DILUTE SOLUTIONS AT THE FREEZING POINT. 339 



paper the strengths are referred to 1000 grammes of solution. Let us denote this 

 concentration hy the symbol ra. When a second quantity of solution is put into the 

 cell, we have to add the amount of solute in it to the amount already present in the 

 cell in order to calculate m. 



It will be noticed that, as long as we simply add successive quantities of stock 

 solution without withdrawal, the values of m, calculated in terms of weights, are 

 independent of any contraction on mixing the liquids. If this contraction is appre- 

 ciable, we shall find that, when we come to level the solution, the weight withdrawn 

 is a little less than the total weight of stock solution added. From a knowledge of 

 the weight withdrawn, however, we can deduce the weight left in the cell, and this 

 is the weight we must use in subsequent calculations. The results will then be 

 independent of any contraction which may have occurred. 



From the value of the concentration in terms of the weight of solvent, we can 

 calculate the number of solvent molecules which are present to each molecule of 

 solute. The molecular weight of water being 18, the number required is the 



reciprocal of m X : r or 7 - for those substances like potassium chloride in which 

 1000 lorn 



the molecular is also the electrically equivalent weight, and for bodies such as 

 sulphuric acid, whose equivalents are H 2 SO 4 , &c., its value is 2 X -i . These 



JLoTTt 



values are tabulated as N in the final results. 



2. Calculation of the Conductivity. The mean value of the resistance of a given 

 solution in the cell and the mean temperature at which the measurements were made 

 are calculated from the observations. The temperature is usually within a tenth of a 

 degree of zero, so that an approximate knowledge of the temperature coefficient is 

 enough to enable the resistance at the freezing point to be deduced with sufficient 

 accuracy. 



This value has then to be corrected for the level. The liquid in the cell stands 

 higher than it did at the beginning, or after the last withdrawal, by an amount pro- 

 portional to the total weight of solution which has subsequently been added. It is 

 known that 1 gramme withdrawn from the liquid increases the measured resistance 

 by '31 per cent., so that it is easy to calculate what the resistance would be in each 

 case if the solution were levelled by means of the withdrawing apparatus. 



The value thus found is entered as E, in the tables of results. Its reciprocal is a 

 measure, in arbitrary units, of the conductivity of the solution, and, if the correspond- 

 ing value for the conductivity of the solvent is subtracted from it, we have a measure 

 of the conductivity of the solute at a given dilution, on the assumption that the 

 conductivity of a mixture is equal to the sum of the conductivities of its constituents. 

 This supposition is always correct for salts like potassium chloride, &c., in which con- 

 ductivity is proportional to concentration at great dilution, for in stronger solu- 

 tions the correction for the solvent becomes inappreciable. For solutions of acids, 



2x2 



