Three forces are applied to the machine component ABD asshown. Knowing that the cross section containing point H is a20 3 40-mm rectangle, determine the principal stresses and themaximum shearing stress at point H.
Reference Electrode There is no way to measure reduction potential of an isolated half reaction Only the difference is potential between 2 half cells can be added In order to assign E nought red to half reactions, reference electrode chosen, where the cell potential = 0.0 V Standard H Electrode 2H++2e>H2 EH+=0.0 V reversible not at equilibrium can be oxidation or reduction Example 5: Galvanic Cell Zn/Zn2+ Zn>Zn2++2e anode 2H++2e_>H2 cathoden+2H+>Zn2++H2 Ecell= ErEo or Ecell= EcEa 0.76=0VEZn2+=0.76 EZn2+ Ered table 20.1 in the book -oxidized+e→ reduced ions elements or compounds Top to bottom down E nought red low value Ered<0, easily oxidized Value Ered=less likely to undergo reduction Sign Ered attached to H+/H2 E red>0, easily reduced to undergo reduction F+E2>2F E=2.87 (most easily reduced) Li++e>Li Erednought= 3.05, reverse reaction will occur Using E cell to Calculate E red galvanic cell 2Ag++Cu>2Ag+2Cu2+ Ecell=0.46 V cu 0.34 V Ag+ reduction Ecell= EAg+ECu 0.46 V=EAg+(0.34) =EAg+=0.80V Fixed Spontaneity 2 half reactions Ecell >0 delta G<0 reaction is spontaneous More + reduction occurs as written (reduction Less + Enought red forced to go in reverse oxidation E cell 1st Half reaction more + goes up reduction, other half decreases oxidation Left + half reaction, right half reaction Example 6: Cr+Au>Au3++Cr3+ 1.5+0.74=2.24 V Cr3++3e→ Cr goes in the reverse direction Au3++3e>Au Example 7: Cd2++e2→ Cd occurs in the forward direction Mg2++2e→ Mg occurs in the reverse direction Example 8:Co2++2e>Co 1.50+(0.28)=1.78 V 1 Au3++3e>Au Spontaneity Redox Ecell>0 Galvanic cell=spontaneous Electrolytic cell=non spontaneous Ecell<0 Example 9: 6I+BrO3+6h+>3i2+bR+3h2O 1.440.54=0.9 V i2+2E>2i BrO3+gH++6e=>Br+3H2O Example 10: Au+Al3+>Au3++al 1.661.5 3.16 V nonspontaneous Ecell and delta G delta G max work at STP Max work=nFEcell F=96486 C Delta G= nFEcell Max work=mol e(C/mol)x(J/C)=J Example 11: Au3++Al>Au+Al3+ Ecell= 3.16 V 3(96485)3.16 =915 kJ/mol Applications Equilibrium K delta G= RTlnK Ecell= RT/nF (LnKc) Example 12: 6I+BrO3+6H+>3I2+Br+3H2O Ecell=0.9(6)96486/8.314(298)= 210.3 k=2.1x10^90 Ecell= Ecell nought RT/nF (lnQ) [Nernst Equation] where [M] and P atm Example 13: Fe3++e_>Fe2+ 0.77 Co2++2e>Co 0.28 V 1.05=0.77+0.28 2Fe3++Co>2Fe2++Co2+ net 105(8.314)(298)/2(96485) ln[0.250)^2)(0.0050)/(0.0100)^2)] =0.98 V Example 14: Will be on exam H2+Cu2+>2H++Cu 0.340=0.34 2e [H+] 8.44x10^6(0.050) log(6.5x10^4)=3.19 0.42=0.348.314(298)/2(96485) ln[H+]^2/0.050 *Clicker* [Al3+][OH]^12/P^3O2 Q=[OH_]^12 Electrolytic Cell Nonspontaneous Electrical E to force a nonspontaneous reaction to occur Must be molten Electrodes switch Anode and oxidation cathode reduction Rechargeable batteries Example 15: NaCl (80 degrees C) Inert electrodes cathode Na++e→ Na anode 2Cl-->cl2+2e- 2Na++2e>2Na 2Na++2Cl>2Na+Cl2 net Electrical Conduction only occurs at the surface of electrodes More complex Other competing reactions expected Example 16: K2SO4 in H2O KS2O52 H2+O2(actual) Why oxidation and reduction potentials 2 2.92 2K++2e>2k 2H2O+2e>H2+2OH 0.83 0.83+2.92 cathode Anode S2O82+2e>2SO42 2.01 V O2+4H++4e >2H2O 1.23 2.922.01=4.93 V Enought cell =2.06 V Net 2H2O+2e>H2+2OH0 2H2O>O2+2H2 2H2O>O2+4H++2e K2SO4 is a charged carrier also known as an electrolyte Using Reduction Potentials to predict electrolysis products Cathode can be Cu2++2e>Cu 0.34 V or2H2O+2e>H2+2OH Anode can be Br2+2e>2Br 1.07 O2+4H++4e_>2H2O 1.23 more + easier to reduce , more easier to oxidize - net Cu2++2Br→ Cu+Br2 Example 17: 2H2O+2e>H2+2OH Anode S+2e>S2 0.48 V 2 H2O+S2>H2+S+2OH Kinetics of electrolysis 1C= 1 A(s) 1 F=96485 C/mol*e q=lt=nF electrochemical cells (kinetic changes) Electroplating Metal deposited or lost, half reaction and stoich Mass of metal (mol of metal/MM)(coefficient of e/cofficient m)=ne Calculations 2e+Ni2+>Ni current 0.150A(12.2 min(60)/96485=1.138x10^3/2(158.69 g Ni)=0.033 g Ni Example 18: 0.8 A(t)/96485 Ag++e>Ag 2.5gx1 mol/107.9x1 mol e/1 mol Agx2 mol/1 mol= 0.02317 mol e(96485 C)/8x60=46.6 min *clicker* 1 gx 1 mol e/1 mol Ag x 2 mol/ 1molx 96485/ 1moolx 1/65.3 minx1/60 =0.250 A Applications Batteries and electroplating Batteries Galvanic cells, + charged, linked in series to get higher voltage’ Two classes 1. Primary cell non rechargeable Alkaline dry cell 2. Secondary rechargeable Pb storage battery Alkaline Battery Zn/MnO2 battery 1.5 V Basic or alkaline electrolyte Not rechargeable Longer life, increase in current, less expensive Anode Zn+2OH0 > ZnO+H2O+2e Cathode 2MnO2+H2O+2e>Mn2O3+2OH Ni Cad battery Ni, Cd are toxic so the disposal is a problem 3 Rechargeable Increase in density, releases energy quickly, can be recharged rapidly Anode Cd+2OH0>Cd(OH)+2e Cathode NiO2+2H2O+2e>Ni(OH)2+2OH Important properties shelf life, rate energy output, energy vs density, specific energy Ni MM batteries 1.35 V Rechargeable Laptops Advantages 50% more power per vv, is useful longer Anode MM+OH>M+h2O+e Cathode MM+NiO(OH)>Ni(OH)2+M Lithium ions batteries Rechargeable High specific energy with low mass high energy density No oxidation or reduction reaction Li+ ions are moved from graphite to CO2O called intercalation Transport of Li+ Uncharged no Li Charge Li leave LiCOO2 to graphite liCoO3+C6>Li1x+LixC6 discharges=power discharge Li1xCoO2+LixC6>Li1x+yCoO2 Fuel cells galvanic cells with reagents operate with reagents Clean burning, no electrode ions increase temperature to run HO fuel cell ● Cathode C2+h2O+4e>4OH ● Anode H2+2OH>2H2O+2e ● Electrolyte at 200 degrees celsius, 2 porous electrodes with Pt Application electroplating current transfer e to other metals Run electrolytically Uses Separate metals in aq solutions, separated by electrolysis Decrease in voltage that gradually increases 1st Ag+e→ Ag 0.80 V 2nd Cu2++2e_.Cu 0.34 V 3rd Zn2++2e→ Zn -0.76 Al from bauxite ore-> NaOH to get AlO2 and CO2 to Al2O3*nH2O then AlF63- that leads to AlOF62- ->Al2O62-+AlF63→ Al Electroplating metals 4 Cu electrolysis that precipitates other metals There will be more kinetics of this chapter not applications Corrosion Fe steel is iron Stress leaves corrosion, protective coating Fe>Fe2++2e anode cathode CO2+2H2O+4e>4OH prevents coating galvanizing Zn ( a sacrifice coating), alloys Ni and Cr cathodic metals that sacrifice other metals however needs to be replace by other metals over time such as Mg 5