The results of nitrations at 25°C by 34 varieties of mixed acids, with which comparatively uniform nitrations may be expected, are shown in Appendix Table V. Comparing the relation between the nitrogen content and the composition of waste acids with the free energy of nitrating acid (Fn), that is calculated by assuming T as 25°C, the theory of the cellulose nitration is discussed as follows.
(1) Calculation of Fn. If the free energy of pure nitric acid is taken as standard zero, the free energy of the nitrating acid containing one mol of nitric acid (Fn) can be calculated by the equation-Fn=RT/x∫x0Pn/pdx-that is derived from Nernst's equation. Where x is the ratio of mol fractions of components; in the case of NO₃H.H₂O-System it is the ratio of mol fraction of nitric acid to that of water, and in the case of Nitric acid. Aqueous sulphuric acid solution-System it is the ratio of mol fraction of nitric acid to that of aqueous sulphuric acid solution.
(2) Theory of nitration. In the nitration of cellulose, the nitrogen content of nitrocellulose increases until it reaches a equilibrium with the nitrating acid. In other words, the nitrating capacity of the nitrating acid may be measured by its free energy. Although the effective nitric acid for nitration has been suggested by various forms, the esterifying capacity of nitrating acids can be estimated by the free energy of the nitrating acids containing one mol of nitric acid (Fn) in the scope of ordinary industrial mixed acid.
(3) Farmer's view of nitration mechanism. Farmer has proposed that the nitration of cellulose depends on the pseudo nitric acid in nitrating acid. But, since its concentration in mixed acids has not yet been determined, the free energy of the nitrating acid containing one mol of pseudo nitric acid (Fp. n) can not be calculated. In ordinary industrial mixed acid, however, its nitrating capacity can be estimated by Fn instead of Fp. n, for in these mixed acids the concentration of the uncombined pseudo nitric acid may be assumed constant if water content is not too small.
(4) Curves of iso-nitrogen content and iso-free energy. There is an intimate relation between the curve of equal nitrogen content and the curve of equal free energy in NO₃SH.SO₄H₂.H₂O-triangular coordinates diagram, and this fact explains that the nitrating capacity of acid mixture depends on its free energy (Fn). However, as the ratio of SO₄H₂ to H₂O by mol% approaches to 1, these curves break their parallerism. Perhps, this is due to various causes, but one of them is the cellulose-swelling action of the mixed acid used.
(5) Function of sulphuric acid in mixed acid. In addition to the dehydrating action, which means the maintaining the free energy of nitric acid at high level, sulphuric acid in mixed acids acts on cellulose as a swelling agent and affects on the uniformity of nitration degree, that has an influence upon the mean nitrogen content of nitrocellulses.

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