The velocity of consecutive chemical reactions

While investigating the rate of decomposition of phosphine, page 224, we had occasion to point out that the aotion may take place in two stages — 

Suppose, for example, a substance A forms an intermediate compound M, and this, in turn, forms a final product B. If the speed of the reaction A = M, is one gram per T00 00ff second, when the speed of the reaction M = B, is one gram per hour, the observed order of the complete reaction 

however, the velocities of the two reactions are of the same order of magnitude, the order of the complete reaction will not fall under any of the simple types discussed on page 218, and therefore some changes will have to be made in the differential equations representing the course of the reaction. Let us study some examples. 

In a great number of physical problems, the interrelations of the variables are represented in the form of a system of such equations. The simplest class occurs when each of the dependent variables is a function of the independent variable. 

The simultaneous equations are said to be solved when each variable is expressed in terms of the independent variable, or else when a number of equations between the different variables can be obtained free from differential coefficients. To solve the present set of differential equations, first differentiate (2), 

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