W. P. White — Melting Point Determination. 457 



It is, in fact, a direct result of the melting point lowering due 

 to the impurity, and an expression for it can be derived from 

 the law of the lowering. This takes a very simple form for 

 the most common and important case, namely, that in which 

 the depression of the melting point is proportional to the 

 amount of impurity. A discussion of this case will serve to 

 show the usual character of this important effect. 



In order to define a melting point curve, two quantities are 

 necessary, and usually sufficient — the temperature rise (dO) and 

 the quantity of heat (dQ) required to cause it. Indeed, the true 

 melting point curve is only the graphic expression of the rela- 

 tion between these two, that is, of the quotient -=— ■ When the 

 temperature rise is plotted against time, the time really serves 

 only as an approximate measure of the added heat. -y-r- is, 



however, by definition, the specific heat.* Hence a melting 

 body as a rule is completely accounted for thermally if it is 

 treated as a body of enormously variable specific heat, and this 

 is often the simplest and easiest way of dealing with it. 



The effect of impurity, then, on the melting curve is its 



effect on the quotient, — —, which is found as follows for the 



case where the melting point lowering is proportional to the 

 amount of impurity present. 



Let the melting point of the perfectly pure substance be 

 taken as the temperature zero ; (the temperatures during melt- 

 ing will then be negative and will decrease numerically as the 

 substance becomes hotter.) Let be the lowering of the 

 melting point in the actual case. The temperature, O , is then 

 the temperature at which the impurity present has just suffi- 

 cient concentration to bring the whole mass of solvent into 

 fluid condition. Next, let half the solvent be crystallized by 

 lowering the temperature. The concentration of the impurity 

 is now double what it was before, and the lowering of tempera- 

 ture by hypothesis also double, or equal to 2d ; similarly, one 

 third of the solvent will remain liquid at 3# . Or, if A is the 



fractional part of the solvent left in a liquid form, Aoo-^-. 



K 



This may be written A =— -r- where K is a constant to be 

 determined. 



* » may, of course, also be so measured as to equal the heat capacity. 



As the two are proportional to each other for the same charge, the distinc- 

 tion is of no importance here. 



