Relationship between Homogeneous Equilibrium and the Law of Mass Action (Part B)

 

"Relationship between Homogeneous Equilibrium and the Law of Mass Action (Part B)"

Case B- In gaseous reaction when no of moles increases:

Suppose the decomposition of PCl₅

PCl₅    à    PCl₃   +   Cl₂    

t=0                   a                   0            0

t=eq              (a-x)                x            x

Total no of moles “N” are (a-x) + x + x  = a

Expression for K_c:

[PCl₅] = (a-x)/V

[PCl₃] = x/V

[Cl₂] =   x/V

K_c =   [PCl₃][ Cl₂]   

             [PCl₅]

K_c =        [x/V] [x/V]                      

               (a-x)/V

K_c =           x²                        

           (a-x)V

Reaction will move towards forwards direction when there is increase in volume that decreases K_c

to make K_c constant.

Expression for K_p:

P_PCl5 =   (a-x) P

              (a+x)

P_Cl2 =      (x)  P

             (a+x)

P _PCl5 =     (x)  P

              (a+x)

Put the values in K_p expression

K_p =     P_PCl3 P_Cl2               

                 P_PCl5

 

     

                     (x) P    .   (x) P

      K_p =        (a+b)    (a+b)             =      x²      P         

                            (a-x) P                     (a²-x²)

                            (a+x)

 

Reaction will move towards backward direction when there is increase in pressure that increases K_p to make K_p constant.

Expression for K_x:

X_PCl5 =   (a-x)

              (a+x)

X_Cl2 =      (x)     

             (a+x)

X _PCl5 =     (x)  

              (a+x)

Put the values in K_x expression

K_x =     X_PCl3 X_{Cl2      *}        

                 X_PCl5

           (x)     .      (x)

K_x =     (a+b)    (a+b)          =      x²                 

                   (a-x)                      (a²-x²)

                   (a+x)

 

This equation highlights that the rate of reaction at equilibrium is proportional to the concentrations of reactants, as per the Law of Mass Action.

Conclusion:

Homogeneous and heterogeneous equilibrium are distinct types of chemical equilibrium, each with its own characteristics and application of equilibrium constants, be it K_c or K_p. The Law of Mass Action is a universal principle that governs both types, emphasizing the significance of reactant concentrations in reaching a state of equilibrium. Understanding these concepts is fundamental to grasping the intricacies of chemical equilibrium and its role in the behavior of chemical reactions. Whether dealing with gases, liquids, or solids, these principles and equilibrium constants play a central role in the world of chemistry.