Chapter 7 Electrochemistry 87.2 Conductivity and its application Out-class extensive reading Levine: pp. 506-515 16.5 electric conductivity 16.6 Electrical conductivity of electrolyte solutions
Chapter 7 Electrochemistry §7.2 Conductivity and its application Out-class extensive reading: Levine: pp. 506-515, 16.5 electric conductivity 16.6 Electrical conductivity of electrolyte solutions
87.2 Conductivity and its application 4. Molar conductivity (2)Concentration-dependence of molar conductivity ZEITSCHRIFT FUR ELEKTROCHEMIE Z f. Elektroch Bd. 13 CBER IONENBEWEGLICHKEITEN IM WASSER Ne, to, S, BI dieser Zeitschrift Begrime Aequivalentleitvermogea Jahren entstammenden Arbeiten von Folge des damal eeL verdannter sturen therten Bild! der relativ ere zunachst richtigen Werte ab und nicht einmal einheitlich behandeln, sondern die won Herrn Drucker far loner gesondert betrachtet. o, oooI n. abgeleitete Zahl 313, die Bei dem zweiten Versuch lagen far ver Friedrich Kohlrausch
(2) Concentration-dependence of molar conductivity 4. Molar conductivity Friedrich Kohlrausch §7.2 Conductivity and its application
87.2 Conductivity and its application 5. Kohlrausch's empirical formula Es hatte sich gefunden, dass das Equivalent leitvermogen 4 sehr verdunnter Losungen von starken Salzen sich merklich vollkommen, nam. lich bis auf einige Zehntausendstel seines Wertes durch den einfachen Ausdruck wiedergeben AsCA lasst") d=Pn wo n die Konzentration der LOsung, Ao und P Konstanten des betreffenden Salzes bedeuten Die Gleichung besagt also, dass der Abfall des Aequivalentleitvermogens, wenn man ihn von der in der gleichung als grenzwert bei unend licher Verdannung auftretenden Grosse Ao an rechnet, der Quadratwurzel aus der Konzentra- tration proportional verlauft M0-Avc Kohlrausch's square root law
m m A c = − 5. Kohlrausch’s empirical formula §7.2 Conductivity and its application Kohlrausch’s Square Root Law
87.2 Conductivity and its application 6. KohIrausch's law of independent migration The difference in of the two electrolytes Electrolytes /S mol-l cm containing the same cation or anion is the HCI 426.16 same. The same differences in A led Kohlrausch to postulate that molar LICI 11503 conductivity at infinite dilution can be Nacl 12645 broken down into two contributions by the Ions KCI 14985 LINO 110.14 10=+A NanO3 12156 KNO 144.96 ionic conductivities at infinite dilution
m m, m, = ++ − ionic conductivities at infinite dilution The difference in of the two electrolytes containing the same cation or anion is the same. The same differences in led Kohlrausch to postulate that molar conductivity at infinite dilution can be broken down into two contributions by the ions. m m 6. Kohlrausch’s law of independent migration Electrolytes /S mol-1 cm2 HCl 426.16 LiCl 115.03 NaCl 126.45 KCl 149.85 LiNO3 110.14 NaNO3 121.56 KNO3 144.96 m §7.2 Conductivity and its application
87.2 Conductivity and its application 6. KohIrausch's law of independent migration +2 入+v m+ Am at infinite dilution is made up of independent contributions from the cationic and anionIc species. How can we determine the limiting Question: molar conductivity of weak electrolyte? How to measure the ionic conductivity at infinite dilution?
m m m , , = ++ − m at infinite dilution is made up of independent contributions from the cationic and anionic species. m m, m, v v = + + + − − 6. Kohlrausch’s law of independent migration §7.2 Conductivity and its application How can we determine the limiting molar conductivity of weak electrolyte? Question: How to measure the ionic conductivity at infinite dilution?
87.2 Conductivity and its application 7. Measuring limiting molar conductivity of ions B =G I Ac,ZF(U++U) c,F(U++U) cZF(U++U C..F(UM +U 1=AU Z,C, F; I=AUZ_C_F For uni-univalent electrolyte 1=1++1=Ac,Z,F(U++UJ F(++U2) G ACZF(U++U m+
7. Measuring limiting molar conductivity of ions c－, Z－, U－; c＋, Z＋, U＋; B A C I+ = AU+Z+ c+F; I− = AU−Z − c−F I = I++ I− = Ac+Z+F(U++ U− ) V Ac Z F U U G ( ) + + + + − = ( ) ( ) ( ) + + + − + + + − + + + − = + + = + = = c Z F U U l V c Z F U U A l V Ac Z F U U A l G c c Z F U U m ( ) − + + + + = For uni-univalent electrolyte: ( ) − + m = F U +U − + m = m, + m, m U F + ,+ = m U F − ,− = §7.2 Conductivity and its application
87.2 Conductivity and its application 7. Measuring limiting molar conductivity of ions Am= F(Ut +U_) U U +U n2+ n 2+=4 U +U n.十 UF 1m(++U)F To measure Am+ or Am., either t, and t or U+ and U. must be determined
, ( ) m m U F U U F + + + − = + m m , t =+ + − m − = m , t To measure m,+ or m,- , either t+ and t - or U+ and U- must be determined. + − + + + = U U U t + − − − + = U U U t 7. Measuring limiting molar conductivity of ions §7.2 Conductivity and its application ( ) − + m = F U +U m U F + ,+ =
87.2 Conductivity and its application Influential factors for 1)Nature of ions Ions I r/nm 102 am Ions r/nm 10 3.4982 OH Lit 0.68 0.387 FCB 0.554 Nat 0.98 0.501 181 0.763 K+ 1.37 0.735 1.96 0.784 Mg2+ 0.74 1.061 CO32- 1.66 Ca2+ 104 1.190 cO 1.48 104 1.189Fe(CN)3- 3.030 A+ 0.57 189 fe(cn)6 4.420 F 0.67 2.04 L 1.04 2.09 Charge; Radius; charge character; transfer mechanism
ions r / nm 102 ions r / nm 102 H+ − 3.4982 OH¯ − 1.98 Li+ 0.68 0.387 F¯ 1.23 0.554 Na+ 0.98 0.501 Cl¯ 1.81 0.763 K+ 1.37 0.735 Br¯ 1.96 0.784 Mg2+ 0.74 1.061 CO3 2− − 1.66 Ca2+ 1.04 1.190 C2O4 2− − 1.48 Sr2+ 1.04 1.189 Fe(CN)6 3− − 3.030 Al3+ 0.57 1.89 Fe(CN)6 4− − 4.420 Fe3+ 0.67 2.04 La3+ 1.04 2.09 1) Nature of ions Charge; Radius; charge character; transfer mechanism Influential factors for m m m §7.2 Conductivity and its application
87.2 Conductivity and its application Transport mechanism of hydrogen and hydroxyl ions Grotthus mechanism(1805) Delocalization of protons in Liquid Water H J. Bakker and H.K. Nienhuys We find that the vibrational potential of the o-H stretch vibrations of liquid water shows extreme anharmonicity that arises from the o-H..O hydrogen bond interaction we observe that already in the second excited state of the The ion can move along an O-H stretch vibration, the hydrogen atom becomes delocalized between the oxygen atoms of two neighboring water molecules, The energy required for this extended hydrogen-bond network delocalization is unexpectedly low and corresponds to less than 20% of the dissociation energy of the O-H bond of the water molecule in the gas phase Science.2002.297:587-590
Transport mechanism of hydrogen and hydroxyl ions Grotthus mechanism (1805) The ion can move along an extended hydrogen-bond network. Science, 2002, 297:587-590 §7.2 Conductivity and its application
87.2 Conductivity and its application Evolution of scientific concepts Thinking mapping 宏观 微观 动力学 U
Evolution of scientific concepts Thinking mapping §7.2 Conductivity and its application