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Electrolysis : Equivalent Conductivity |
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If a cell is formed containing two platinum electrodes 1 cm2 in area, placed parallel to each other at a distance of 1 cm. apart, the current in amperes which passes through a solution of an electrolyte between the plates, when the latter are at a difference of potential of 1 volt, is denned as the conductivity of the solution, and is denoted by k. The conductivity of a solution depends on the concentration. If we start with a solution containing i gm. equivalent of electrolyte per litre (e.g., HCl, or KCl, or ½H2SO4, or ½CuSO4), we shall have a certain number of ions between the electrodes in the cell, and the current carried by these ions will be equal to the conductivity of the solution. If we dissolve twice as much electrolyte in a litre, the actual conductivity will be greater, although there may really be a smaller fraction of salt molecules broken up into ions than in the more dilute solution. Again, if we dilute the solution containing 1 gm. equiv. per litre to one containing 0.01 gm. equiv. per litre, the actual conductivity will be less, as there are fewer ions between the electrodes, although a larger fraction of salt may be ionised. To make a fair comparison between the ionisations of these various solutions we must divide the conductivity k by the number of gm. equiv. of salt per c.c. in the solution, c, and the quotient k/c is called the equivalent conductivity, denoted by Λ. Thus Λ = k/c. Thus, if we have 1 gm. equiv. in 106 litres practically completely ionised, giving a certain conductivity k1 and we then dilute the solution to 107 litres, we obtain a smaller conductivity, k2. But if we imagine all the ions present to be collected into 1 c.c. in each case, we should have two identical solutions, since the numbers of ions are equal, and thus Λ is the same for both. It is found by experiment that the equivalent conductivity of an electrolyte increases gradually with the dilution. The curves in
show the equivalent conductivities of a few electrolytes plotted against the square root of the concentrations in gm. equiv. per litre. This result can be explained in two ways. It may be assumed that the electrolyte is completely dissociated into ions at all concentrations, but that the speeds of the ions carrying the current increase as the solution becomes more dilute, until in very dilute solution the ionic speeds (for a given potential gradient between the electrodes) become constant. Or it may be assumed that the speeds of the ions are practically constant at the various concentrations but the dissolved electrolyte is incompletely ionised, the ionisation increasing with dilution until, at very high dilutions, the electrolyte has become completely ionised. When this occurs, the equivalent conductivity becomes constant, and this limiting value, corresponding with complete ionisation, is called the equivalent conductivity at infinite dilution, denoted by Λ∞. Since there are now only ions in the solution, the ratio k/c, or Λ, has become constant. The ratio of the equivalent conductivity at any dilution, v, to that at infinite dilution, i.e., to the limiting conductivity for infinite dilution when all the electrolyte is ionised, gives, on the theory of incomplete ionisation, the degree of ionisation, α, corresponding with the given dilution: Λv/Λ∞ = α. The dilution is the reciprocal of concentration, i.e., v is the number of cm3 containing 1 gm. equivalent of total electrolyte. In practice, the concentration is usually measured in gm. equiv. per litre, and the dilution in litres per gm. equiv. The change of Λ with dilution in the case of weak electrolytes is too large to be accounted for by varying mobility, and an increase of ionisation must be assumed. The progressive ionisation of a typical weak electrolyte is seen from the table below. Ionisation of Acetic Acid at 18°
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