Chapter 17

Equilibrium: The extent of Chemical Reactions

Homework:12,16,18,19,25,29,31,35,36,41,4548,53,55,63,64,65,67,71,74,81,98,107

Describing Chemical Equilibrium

Chemical equilibrium occurs when the forward rate of a reaction is equal to the reverse rate of the reaction.  Consider the following equilibrium reaction :

     aA + bB ↔ cC + dD

The forward rate is given by:

     rate_f = k_f[A]^a[B]^b

 and the reverse rate is given by:

     rate_r = k_r[C]^c[D]^d

Setting these two rates equal you get:

       k_f[A]^a[B]^b = k_r[C]^c[D]^d

 Solving for the ratio of the constants you get:

      k_f/k_r = [C]^c[D]^d/[A]^a[B]^b

      K = [C]^c[D]^d/[A]^a[B]^b           or simply       K= [Products]^x/[reactants]^y

where the ratio k_f/k_r is called the equilibrium constant and can be given any of several names:

     K_a       Equilibrium constant for an acid
     K_b       Equilibrium constant for a base
     K_eq      Equilibrium constant for a general reaction equation
     K_sp      Solubility product (Note: does not include reactant concentration)
     K_diss.    Dissociation Equilibrium constant

Just to name a few.  But don’t despair!! They are conceptually the same thing that is:

     K_whatever = [Products]^x/[reactants]^y

where x and y are the coefficients of the reactants and products in the balanced chemical equation.

Problem:

For the reaction  H₂  + I₂ ↔ 2HI, the equilibrium concentrations at 490°C are .0862M H₂ , .263 M I₂ and 1.02 M HI. 
a)  What is the equilibrium constant for the reaction.
b)  If 1 mole of H₂ and 1 mole of I₂ are introduced into a 1-liter container at 490°C, what are the concentrations of each substance at equilibrium

 Problem:

Consider the Haber process:     N₂ + 3H₂ ↔ 2NH₃ , show graph of changing concentrations of each species assuming stoichiometric amounts.

Write the equilibrium constant for the reaction.

Equilibrium constants are sometimes expressed in terms of pressure for gaseous reactions. The relation between K_p and K_c can be derived from the ideal gas equation if we assume that the gases in the reaction behave ideally.

PV = nRT   ===>   P = (n/V)RT = MRT therefore:  K_p = K_c(RT)^Dn

where:      Dn = moles gaseous products - moles gaseous reactants

Problem: At 20°C the equilibrium constant for the formation of ammonia is 2.37x10^-3 M^-2.

a)  If 1.00 moles of NH₃ is placed in a 1 liter container, what are the final concentrations of each substance. 

b)  What is the final pressure? 

c)  What is the final pressure of each constituent?

d)  What is the K_p.  

LeChâtelier’s Principle:

If a stress is placed upon a system in equilibrium, the system will shift in such a way as to reduce the stress.      

Problem:

Consider the reaction: H₂ + I₂ ↔ 2HI at 490°C. See previous problem for K_c. At equilibrium [H₂] = .5M, [I₂] = .2M

a)  What is the [HI]?

b)   If the concentration of H₂ is instantly increased to 1 M, in which direction will the reaction shift?

c)  After the increase in [H₂] to 1 M, what are the final concentrations of each substance?

d)   Suppose that in the above equilibrium, the concentration of I₂ is reduced; in which direction will the reaction shift?

e)   Suppose that in the above equilibrium, the concentration of HI is reduced; in which direction will the reaction shift?

f)    In which direction will the reaction shift if the pressure is increased?

g)   What will happen if a nickel catalyst is added to the reaction vessel?

Problem:

Consider the equilibrium reaction:    3H₂ +  N₂  ↔  2 NH₃   +  heat

a)  In which direction will the reaction shift if the pressure is increased?
b)  If the system at equilibrium is heated, in which direction will the reaction shift?

Heterogeneous Equilibrium

Equilibrium reactions can involve a system that is not homogeneous i.e. where one or more of the reactants and /or products are in different phases.  Consider the reaction:   

CaCO_3(s)  ↔  CaO_(s)  +   CO_2(g) 

What is the equilibrium expression for the above reaction.

Problem:

At 20°C  what is the equilibrium constant (K_c) for the vaporization of water.

Effect of Temperature on Equilibrium Constant: The van't Hoff Equation

Just as temperature affects the rate of a chemical reaction, temperature also affects the position of an equilibrium and hence the equilibrium constant. The van't Hoff equation describes how the equilibrium constant varies with temperature.

ln(K₂/K₁) = (-DH^o_rxn/R) x (1/T₂-1/T₁)

Problem:

What can the van't Hoff equation be used to find?