dissolve until they are equal o If Q<Ksp, the salt will precipitate until they are equal Selective Precipitation Ions One can use differences in solubility's of salts to separate ions in a mixture First Law of Thermodynamics Recall that energy cannot be created nor destroyed Therefore, the total energy of the universe is a constant Energy can, however, be converted from one form to another or transferred from a system to the surroundings or vice versa Spontaneous Processes Spontaneous processes are those that can proceed without any outside intervention Processes that are spontaneous in one directions are non-spontaneous in the reverse direction Processes that are spontaneous at one temperature may not be spontaneous at other temperatures Reversible Process
In a reversible process, the system changes in such a way that the system and surroundings can be put back in their original states by exactly reversing the process Irreversible Processes Irreversible processes cannot be undone by exactly reversing the change to the system Spontaneous processes are irreversible (without outside intervention) Entropy Entropy (S) is a term coined by Rudolph Clausius in the 19 century Clausius was convinced of the significance of the ratio of heat delivered and the temperature at which it is delivered q_ E=q+w T Entropy can be thought of as a measure of the randomness of a system H is related to the various modes of motion in molecules Like total energy, E, and enthalpy, H, entropy is a socalled state function (pg. 254) Therefore, S=Sfinal-Sinitial For a process occurring at constant temperature (an isothermal process), the change in entropy is equal to the heat that would be transferred if the process were reversible divided by the temperature: S= qrev T Second Law of Thermodynamics States that the entropy of the universe increases for spontaneous processes, and the entropy of the universe does not change for reversible processes. In other words: For reversible processes... Suniv=Ssystem+Ssurroundings=0 For irreversible processes Suniv=Ssystem+Ssurroundings>0 These last truths mean that as a result of all spontaneous processes the entropy of the universe increases Entropy and Physical States Entropy increases with the freedom of motion of molecules Therefore , S(g)>S(l)>S(s) Solutions Generally, when a solid is dissolved in a solvent, entropy increases
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Entropy Changes In general, entropy increases when o Gases are formed from liquids and solids o Liquids or solutions are formed from solids o The number of gas molecules increases o The number of moles increases Entropy increases with increasing temperature Third Law of Thermodynamics
The entropy of a pure crystalline substance at absolute zero is 0 Standard Entropies These are molar entropy values of substances in their standard states Standard entropies tend to increase with increasing molar mass Larger and more complex molecules have greater entropies Entropy Changes Entropy changes for a reaction can be estimated in a manner analogous to that by (reactants) Where n and m are the stoichiometric coefficients in the balanced chemical equation Entropy Changes in Surroundings Heat that flows into or out of the system changes the entropy of the surroundings So for an isothermal process: Ssurr= -qsys T At constant pressure, qsys Entropy Change in the Universe The universe is composed of the system and the surroundings Suniv=Ssystem+Ssurroundings o For spontaneous processes Suniv>0 o For non-spontaneous processes Suniv<0 o For a system at equilibrium Suniv=0 This becomes: Suniv=Ssys+ -Hsys T Multiplying both sides by T, G= -TSuniv=Hsys -TSsys Gibbs Free Energy -TSuniv is defined as the Gibbs free energy, G When Suniv is positive, G is negative Therefore, when G is negative, a process is spontaneous The free energy represents the maximum energy available to do useful work Note: the word `free' means `available' If G is negative, the forward reaction is spontaneous If G is 0, the system is at equilibrium If G is positive, the reaction is spontaneous in the reverse direction Standard Free Energy Changes f f(reactants) Where n and m are the stoichiometric coefficients Free Energy and Temperature C = So how does change with temperature? There are two parts the to free energy equation:
o - the enthalpy term o - the entropy term The temperature dependence of free energy, then, comes from the entropy term Gibbs Free Energy Temperature Dependence = + + + + + + -, spontaneous +, non-spontaneous -/+, favorable at lower temperatures -/+, favorable at higher temperatures
Free Energy and Equilibrium Under any conditions, standard or non-standard, the free energy change can be found this way: +RTlnQ ) At equilibrium, Q=K, and G=0 +RTlnK =-RTlnK or, K=e-G The larger the value Entropy on the Molecular Scale Ludwig Boltzmann described the concept of entropy on the molecular level Temperature is a measure of the average kinetic energy of molecules in a sample Molecules exhibit several types of motion: o Translational: Movement of the entire molecule from one place to another o Vibrational: Periodic motion of atoms within a molecule o Rotational: Rotation of the molecule on about an axis or rotation about bonds Boltzmann envisioned the motions of a sample of molecules at a particular instant in time o This would be akin to taking a snapshot of all the molecules He referred to the sampling as a microstate of the thermodynamic system Each thermodynamic state has a specific number of microstates, W, associated with it Entropy is S=klnW where k is the Boltzmann constant, 1.38 x 10-23 J/K The change in entropy for a process, then, is S=klnWfinal -klnWinitial =kln(Wfinal/Winitial) Entropy increases with the number of microstates in the system The number of microstates and therefore the entropy tends to increase with increases in o Temperature o Volume o The number of independently moving molecules W represents the number of different ways that the energy can be distributed over the available energy levels Electrochemical Reactions- in electrochemical reactions, electrons are transferred from one species to another
/RT
Oxidation and Reduction An atom (ion) is oxidized when it loses electrons An atom (ion) is reduced when it gains electrons In order to keep track of what loses electrons and what gains them, we assign oxidation numbers What is reduced is the oxidizing agent What is oxidized is the reducing agent Assigning Oxidation Numbers Elements in their elemental form have an oxidation number of 0 The oxidation number of a monatomic ion is the same as its charge Nonmetals tend to have negative oxidation numbers, although some are positive in certain compounds or ions Oxygen has an oxidation number of -2, except in the peroxide ion in which it has an oxidation number of 1 Hydrogen is -1 when bonded to a metal, +1 when bonded to a nonmetal The sum of the oxidation numbers in a neutral compound is 0 The sum of the oxidation numbers in a polyatomic ion is the charge on the ion Half-Reaction Model Balance the equation of an oxidation-reduction (redox) reaction via the half-reaction method Treat oxidation and reduction as 2 separate processes Balance these half-reactions Combine them to attain the balanced equation for the overall reaction 1. Assign oxidation numbers to determine which is oxidized and which is reduced 2. Write the oxidation and reduction half-reactions Since the manganese goes from +7 to +2, it is reduced Since the carbon goes from +3 to +4, it is oxidized 3. Balance each half-reaction a. Balance elements other than H and O b. Balance O by adding H2O c. Balance H by adding H+ d. Balance charge by adding electrons 4. Multiply the half-reaction by integers so that the electrons gained and lost are the same 5. Add the half-reactions, subtracting things that appear on both sides 6. Make sure the equation is balanced according to mass 7. Make sure the equation is balanced according to charge Balancing in Basic Solution If a reaction occurs in basic solution, once can balance it as if it occurred in acid Once the equation is balanced, add OH- to each side to "neutralize" the H+ in the equation and create H2O in its place If this produces H2O on both sides, you might have to subtract water from each side Voltaic Cells In spontaneous oxidation-reduction reactions, electrons are transferred and energy is released We can use that energy to do work if we make the electron flow through an external device We call such a setup a voltaic cell
To obtain a useful current, we separate the oxidizing and reducing agents so that electrons transfer through an external wire The anode is the electrode at which oxidation occurs The cathode is the electrode at which reduction occurs Once even one electron flows from the anode to the cathode, the charges in each beaker would not be balanced and the flow of electrons would stop Therefore, we use a salt bridge, usually a U-shaped tube that contains a salt solution, to keep the charges balanced Cations move toward the cathode Anions move toward the anode A minus sign can be assigned to the anode in a voltaic cell In all electrochemical cells, electrons flow in the external circuit from the anode to the cathode and negative ions move from the cathode compartment, through the salt bridge, to the anode compartment EMF (Electromotive Force) Water only spontaneously flows one way The potential difference between the anode and cathode in a cell is called the emf, which is also called the `force causing electrons to mvoe' It is also called the cell potential, and is designated Ecell The cell potential is measured in volts (V) 1 V= 1 J/C Standard Reduction Potentials Standard Reduction potentials for many electrodes have been measured and tabulated Standard Hydrogen Electrode Their values are referenced to a standard electrode (SHE)