Explicit Solution for the General Three Component System

Explicit Solution for the General Three Component System 

A convenient way to derive the explicit expression for the time course of the reaction in the general three component system [Eq. (3)] is first to reduce the matrix K [Eq. (10)] to a 2 X 2 matrix. This is possible because the constraint given by the law of conservation of mass tells us that the system is over determined with regard to amounts, i.e., only two of the three amounts Ui, U2, and as need be specified to determine the system. First, let us shift the origin of the natural coordinate system to the equi- 

Because the last entry in the vector V( — o ) is zero and all the elements of the last row of the matrix VKV are zero, the last column of the matrix VKV-i does not contribute to the transformation. Hence, Eq. (A40) is an equation in two dimensional space instead of three. Consequently, let us define 

It will be convenient to determine the left rather than the right characteristic vectors. Except for a possible discrepancy in length, which determines the size of unit amounts of the various species these vectors form the rows of the inverse matrix used to transform compositions from the A to the B system of coordinates (see footnote Section IV,A,4,a). These  

These matrices 2 and 2 transform compositions between the natural and characteristic systems in the two dimensional spaces  

---

II. Explicit Solution for the General Three Component System. 372... 

---