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Concept 03 / 07Electrochemistry

Conductance of Electrolytic Solutions: Conductivity and Molar Conductivity

Resistance, resistivity, conductance and conductivity of electrolytic solutions, cell constant and its determination with standard KCl, molar conductivity and its units, factors affecting conductivity, and variation of conductivity and molar conductivity with concentration for strong and weak electrolytes.

Figure 1
Electrolytic (ionic) conductance is due to the movement of ions in solution or melt, unlike metallic conductance (electrons). It depends on the nature of the electrolyte (strong or weak), size and solvation of ions, nature and viscosity of the solvent, concentration, and temperature (increases with temperature, unlike metals). Definitions. Resistance R=ρlAR = \rho\frac{l}{A}, where ρ\rho is the resistivity (Ω m\Omega\,\mathrm{m}). Conductance G=1RG = \frac{1}{R} (siemens, S). Conductivity κ=1ρ\kappa = \frac{1}{\rho} (S m−1\mathrm{S\,m^{-1}} or S cm−1\mathrm{S\,cm^{-1}}): the conductance of a solution between electrodes 1 cm21\,\mathrm{cm^{2}} in area and 1 cm1\,\mathrm{cm} apart. Cell constant G∗=lAG^{*} = \frac{l}{A}, so κ=G∗R\kappa = \frac{G^{*}}{R}. It is found by measuring the resistance of a standard KCl solution of known conductivity (for 0.1 M0.1\,\mathrm{M} KCl at 298 K298\,\mathrm{K}, κ=0.0129 S cm−1\kappa = 0.0129\,\mathrm{S\,cm^{-1}}). Measurements use alternating current (to prevent electrolysis and polarisation) in a Wheatstone bridge. Molar conductivity. The conductivity per unit molar concentration, representing the conducting power of all the ions from one mole of electrolyte: Λm=κc\Lambda_{m} = \frac{\kappa}{c}; with κ\kappa in S cm−1\mathrm{S\,cm^{-1}} and cc in mol L−1\mathrm{mol\,L^{-1}}, Λm=1000 κc\Lambda_{m} = \frac{1000\,\kappa}{c} in S cm2 mol−1\mathrm{S\,cm^{2}\,mol^{-1}}. (1 S m2 mol−1=104 S cm2 mol−11\,\mathrm{S\,m^{2}\,mol^{-1}} = 10^{4}\,\mathrm{S\,cm^{2}\,mol^{-1}}.) Variation with concentration. Conductivity κ\kappa decreases on dilution, because the number of ions per unit volume decreases. Molar conductivity Λm\Lambda_{m} increases on dilution (see figure), because Λm\Lambda_{m} is the conductance of the whole volume containing one mole, and that volume grows faster than κ\kappa falls. Strong electrolytes (KCl, NaCl, HCl) are fully ionised; Λm\Lambda_{m} increases slowly on dilution as interionic attractions weaken, following the Debye-Huckel-Onsager equation Λm=Λm∘−Ac\Lambda_{m} = \Lambda_{m}^{\circ} - A\sqrt{c}. Plotting Λm\Lambda_{m} against c\sqrt{c} gives a straight line whose intercept is the limiting molar conductivity Λm∘\Lambda_{m}^{\circ} (at infinite dilution). AA depends on the type of electrolyte (1-1, 2-1, 2-2). Weak electrolytes (acetic acid, NH4OH\mathrm{NH_{4}OH}) are only partly ionised; Λm\Lambda_{m} rises steeply at low concentrations, as the degree of dissociation increases sharply on dilution. Λm∘\Lambda_{m}^{\circ} cannot be obtained by extrapolation; Kohlrausch's law is used instead. Key Takeaways: - κ=G∗R\kappa = \frac{G^{*}}{R}; G∗=lAG^{*} = \frac{l}{A} from standard KCl. - Λm=1000 κc\Lambda_{m} = \frac{1000\,\kappa}{c} (S cm2 mol−1\mathrm{S\,cm^{2}\,mol^{-1}}). - On dilution: κ\kappa falls, Λm\Lambda_{m} rises. - Strong: Λm=Λm∘−Ac\Lambda_{m} = \Lambda_{m}^{\circ} - A\sqrt{c}; weak: steep rise, no extrapolation. - Pitfall: keep units consistent; κ\kappa in S cm−1\mathrm{S\,cm^{-1}} needs the factor 10001000 with cc in mol L−1\mathrm{mol\,L^{-1}}. Brain-Teaser 1: The resistance of a conductivity cell containing 0.1 M0.1\,\mathrm{M} KCl (κ=1.29 S m−1\kappa = 1.29\,\mathrm{S\,m^{-1}}) is 100 Ω100\,\Omega. Find the cell constant. The same cell filled with 0.02 M0.02\,\mathrm{M} KCl shows 520 Ω520\,\Omega; find the conductivity and molar conductivity of this solution. Solution: G∗=κR=1.29×100=129 m−1=1.29 cm−1G^{*} = \kappa R = 1.29 \times 100 = 129\,\mathrm{m^{-1}} = 1.29\,\mathrm{cm^{-1}}. For 0.02 M0.02\,\mathrm{M}: κ=1.29520=2.48×10−3 S cm−1\kappa = \frac{1.29}{520} = 2.48 \times 10^{-3}\,\mathrm{S\,cm^{-1}}. Λm=1000×2.48×10−30.02=124 S cm2 mol−1\Lambda_{m} = \frac{1000 \times 2.48 \times 10^{-3}}{0.02} = 124\,\mathrm{S\,cm^{2}\,mol^{-1}}. Brain-Teaser 2: The conductivity of 0.2 M0.2\,\mathrm{M} KCl at 298 K298\,\mathrm{K} is 0.0248 S cm−10.0248\,\mathrm{S\,cm^{-1}}. Find its molar conductivity. Solution: Λm=1000×0.02480.2=124 S cm2 mol−1\Lambda_{m} = \frac{1000 \times 0.0248}{0.2} = 124\,\mathrm{S\,cm^{2}\,mol^{-1}}. Brain-Teaser 3: Why does the conductivity of a solution decrease on dilution while its molar conductivity increases? Solution: Conductivity refers to a fixed 1 cm31\,\mathrm{cm^{3}} of solution: dilution reduces the number of ions in it, so κ\kappa falls. Molar conductivity refers to the volume containing one mole of electrolyte: on dilution this volume increases, and for strong electrolytes interionic attraction decreases while for weak electrolytes more molecules ionise, so the total conductance of that volume increases.

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