[<< wikibooks] AP Chemistry/Equilibrium
Chemical equilibrium is when the concentrations of the products and the reactants in a reaction are in balance; there is no net exchange as the rate of the forward reaction is equal to the backward reaction. A dynamic equilibrium is achieved when there is a lack of change in a system as inputs and outputs remain in balance. In a dynamic equilibrium, chemicals are reacting rapidly at the molecular scale, while their concentrations remain constant on the macroscopic scale. Compounds which are in a dynamic chemical equilibrium are studied and described using the concepts of chemical equilibrium.


== Equilibrium Law ==
The equilibrium law states that the concentrations of the products multiplied together, divided by the concentration of the reactants multiplied together, equal an equilibrium constant (K). The equilibrium constant is a number which depends on the reaction and the temperature of the reaction mixture when equilibrium is attained.
The letter K is reserved as the symbol for the equilibrium constant. A specific type of the equilibrium constant can be notated with a subscript:

  
    
      
        
          K
          
            c
          
        
      
    
    {\displaystyle K_{c}}
   = concentration is in molarities

  
    
      
        
          K
          
            p
          
        
      
    
    {\displaystyle K_{p}}
   = partial pressures of gases represent reactant and product amounts

  
    
      
        
          K
          
            s
            p
          
        
      
    
    {\displaystyle K_{sp}}
   = solubility product

  
    
      
        
          K
          
            a
          
        
      
    
    {\displaystyle K_{a}}
   = acid ionization constant

  
    
      
        
          K
          
            b
          
        
      
    
    {\displaystyle K_{b}}
   = base ionization constant

  
    
      
        
          K
          
            f
          
        
      
    
    {\displaystyle K_{f}}
   = formation constantThe specific equilibrium law depends on the equilibrium reaction under study. A general equilibrium reaction can be written as:

  
    
      
        α
        A
        +
        β
        B
        ⇌
        σ
        S
        +
        τ
        T
      
    
    {\displaystyle \alpha A+\beta B\rightleftharpoons \sigma S+\tau T}
  The general equilibrium law for the above reaction is written as:

  
    
      
        K
        =
        
          
            
              {
              S
              
                }
                
                  σ
                
              
              {
              T
              
                }
                
                  τ
                
              
            
            
              {
              A
              
                }
                
                  α
                
              
              {
              B
              
                }
                
                  β
                
              
            
          
        
      
    
    {\displaystyle K={\frac {\{S\}^{\sigma }\{T\}^{\tau }}{\{A\}^{\alpha }\{B\}^{\beta }}}}
  Compounds in a liquid or solid state should not be included in the equilibrium law because they have a constant concentration during a reaction. For example, for the reaction:

  
    
      
        C
        
          H
          
            4
          
        
        (
        g
        )
        +
        2
        
          O
          
            2
          
        
        (
        g
        )
        ⇌
        C
        
          O
          
            2
          
        
        (
        g
        )
        +
        2
        
          H
          
            2
          
        
        O
        (
        l
        )
      
    
    {\displaystyle CH_{4}(g)+2O_{2}(g)\rightleftharpoons CO_{2}(g)+2H_{2}O(l)}
  The equilibrium law is:

  
    
      
        
          K
          
            c
          
        
        =
        
          
            
              {
              C
              
                O
                
                  2
                
              
              }
            
            
              {
              C
              
                H
                
                  4
                
              
              }
              {
              
                O
                
                  2
                
              
              
                }
                
                  2
                
              
            
          
        
      
    
    {\displaystyle K_{c}={\frac {\{CO_{2}\}}{\{CH_{4}\}\{O_{2}\}^{2}}}}
  Aqueous solutions and gases are included in the equilibrium law. For the below reaction:

  
    
      
        N
        
          H
          
            3
          
        
        (
        g
        )
        +
        
          H
          
            2
          
        
        O
        (
        l
        )
        ⇌
        N
        
          H
          
            4
          
          
            +
          
        
        (
        a
        q
        )
        +
        O
        
          H
          
            −
          
        
        (
        a
        q
        )
      
    
    {\displaystyle NH_{3}(g)+H_{2}O(l)\rightleftharpoons NH_{4}^{+}(aq)+OH^{-}(aq)}
  The equilibrium law is:

  
    
      
        
          K
          
            c
          
        
        =
        
          
            
              {
              N
              
                H
                
                  4
                
                
                  +
                
              
              }
              {
              O
              
                H
                
                  −
                
              
              }
            
            
              {
              N
              
                H
                
                  3
                
              
              }
            
          
        
      
    
    {\displaystyle K_{c}={\frac {\{NH_{4}^{+}\}\{OH^{-}\}}{\{NH_{3}\}}}}
  


== Finding the Value of the Equilibrium Constant ==
In the equation:

  
    
      
        
          
            H
            
              2
            
            
              
            
          
          
            (
            g
            )
          
          +
          
            Cl
            
              2
            
            
              
            
          
          
            (
            g
            )
          
          
            
              
                
                  
                    
                      ↽
                    
                    
                    
                    
                      −
                    
                  
                
              
              
                
                  
                    
                      −
                    
                    
                    
                    
                      ⇀
                    
                  
                
              
            
          
          2
          
          HCl
          
            (
            g
            )
          
        
      
    
    {\displaystyle {\ce {H2 (g) + Cl2 (g) <=> 2HCl (g)}}}
  The equilibrium law is:

  
    
      
        
          K
          
            c
          
        
        =
        
          
            
              {
              H
              C
              l
              
                }
                
                  2
                
              
            
            
              {
              
                H
                
                  2
                
              
              }
              {
              C
              
                l
                
                  2
                
              
              }
            
          
        
      
    
    {\displaystyle K_{c}={\frac {\{HCl\}^{2}}{\{H_{2}\}\{Cl_{2}\}}}}
  The most direct method for finding the value of the equilibrium constant 
  
    
      
        
          K
          
            c
          
        
      
    
    {\displaystyle K_{c}}
   is by measuring the concentration of each of the reactants and products, and plugging in their values in the equilibrium law. For example, if the concentration at equilibrium for the above reaction are determined as 
  
    
      
        {
        
          H
          
            2
          
        
        }
        =
        1.0
        ×
        
          10
          
            −
            8
          
        
      
    
    {\displaystyle \{H_{2}\}=1.0\times 10^{-8}}
   , 
  
    
      
        {
        C
        
          l
          
            2
          
        
        }
        =
        3.4
        ×
        
          10
          
            −
            6
          
        
      
    
    {\displaystyle \{Cl_{2}\}=3.4\times 10^{-6}}
   , and 
  
    
      
        {
        H
        C
        l
        }
        =
        0.802
      
    
    {\displaystyle \{HCl\}=0.802}
  , they can be plugged into the equilibrium law to solve for 
  
    
      
        
          K
          
            c
          
        
      
    
    {\displaystyle K_{c}}
  :

  
    
      
        
          K
          
            c
          
        
        =
        
          
            
              {
              H
              C
              l
              
                }
                
                  2
                
              
            
            
              {
              
                H
                
                  2
                
              
              }
              {
              C
              
                l
                
                  2
                
              
              }
            
          
        
      
    
    {\displaystyle K_{c}={\frac {\{HCl\}^{2}}{\{H_{2}\}\{Cl_{2}\}}}}
  becomes

  
    
      
        
          K
          
            c
          
        
        =
        
          
            
              {
              0.802
              
                }
                
                  2
                
              
            
            
              {
              1.0
              ×
              
                10
                
                  −
                  8
                
              
              }
              {
              3.4
              ×
              
                10
                
                  −
                  6
                
              
              }
            
          
        
      
    
    {\displaystyle K_{c}={\frac {\{0.802\}^{2}}{\{1.0\times 10^{-8}\}\{3.4\times 10^{-6}\}}}}
  After plugging in the concentrations, do the appropriate arithmetic to find the value of 
  
    
      
        
          K
          
            c
          
        
      
    
    {\displaystyle K_{c}}
  . In this case 
  
    
      
        
          K
          
            c
          
        
        =
        1.89
        ×
        
          10
          
            13
          
        
      
    
    {\displaystyle K_{c}=1.89\times 10^{13}}
  .


== Uses of the Equilibrium Law ==
The value of the equilibrium constant connotes the extent to which, in a chemical reaction, reactants are converted into products. Thus, from the equilibrium constant K, one can infer the composition of an equilibrium mixture. If the equilibrium constant is very large (i.e. above 
  
    
      
        
          10
          
            10
          
        
      
    
    {\displaystyle 10^{10}}
  ), the amount of products present at equilibrium is greater than the amount of reactants, which means that the reaction goes to completion. If K equals 1, the amount of products present at equilibrium is the same as the amount of reactants. When K is very small (i.e. below 
  
    
      
        
          10
          
            −
            10
          
        
      
    
    {\displaystyle 10^{-10}}
  ), the amount of products formed is extremely small; no visible reaction takes place.


=== Spontaneous Reactions ===
A spontaneous reaction is a reaction that will proceed without any outside energy or driving force. A spontaneous reaction has an equilibrium constant greater than 1. A reaction will be nonspontaneous if the equilibrium constant is less than 1.


=== The Reaction Quotient ===
The reaction quotient (Q) is a value that can be obtained by plugging in the values of the required concentrations
into the equilibrium law. The equilibrium constant is the value 
  
    
      
        
          K
          
            c
          
        
      
    
    {\displaystyle K_{c}}
   when the reaction is at equilibrium.
If the chemicals in the reaction are not at equilibrium, then the value obtained by the equilibrium law is called the
reaction quotient. Q has the same form as the equilibrium law, except 
  
    
      
        
          K
          
            c
          
        
      
    
    {\displaystyle K_{c}}
   is replaced by Q. 
Four properties may be derived from this definition of the reaction quotient, Q:

If Q = 
  
    
      
        
          K
          
            c
          
        
      
    
    {\displaystyle K_{c}}
  , the reaction is at equilibrium.
If Q does not change with respect to time, the reaction is at equilibrium and thus, Q = 
  
    
      
        
          K
          
            c
          
        
      
    
    {\displaystyle K_{c}}
  .
If Q < 
  
    
      
        
          K
          
            c
          
        
      
    
    {\displaystyle K_{c}}
  , the reaction will move to the right (the forward direction) in order to reach equilibrium.
If Q > 
  
    
      
        
          K
          
            c
          
        
      
    
    {\displaystyle K_{c}}
  , the reaction will move to the left (the reverse direction) in order to reach equilibrium.