Chapter 17 & 18 notes
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Date Created: 04/03/16
Chapter 17 & 18 AS ENTROPY INCREASES SO DOES MOLAR MASS, The state of matter. S system- going from o l to gas – (+Sys) endothermic o g to s- (- Sys) exothermic o s to l (+ Sys) endothermic o s to l (+ Sys) endothermic If you have all values and the reaction is not standard and youre trying ot find Temperature, set G is set to 0. Spontaneous reactions can occur at fast or slow speeds depending on the catalysts. Spontaneous reactions occur without ongoing outside intervention. Some characteristics of spontaneous reactions are irreversible reactions, they can be fast or slow, substantial amounts of products at equilibrium and release free energy, increase in entropy (disorder, or randomness) (S) is spontaneous. The state with the highest entropy also has the greatest dispersal of energy. A state in which a given amount of energy is more highly dispersed (or more highly randomized) has more entropy than a state in which the same energy is more highly concentrated. S=klnW as W increases, entropy increases. W is the number of possible microstates that can result in the macrostate. Second law of thermodynamics: for any spontaneous process, the ∆ Suniv>0 entropy of the universe increases ( ) the criterion for spontaneity is the entropy of the universe. ∆S=S final−Sinitial Since S final is greater than S initial, S is positive and the process is spontaneous according the second law. The entropy of a sample of matter increases as it changes from state from solid to a liquid or from liquid to gas. The gaseous state is more disorderly than the liquid state. S for a process involving changes of state, in general S 0 o the phase transition from a solid to a liquid o the phase transition from a solid to a gas o the phase transition from liquid to a gas o an increase in the number of moles of a gas during a chemical reaction. A chemical system proceeds in a direction that increases the entropy of the universe, it proceeds in the direction that has the largest number of energetically equivalents ways to arrange its components. Even if a reaction is thermodynamic spontaneous it can be kinetically slow. Kinetics look at the process, thermodynamics looks at the beginning and end. Most spontaneous reactions are exothermic some can just as well be endothermic. So enthalpy cannot be a sole criterion for determining spontaneity. ∆ Suniv=∆Ssys+∆Ssurr theentropyof theuniversemustincrease for a process¿bespontaneous. The entropy of the system can decrease as long as the entropy of the surroundings increases by a greater amount so that the overall entropy of the universe undergoes a net increase. For S univ to be positive S surr must be positive and greater in absolute value than S sys An exothermic process increases the entropy of the surroundings 2 An endothermic process decreases the entropy of the surroundings. Freezing of water is not spontaneous at all temperatures, but it is nonspontaneous above 0 degrees C. Because the magnitude of the increase in the entropy of the surroundings due to the dispersal of energy into the surroundings is temperature dependent. Entropy is a measure of energy dispersal (joules) per unit temperature (kelvins). The higher the temperature, the lower amount of entropy. The higher the temperature, the smaller the the impact. (surroundings) ∆ S univ=∆ S negati)+∆ S su(positive∧largeatlowtemp , positive∧smalla) hightemp . Lower temp- Spontaneous Higher temp- Nonspontaneous A process that emits heat into the surroundings ( q sys negative) INCREASES the entropy of the surroundings ( positive S surr) A process that absorbs heat from the surroundings (q sys positive) DECREASES the entropy of the surroundings ( negative S surr) The magnitude of the change in entropy of the surroundings is proportional to the magnitude of q sys. ∆ Ssurr ∝−qsys ∆ Ssurr ∝ T inversely proportional with temperature, the higher the temperature the lower the magnitude of S surr for a given amount of heat exchanged ∆ Ssurr=−qsys T at constant temperature. 3 the followingequationsaysat exothermic processesarespontaneous at low temperatures, a given negative q produces some smaller positive S surroundings. −∆H sys ∆ Ssurr= T qsys=∆Hsys if S universe is positive and the reaction is spontaneous… Gibbs Free Energy: ∆ Suniv=∆Ssys+∆ Ssurr ∆ H sys ∆ Suniv=∆Ssys− T −T ∆Suniv=−T ∆Ssys+T∆ H sys T ¿∆ Hsys−T ∆Ssys −T ∆Suniv=∆ H−∆ S ∆ G=∆H−T ∆S ∆G=−T ∆Suniv G is proportional to the negative of S univ. a decrease in G corresponds to a spontaneous process. ( G0) A increase in G corresponds to a nonspontaneous process. (G0) −¿ ¿ ¿¿ Spontaneous ∆ H¿ +¿ ¿ −¿ Nonspontaneous ∆ H¿ 4 −¿ ¿ −¿ ¿ Spontaneous, Nonspontaneous ∆ H¿ +¿ +¿ ¿ Nonspontaneous, Spontaneous ∆ H¿ ForGas:thestandard state for agasis1atm. For Liqiud∨Solid : the standard for a liquid or a solid is pure substance in its most stable forma t pressure is at 1 atm. often at 25C. ∆ S°rxn=∆S° products−∆ S°reactants (standard entropy change) theentropyof a perfectcrystalat absolutezerois zero(0k) Standard entropies (S) are normally given. ∆ S°rxn=Σn Sp (product−Σn Sr(reactants) ∆ H°rxn=Σn Hp f products−Σn r ° f (reactants) unlike enthalpies of formation, which are zero for elements in their standard states, standard entropies are always nonzero at 25C Standard change in free energy ( Grxn.) using equation ∆ G°rxn=∆ H °rxn−T ∆S°rxn the free energy of formation ( Gf) is the change in free energy when 1 mole of a compound in its standard state forms from its constituent elements in their standard states. The free energy of formation of formation of pure elements in their standard states is zero. ∆ G°rxn=Σn ∆p° f (product−Σn ∆r° f (reactants) 5 if a chemical equation is multiplied by some factor, then G rxn is also multiplied by the same factor. If the chemical equation is reversed, then G rxn changes sign. If a chemical equation can be expressed as the sum of a series of steps, then G rxn for the overall equation is the sum of the free energies of reactions for each step. Free energy is “free” because the change of free energy of a chemical reaction represents the max amount of energy available to do work (if Grxn is negative) for many reactions; the amount of free energy is less than the change in enthalpy. We see that the system is negative, and the reaction is spontaneous, this is only possible because some of the emitted heat goes to increase the entropy of the surroundings by an amount sufficient to make the change in entropy of the universe positive. In the real world the amount of G is even less than what is given because energy is lost in the surrounding heat. Reversible reaction- reaction that achieves the theoretical limit with respect to free energy. It occurs slowly, and can be drawn out in small increments. Irreversible reactions- all real reactions, and therefor don’t achieve the theoretical limit of available free energy. Grxn represents the minimum amount of energy required to make the reaction occur. Free energy change of a reaction under nonstandard conditions (Grxn) ∆ Grxn=∆G°rxn+RTlnQ 6 o standard conditions- under standard conditions, P= 1 atm and Q= 1 under standard conditions Q will always be equal to one. And ln(1)=0 the value of Grxn will be equal to Grxn o equilibrium conditions- Q=Kp , (RtlnQ is always going to equal magnitude but is always opposite sign of Grxn and Grxn will be equal to zero, and reaction is not spontaneous in either direction as expected for a reaction at equilibrium. o Other nonstandard conditions- under these conditions Grxn so the reaction is spontaneous in the forward direction. ∆ G°rxn=−RTlnK o when K <1, ln K is (-) and Grxn (+) under standard conditions (Q=1) the reactions is spontaneous in the reverse direction. o When K>1, ln K is (+) and Grxn is (-) under standard conditions ( Q=1) the reaction is spontaneous in the forward direction. o When K=1, ln K= 0 and Grxn is zero. The reaction happens to be at equilibrium under standard conditions. The temperature dependence of the equilibrium constant ∆ G°rxn=−RTlnK (equilibrium constant) ∆ G°rxn=∆ H °rxn−T ∆S°rxn(Temperature dependent) −RTlnK=∆ H °rxn−T ∆S°rxn(combined equations) −lnK= −∆H°rxn− T ∆S°rxlnK=−∆ H°rxn 1 +∆ S°rxn RT RT R (T R equation can also be expressed in a two-point form: 7 K2 −∆ H°rxn 1 1 lnK1= R T 1 T 2) the first law of thermodynamics states that energy can be neither created or destroyed. The second law of thermodynamics implies that for every energy transaction, some energy is lost to the surroundings; this lost energy is nature’s heat tax. Both spontaneous and nonspontaneous processes can occur, but only spontaneous processes can take place without outside intervention. Thermodynamics is the study of spontaneity of reactions, not to be confused with kinetics, the study of rate of reactions. The second law of thermodynamics states that for any spontaneous process, the entropy of the universe increases. Entropy (S) is proportional to the number of energetically equivalent ways in which components of a system can be arranged and is a measure of energy dispersal per unit temperature. For a process to be spontaneous, the total entropy of the universe (system plus surroundings) must increase. The entropy of the surroundings increases when the change in enthalpy of the system (H sys) is (-) (i.e. for exothermic reactions.) The change in entropy of the surroundings for a given H sys depends inversely on temperature- the greater the temperature, the lower the magnitude of S surr. Gibbs free energy, G, is a thermodynamic function that is proportion to the negative of the change in the entropy of 8 the universe. A negative G represents a spontaneous reaction and a positive G represents a nonspontaneous reaction. We can calculate the standard change in entropy for a reaction similarly to the way we calculate the standard change in enthalpy for a reaction: by subtracting the sum of the standard entropies of the reactants multiplied by the stoichiometric coefficients from the sum of the standard entropies of the products multiplied by their stoichiometric coefficients. Standard entropies are absolute: an entropy of zero is established by the third law of thermodynamics as the entropy of a perfect crystal at absolute zero. The entropy of a substance at a given temperature depends on factors that affect the number of energetically equivalent arrangements of the substance; these include the state, size, and molecular complexity of the substance. There are three ways to calculate Grxn applies only to standard conditions, and most real conditions are not standard. Under nonstandard conditions we can calculate ∆Grxn=∆G°rxn+RTlnQ Under standard conditions, the free energy change for a reaction is directly proportional to the negative of the natural log of the equilibrium constant, K; the more negative the free energy change (i.e. the more spontaneous the reaction) the large the equilibrium constant. 9 We can use the temperature dependence of Grxn, as given by ∆ G°=∆ H°−T ∆S° to derive an expression for the temperature dependence of the equilibrium constant. Definition of Entropy: Change in Change in entropy of S=klnW Entropy: the universe: −23 k=1.38∗10 J/K ∆ S=Sf −S I ∆ Suniv=∆Ssys+∆Ssurr Change of entropy of Changes in Gibbs Standard change in the surroundings: Free energy: entropy: −∆Hsys ∆G=∆ H−T ∆S ∆ S°rxn=Σn S° p−Σn S° ∆Ssurr= p r r T Methods for The relationship The relationship calculating free between Grxn & between Grxn and K energy: Grxn ∆ G°rxn=−RTlnK ∆ G°rxn=∆ H °rxn−T ∆S°rxn ∆ Grxn=∆G°rxn+RTlnQ ∆ G°rxn=Σn p° p−Σn r° R=8.314 J/mol*K r ∆G°rxn overal=∆G°rxn (1+∆G°rxn(2) K 2 −∆ H°rxn 1 1 Temperature lnK= −∆H °rxn 1 + ∆S°rxln = ( − ) dependent of the R (T R K1 R T 1 T 2 equilibrium constant. Electrochemistry is the study involves studying the movement of electrons. Oxidized lost of electrons (anode) Reduction gained electrons (cathode) LEO the lion goes GER (loss of electrons is oxidation) (gains of electrons is reduction) OIL RIG (Oxidation is loss) (Reduction is gain) Rules for assigning oxidation states; oxidation of a free element is 0, the oxidation state of a monoatomic ion is 10 equal to its charge, the sum of the oxidation states of all atoms (neutral molecule is 0) ( in an ion is equal to the charge of the ion), metal ions have positive oxidation states, group 1a has +1, 2a has 2+. Oxidation occurs when an atoms oxi state increases during a reaction Reduction occurs when an atoms oxi state decreases during a reaction Steps to a half reaction method of balancing aq. Redox equations in a acidic solution: o Assign oxi states o Separate the overall reaction into two half reactions o Balance each half reaction with respect to mass o Balance each half reaction with respect to charge o Make the number of electrons in both half reactions equal o Add the two half reactions together Steps to a half reaction method of balancing a basic solution o Assign oxi states o Separate the overall reaction into two half reactions o Balance each half reaction with respect to mass Balance all elements other than H and O H O Balance O by adding 2 +¿ Balance H by adding H¿ + - Neutralize H by adding enough OH to neutralize each H . add the same number of OH ions to each side of the eq. 11 o Balance each half reaction with respect to charge o Make the number of electrons in both half reactions equal o Add the half reactions together o Verify that the reaction is balanced. Electrical current is the flow of electric charge. The general device electrochemical cell is the generation of electricity through redox reactions is normally carried out. A voltaic (or galvanic) cell is an electrochemical cell that produces electrical current from a spontaneous chemical reaction. Electrolytic cell consumes electrical current to a drive a nonspontaneous chemical reaction. Oxidation and reduction half reactions are kept separate in half cells. Electrodes are conductive surfaces through which electrons can enter or leave the half cells. Each metal strip reaches equilibrium with its ions in solution according to their half reactions. The rates of electrons flowing through a wire is analogous to the rate of water moving through a stream. Electron current is measured in AMPS (A) o Electrical current is driven by a difference in potential energy, potential difference. Potential difference (Electromotive force, emf) is a measure of the difference in potential energy (J) per unit (C). the SI unit of potential difference is volt (V), which is equal to 1 J/ C 12 In a voltaic cell, the potential difference between the two electrodes is the cell potential (Ecell) or cell emf. o Standard cell potential (Ecell) or standard emf. o In all electrochemical cells, the electrode where the oxidation occurs is the anode, and where the reduction occurs is the cathode. o In a voltaic cell, the anode is more (-) charged electrode and label it with (-) sign o Cathode is more (+) charged and labeled with a (+) sign o Salt bridge- is the pathway in which the counter ions can flow between the without the solutions totally mixing. The negative ions within the salt bridge flow to neutralize the accumulation of positive charge at the anode, and the positive ions flow to neutralize the accumulation of negative charge at the cathode. o Salt bridge completes the circuit. o In a voltaic cell, electrons flow from the more negatively charged electrode to the more positively charged electrode. (electrons are negatively charged and flow away from the more (-) charged electrode.) Electrochemical cell notation (cell diagram, or line notation)- we write the oxidation half reaction on the left and the reduction on the right. A double vertical line, indicating the salt bridge, separates the two half reactions. Substances in different phases are separated by a single vertical line. that represents the boundary between the phases. 13 For some redox reactions, the reactants and the products of one or both of the half reactions may be in the same phase. In these cases, we separate the reactants and the products from each other with a comma in the line diagram. Such cells use an inert electrode, such as (Pt) platinum or graphite, as the anode or cathode or both. Standard electrode potential- the electrode in each half cell as having its own individual potential. Higher potential to lower potential. When the cells are connected, electrons flow from the electrode with more negative charge ( greater potential energy) to the electrode with more positive charge ( less potential energy) SHE- standard hydrogen electrode- chosen to have a potential zero. E°cell=E° final−E°initial E°cell=E°cathode−E°anode remember that the more negative the electrode potential is, the greater the potential energy of an electron at that electrode (because negative charge repels electrons) if we connected a more positive electrode the would have a more positive voltage (lower potential energy for an electron) the electrode potential of the standard hydrogen (SHE) is exactly zero. The electrode in any half-cell with a greater tendency to undergo reduction is positively charged relative to the SHE and therefor has a positive E. The electrode in any half cell with a lesser tendency to undergo reduction ( or greater tendency to undergo 14 oxidation) is (-) charged relative to the SHE and therefor has a (-) E The cell potential of any electrochemical cell (Ecell) is the difference between the electrode potentials cathode and the anode E°cell=E °cat−E°an Ecell is positive for spontaneous reactions and negative for nonspontaneous reactions. E(V) (+)= stronger oxidizing agent, and weaker reducing agent. (-) =weaker oxidizing agent, and stronger reducing agent. An electrode has a (-) electrode potential. A negative electrode potential indicates that an electron at that electrode has greater potential energy than it has at a standard hydrogen electrode. N.I.O- More Negative is Oxidation P.I.R- More Positive is Reduction The half reaction with a more positive electrode potential attracts electrons more strongly and will undergo reduction. The half reaction with a more negative electrode potential repels electrons more strongly and will undergo oxidation. Any reduction reaction when paired with a reverse of any reactions on the table are spontaneous. Metals dissolving an in acid: HNO bu3 not in HCl---- would be anything above hydrogen but below ClO which would be Ag. 15 For a spontaneous redox reaction (one that will proceed in the forward direction when all the reactants and products are in their standard states) o G is negative ( <0) o Ecell is positive (>0) o K>1 o Products favored For a nonspontaneous redox reaction (one that proceed in the reverse direction when all reactants and products are in their standard states) o G is positive (>0) o Ecell is negative (<0) o K<1 Relationship between G and Ecell potentialenergydiffe¿Jn−Maximumwork(Wmax) E= charg( ¿) −Charge(q) wmax−qE°cell - wmax−nFE°cell mole−¿ 96,485C F= ¿ - Faraday’s constant ∆ G°=−nFE°cell - relating G and E. based on conceptual reasoning what is the reason why a reaction with I d2es not oxidize Br , Br is more electronegative than I. if two atoms were in competition for the electron, the electron would go to the more electronegative atom (Br). therefor I doe n2t spontaneously gain electrons from Br . - 16 The relationship between Ecell and K o ∆ G°rxn=−RTln K −nFE°cell=−RTlnK o RT o E°celnFln K mole ,∧lnK=2.303logK R=8.314 J ,T=298.15,F=485C mol∗K ¿ ∆G°=−nFE°cell ∆G°rxn=−RTlnK G E cell K E°cell=592logK n .0592V E°cell=n logK 17 ∆ G=∆G°+RTlnQ −nFEcell=−nFE°cell+RTlnQ RT Ecell=E °cell−lnQ nF lnQ= .0592VlogQ n Nernst Equation: .0592V o Ecell=E °cell−n logQ if Q=1 therefor E cell=Ecell o when a redox reaction within a voltaic cell occurs under conditions in which Q<1, the greater the concentration of reactants relative to products drive reaction to the right, resulting E cell cell o when a redox reaction within an electrochemical cell occurs under conditions in which Q> 1 the greater the concentration of the products relative to reactants drives the reaction to the left, resulting in E cell cell o when a redox reaction reaches equilibrium, Q=K the redox reaction has no tendency to occur in either direction and E cell Electrons spontaneously flow from the half cell within the lower copper ion concentration to the half cell with the higher copper ion concentration. Therefor the flow of electrons has the effect of increasing the concentration of 2+ Cu in the dilute cell and decreasing the concentration of Cu 2+ in the concentration half cell. 18 Dry cell batteries- are batteries like flashlight batteries that don’t contain large amounts of liquid water. Where zine acts as an anode, zinc is oxidized to the reaction. And the carbon rod is the cathode. Alkaline batteries- zinc is oxidized, have a longer working life. Lead-acid storage batteries- lead is being oxidized, and Fuel cells- electrons flow to the cathode. Electrolysis- o Of water- oxygen and hydrogen. o Spontaneous: produces electrical current, occurs in voltaic cells. o Nonspontaneous: consumes electrical current, occurs in electrolytic cells. In all electrochemical cells: o Oxidation occurs at the anode. o Reduction occurs at the cathode. In voltaic cells: o The anode is the source of electrons and has a (-) charge anode. o The cathode draws electrons and has a (+) charge cathode. In electrolytic cells: o Electrons are drawn away from anode, which must be connected to the positive terminal of the external power source (anode +) o Electrons are forced to the cathode, which must be connected to the negative terminal of the power source (cathode -) 19 o More positive= less negative o More negative= less positive o N.I.O- More negative is Oxidation o P.I.R- More positive is Reduction o The cation that is most easily reduced (the one with the more positive electrode potential) is reduced first. o The anion that is most easily oxidized (the one with the more negative electrode potential) is oxidized first. C 1A=1 s oxidation- reduction reactions are reactions in which electrons are transferred from one reactant to another in the most common from of fuel cell, an electrical current is created as hydrogen is oxidized and oxygen is reduced; water is the only product. Oxidation is the loss of electrons and corresponds to an increase in oxidation state; reduction is the gain of electrons and corresponds to a decrease in oxidation state. We can balance redox reactions using the half- reaction method, in which the oxidation and reduction reactions are balanced separately and then added. This method differs slightly for redox reactions in acidic and in basic solutions. a voltaic electrochemical cell separates the reactants of a spontaneous redox reaction into two half-cells that are connected by a wire and a means to exchange ions so that electricity is generated 20 in an electrochemical cell, the electrode where oxidation occurs is the anode and the electrode where the reduction occurs is the cathode; electrons flow from the anode to the cathode the rate of electrons flowing through a wire is measure in amperes (A), and the cell potential is measured in volts (V) a salt bridge is commonly used to allow ions to flow between the half-cell solutions and prevent the build up of charge cell diagram or line notation is a technique for symbolizing electrochemical cells concisely by separating the components of the reaction using lines or commas the electrode potentials of half-cells are measured in relation to that of a a standard hydrogen electrode, which is assigned an electrode potential of zero under standard conditions (solution concentrations of 1M, gas pressure of 1atm, and a temperature of 25 C) a species with a highly positive E has a strong tendency to attract electrons and undergo reduction (and its therefore an excellent oxidizing agent) a species with a highly negative E has a strong tendency to repel electrons and undergo oxidation (and its therefore an excellent reducing agent) in a spontaneous reaction, Ecell is positive, the change in free energy (G) is negative, and the equilibrium constant (K) is greater than 1 in a nonspontaneous reaction, Ecell is negative, G is positive, and K is less than 1 Because Ecell, G, and K all relate to spontaneity, we can derive equations relating all three quantities 21 The standard cell potential (Ecell) is related to cell potential (Ecell) by the Nernst equation, Ecell= Ecell- (0.0592V/n)log Q As shown by the Nernst equation, Ecell is related to the reaction quotient (Q); Ecell equals zero when Q Equals K In a concentration cell, the reactions at both electrodes are identical and electrons flow because of a difference in concentration. Nerve cells are a biological example of concentration cells. Batteries are packaged using voltaic cells. Dry-cell batteries, including alkaline batteries, do not contain large amounts of water. The reactions in rechargeable batteries, such as lead-acid storage, nickel-cadmium, nickel-metal hydride, and lithium ion batteries, can be reversed. Fuel cells are similar to batteries expect that fuel-cell reactants must be continually replenished from an external source. An electrolytic electrochemical cell differs from a voltaic cell in that (1) an electrical charge is used to drive the reaction, and (2) although the anode is still the site of oxidation and the cathode the site of reduction, they are represented with signs of those of a voltaic cell (anode +, cathode -) In electrolysis reactions, the anion is oxidized; if there is more than one anion, the anion with the more negative E is oxidized We can use stoichiometry to calculate the quantity of reactants consumed or products in an electrolytic cell. 22 Corrosion is the undesired oxidation of metal by environmental oxidizing agents. When some metals, such as aluminum, oxidize they form a stable compound that prevents further oxidation. Iron, however, does not form a structurally stable compound when oxidized and therefore rust flakes off and exposes more iron to corrosion. Iron corrosion can be prevented by preventing water contact, minimizing the presence of electrolytes and acids, or using a sacrificial electrode. Definition of an Ampere: 1A=1 C/s Definition of a Volt: 1 V= 1 J/C Standard Hydrogen Electrode: −¿≫¿H 2g)E°=0.00V +¿ aq+2e ¿ 2H ¿ Equation for Cell Potential E°cell=E°cathode−E°anode Relating G and Ecell ∆ G°=−nFE°cell mole¿ 96,485C F= ¿ Relating Ecell and K .0592V E°cell= n logK (at 25C) The Nernst Equation 23 .0592V Ecell=E °cell− logQ (at 25C) n o increasing reactants, will shift equation to the right to validate Nernst law: increased reactants= higher E cell 24
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