MATHEMATICS AND CHEMISTRY 409 



error is practically eliminated in the mean value, whilst if the 

 velocity coefficient tends to increase or diminish as the inter- 

 action proceeds, the rise or fall of K is rendered immediately 

 evident and we can compare different stages of the interaction. 

 This equation will not give such a smooth looking series of values 

 of K as the other but is vastly more trustworthy and scientific. 



Besides the straightforward cases of mass action, other diffi- 

 culties are always being met with. Such cases as the following 

 are so frequent in practice that they should be dealt with. 

 Methylic acetate in dilute aqueous solution is almost completely 

 hydrolysed, at a rate depending on the temperature and the 

 nature and concentration of the catalyst, giving rise to methylic 

 alcohol and acetic acid. The student learns from a text-book 

 that the interaction under these conditions may be treated as 

 unimolecular. He treats it so, assuming that the amount of 

 acetate remaining when equilibrium is attained is negligible and 

 carries out a number of experiments. He finds on later investi- 

 gation, however, that only 93 or 94 per cent, of the acetate is 

 hydrolysed at equilibrium. What is he to do ? Are the values 

 of the velocity coefficient he has obtained by considering only 

 the convertible acetate useless ? He cannot simply make fresh 

 calculations from his experiments as he has determined only the 

 concentration of the convertible acetate and not the total ; it is 

 very much more difficult, perhaps, to determine the total amount 

 present. The following problem then remains for solution : 

 Granted that the velocity coefficient of hydrolysis is constant 

 when the complete change of simultaneous hydrolysis and 

 esterification is considered, is it to be expected that by consider- 

 ing only the hydrolysis and the convertible acetate the values of 

 the velocity coefficient should also be constant ? If so, what is 

 the relation between this value of K and the true value ? 

 Another familiar example of the same nature is the conversion 

 of amnionic cyanate into urea studied by James Walker. Such 

 an example presents the difficulties actually experienced and 

 would form a valuable addition to a text-book, especially if it 

 were pointed out what assumptions had been made by the 

 investigator and that others might lead to different conclusions. 



Again, suppose that on the application of the mass action law 

 a constant is obtained. Is this a confirmation of the hypothesis 

 used ? And if a constant be not obtained on any simple assump- 

 tion, what is to be done ? We may determine the order of the 



