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previous chapters. In cases where all (or most) of the kinetic constants 

 are known, equilibrium constants can be found directly, as well as from 

 the rate constants, and also from thermodynamic arguments. All three 

 types of values are found to be in good agreement. The equilibrium 

 constant K for the reaction 



B x + B 2 ^±C 1 + C 2 (18) 



is defined by the equilibrium value of the ratio 



K mm (19) 



where the square brackets indicate concentrations. The constant K is 

 independent of the concentrations of the reactants but may depend on 

 temperature, dielectric constant of the suspending media, pH, ionic 

 strength, and so forth. 



The equilibrium constant K is directly related to the rate constants 

 k x and k 2 . By definition of the latter, the rate of formation of [C ± ] is 

 given by 



^ = k^B^B,] - k^C^C,] 



At equilibrium, this expression must vanish. Rearranging the resultant 

 equation, one finds that 



K = k x \k 2 (20) 



In the case of reactions involving equal numbers of molecules on both 

 sides of the equation, the equilibrium constant K is dimensionless if the 

 same units are used on both sides of the equation. Even if this is not 

 convenient, it is still possible to regard K as dimensionless, provided one 

 regards the square brackets as ratios of the concentrations to those in 

 the standard state. 



In general, the number of molecules on the two sides of the equation 

 are unequal; one must either specify a standard state or treat K as a 

 number with dimensions. Although, for most purposes, the second of 

 these is a satisfactory procedure, it is necessary to use some artificial 

 construct as the standard state to relate K to the Gibbs' free energy G. 



In the last section, it was noted that under isobaric, isothermal con- 

 ditions equilibrium occurred at a minimum for the Gibbs' free energy 

 G; that is, dG must vanish at equilibrium. To relate Gibbs' free energy 

 to K, it is necessary to obtain an expression for dG for a small disturbance 

 of the equilibrium in Equation 18. Symbolically, one may represent 

 G for the reactants in Equation 18 by 



G = V([B x ]G Bl + [B 2 ]G B2 + [C x ]G Cl + [C 2 ]G C2 ) (21) 



