Orthonormal chemical reactions and chemical relaxation. Part 2.—Reactions in non-ideal solutions

Abstract

A general method is described for obtaining the relaxation times, normal coordinates and normal modes of reaction of a non-ideal chemical system. The normal modes are obtained as a set of orthonormal reactions, though the orthonormality condition is more complicated than in dilute solution. Earlier results for the properties of an orthonormal set of reactions (not necessarily the normal modes) in dilute solution hold with but slight modification in the non-ideal case. In particular, the affinity of the kth orthonormal reaction is independent of the extents of reaction of the remaining reactions and is given by -RT& where & is the extent of the kth reaction, in mol/rnol of solvent, measured from equilibrium.

Matrix Methods and Normalization Procedures in Chemical Relaxation

“…We now consider an alternative general procedure for discussing the normal modes of relaxation of a chemical system; this method, originally devised by Jost [I 2] , by Hearon [13] and by Wei and Prater [14] for first-order reactions has been generalized recently by Schwarz [15] and by Hayman [2][3][4]16]. Equation (21) As we shall see, the transformation matrix R can be chosen so that the matrix RTR-1 \}1'L\}1~R is diagonal; the diagonal elements of this matrix, i.e.…”

“…The simplest and most natural normalization procedure is to put Dr equal to the unit matrix [3,4,15,16] so that r:!' = 1; the expressions given above for the effect of an instantaneous T-jump and/or P-jump (Eq.…”

“…where Pi is the chemical potential of the ith substance while <Il x and <l»y are defined by (2) Since it is unnecessary to repeat the full details of our earlier discussions [2][3][4] regarding the physical meaning of the "improper" normal modes of relaxation, we simplify our previous treatment by choosing the reference equilibrium state of our system equal to its final equilibrium state; we distinguish the properties of our system in this state by the addition of a bar, e.g. T. V and mi" We denote the deviations of the molal ratios of our system at time t from those in the above reference state by 0i defined by (i= 1,2, ... ,r).…”

Orthonormal Chemical Reactions and Chemical Relaxation Part 4. Reactions in Solution with Concomitant Entropy and Volume Changes

“…In the present paper we suppose, however, that our system is in thermal contact with a heat bath at a constant terrperature~and that it is fitted with a piston working against a constant pressure pO • (i=1,2, ... ,1'). (2) We denote the usual t.nerrrodynamic properties of our system, per mol of solvent, by V, 8 …”

“…In the present paper we suppose, however, that our system is in thermal contact with a heat bath at a constant terrperature~and that it is fitted with a piston working against a constant pressure pO • (i=1,2, ... ,1'). (2) We denote the usual t.nerrrodynamic properties of our system, per mol of solvent, by V, 8, U, H, F and G and define and (4) (p=1,2, .. • ,w) where SO and VO are the values of 8 and V, respectively, in the reference equilibrium state. We consider altogether w reversible elementary reactions and suppose that the pth such reaction corresponds to the chemical change l'…”