lecture9electrochem2

vfe rt ee ln q vf o g g rt ln q a practical

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Unformatted text preview: A practical form at Since: For gases: 25oC: E ( 25o C ) = E o ( 25o C ) − Nernst Equation 0.0592V log Q v ΔG(T,p) = ΔGo (T)+ RT ln Q(p) →Temp. & press. dependence For solutions: ΔG(T,b) = ΔGo (T)+ RT ln Q(b) →Temp. & concen. dependence Thus: RT RT E (T , p, b) = E (T ) − ln Q ( p, b) = E o (T ) − ln vF vF o ∑ ∑ Products Reactants Temperature, pressure & concentration dependence of emf At equlibrium: Q = K ΔG = 0 E=0 v aJ J v aJ J Concentration dependence of E T=25oC Zn(s) + Cu2+(aq,1M) → Cu(s) + Zn2+(aq,1M) Eo(25oC)=1.10V Zn(s) + Cu2+(aq,2M) → Cu(s) + Zn2+(aq, 0.01M) E(25oC)=? [Cu2+] = 2 M, [Cu−] = 0.01 M 0.0592V 0.0592V 0.01 E ( 25 C ) = E ( 25 C ) − = 1.17V log Q = 1.10V − log v 2 2 o o o • • Concentration Cell Spontaneous reaction when the oxidation and reduction reactions are the same, as long as the electrolyte concentrations are different: driven purely by mixing the more concentrated solution has lower entropy than the less concentrated electrons will flow from the electrode in the less concentrated solution to the electrode in the more concentrated solution oxidation of the electrode in the less concentrated solution will increase the ion concentration in the solution – the less concentrated solution has the anode reduction of the solution ions at the electrode in the more concentrated solution reduces the ion concentration – the more concentrated solution has the cathode Cu(s)⏐ Cu2+(aq) (0.010 M) ⏐⏐ Cu2+(aq) (2.0 M)⏐ Cu(s) 2+ ⎡Cuaq ,2 M ⎤ RT E = Eo − ln ⎣ 2+ ⎦ vF ⎡Cuaq ,0.01M ⎤ ⎣ ⎦ = 0V − ( −0.068V) = 0.068V Activity of ionic solutions For compound MpXq ↔ p M+ + q X-. ideal q Gm = Gm + RT ln γ +p + RT ln γ − ideal q ideal = Gm + RT ln γ +pγ − = Gm + RT ln γ ±p + q define mean activity coefficient γ±, q γ ± = (γ +pγ − )1/( p + q ) Anions and cations are attracted to each other lead to extra stability Ionic solution should be describe by Debye-Huckel limiting law log γ ± = − | z+ z− | AI 1/2 A=0.509 at 25oC, 1 2 bi I is ionic strength: I = ∑ zi bo 2i For MpXq↔ p M+ + q X- of molality b 1 1 b 2 2 o 2 2b I = ( b+ z+ + b− z− ) / b = ( pz+ + qz− ) o = k o 2 2 b b For salt solution like KCl I = b / bo log γ ± ∝ I 1/2 = b1/2 15 Generalize to any electrolyte In using the Nernst equation, we assumed ideal solution for ions RT E = Eo − ln vF ∑ ∑ v aJ J Products v aJJ ∑ ∑ RT = Eo − ln vF Products Reactants Should be a J = γ ± E = Eo − b bo bJvJ Reactants For simplicity, we replace b/bo with b RT ln vF ∑ ∑ v bJ J Products v bJ J Reactants RT ln E=E − vF o v bJ J ∑ ∑ Products Reactants + RT ln vF ∑ ∑ γ Jv Products Reactants v bJ J RT ∑v + ln γ ± J v bJ J vF J γ Jv J Measuring Eo for Electrolytes Pt(s)|H2(g)|HCl(aq)|AgCl(s)|Ag(s) ½H2(g)+AgCl(s) H+(aq)+Cl-(aq)+Ag(s) RT RT RT o 2 2 E=E − ln aH + aCl − = E − ln b − ln γ ± F F F o since ln γ ± ∝ I 1/2 = b1/2 for singe charged compond 2 RT 2 RT o ln b = E − ln γ ± ≈ E o + cb1/2 E+ F F Plot 2 RT E+ ln b vs b½ can determine Eo precisely F Eo+cb Temperature dependence of E • We can determine the ΔG from measurement of E ΔG = −vFE ∂G = −S ∂T So: dE o Δ r S o ∂E ⎞ ΔrS ⎛ → = Eo depends only on T = ⎜ ⎟ dT vF ⎝ ∂T ⎠ p vF ⎛o dE o ⎞ Δ r H o = Δ rG o + T Δ r S o = −vF ⎜ E − T ⎟ dT ⎠ ⎝ This expression provides a non-calorimetric method for measuring ΔrHo Through convention ΔfHo(H+,aq)=0, it allows calculation of ΔfHo of other ions in solution...
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This note was uploaded on 09/25/2013 for the course CHE 301 taught by Professor Raineri,f during the Fall '08 term at SUNY Stony Brook.

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