12. The equilibrium constant

equilibrium constant, concentrations Kc, Kx, Kp, temperature dependence, pressure dependence, equilibrium constant of heterogenous reactions, solubility product constant

Chemical equilibrium

·       Stoichiometry gives the molar ra

tio of the reactants and products, but there is no         full conversion

Equilibrium constant

·    

·        

·       the numerical value of K shows whether the concentration of products or initial materials are dominating in equilibrium.

·       Large K means product dominances

·       small K (minimum 0) means small amount of conversion

·       theoretically there is never a full conversion

·       in equilibrium the forward and backward conversions are equal


Different types of equilibrium constants

·       Kc (equilibrium constant in terms of concentration)

o   this version is what we normally use, where we calculate the equilibrium constant using the molarity of products and initial materials to the power of their stoichiometrical number

·       Kx(equilibrium constant in terms of mole fraction)

o   instead of concentration we can also use the mol fraction of the reactants to
the appropriate power

o   for gas phase reactions

o    

o       

·       Kp (equilibrium constant in terms of partial pressure)

o   we can also use the partial pressure divided by the atmospheric pressure of the reactants to the appropriate power to determine the equilibrium constant

o   for reactions involving gases

o   aA + bB = cC + dD

 , where  partial pressure, p0 atmospheric pressure

·       Relation between Kp and Kx

o      since, accordingly

o      , where is the charge in the number of moles

·       The dimension and numerical value of K varies depending on which type we use

·       Temperature dependence:

o   The value of the equilibrium constant is in exponential relation with the temperature

o     

           


Pressure dependence

·       generally K is not dependent on pressure

·       but Kx is if we have gases and the number of moles changes during the reaction

·       e.g. Ammonia synthesis

o     
                      

·       Kp is constant

·       since we have gases and the number of moles changes Kx changes (increases if we increase the pressure)

·       since Δn= -2 Kx increases

·       equilibrium shifts towards the side with less molecules in case of pressure increase, so in this case towards product formation →Le Chatelier-Braun principle

Equilibrium constant of heterogeneous reactions

·       analogy: vapor pressure

·       the presence of the liquid determines the pressure of the vapor

·       no matter how much liquid is present this is true

·       so for heterogeneous phase equilibria the concentration of the other phase (for example if 3 gases react and there is a drop of water the other phase is the liquid water) shouldn’t be included in K (since it remains constant)

Solubility product constant (Ksp)

·       for very badly soluble salts (mainly precipitates)

·       Ksp represents the equilibrium between the dissolved ions and the remaining undissolved solid

·       aSolid ⇌ bCation+ + cAnion-

·       Ksp=[Cation+]b[Anion-]c  (calculated from the equilibrium concentrations)

·       if Q (reaction quotient, product of the initial ion concentration)>Ksp → precipitation occurs