54 VELOCITY OF REACTION, AND 



tions) be represented by C A , C B , c c , C D , and the constant of reaction 

 for conversion of A and B into C and D (as explained above) be k v 

 and the constant for reaction in the opposite direction of C and D 

 into A and B be k 2 . Then the rate of formation of C and D is given 

 by &! . C A . C B , and the rate of formation of A and B (that is, of dis- 

 appearance of C and D) is given by k^ . c c . c l} . Hence the net 

 velocity of formation of C and D is the difference of these two ex- 

 pressions, or, k^ C A . C E - k 2 c c . C D . But the velocity of reaction is 

 the limit of the change in concentration divided by the change in 

 time when both change and time are infinitely small, that is, velocity 



dc 



= - - , the negative sign being used because C A is decreasing. 

 at . 



Accordingly the equation for the velocity of reaction is 



This equation holds, under the conditions as to constancy of re- 

 sistance laid down above, throughout the course of the reaction, and 

 hence if a, b, c, and d be the initial molecular concentrations of the 

 four substances, and at the end of a time t, the molecular concentra- 

 tions of A and B have changed by an amount - x, and become a - x, 

 and b - x respectively, while C and D have changed also by an equal 

 amount + x, and become c + x and d + x respectively, then the equation 

 becomes 



[2], f t =k l (a- x )(b-x)-k,(c + x)(d + x\ 



If the initial concentrations and the values of & x and & 2 are known, 

 the course of the reaction can accordingly be determined, and the 

 amount of x after any given time be determined by integration of 

 the above equation, remembering that when t = 0, x = 0. The values 

 of fcj and k. 2 can be determined by making measurements at suffi- 

 ciently close intervals of the value of x at different times during the 

 reaction, the initial concentrations being known and substituting in 

 the equation. 



The ratio of the two constants 7^ and k z in the equation for 

 velocity of reaction is equal to the value of the constant K of the 



equation of equilibrium, for at equilibrium - -~ is zero, because 



no change is occurring in the substance, therefore from the 



dc, 

 equation - ~~ = k^ C A . C E - /% c c . C D , we have at equilibrium 



Ctu 



k-i C A ?-B - ^"2 c c C D = 0> 



