Download CE3503 Expectations – Equilibrium Reactions that proceed to

CE3503 Expectations – Equilibrium
Reactions that proceed to equilibrium slowly (hours, e.g. BOD exertion, to decades, radioisotope
decay) require a kinetic approach as introduced during our discussion of kinetics, reactors and
mass balance. Those that proceed more rapidly (milliseconds, e.g. dissociation of strong acid, to
minutes, e.g. air-water equilibria) may be evaluated using an equilibrium approach, i.e. based
on the principles of physical and chemical equilibrium. The latter case is examined here.
Our exploration of equilibria assumes a reversible reaction proceeding in a closed system,
although we will consider the effect of open system conditions on chemical fate. A generalized
reaction, adaptable to several types of equilibria may be written as,
aA  bB  cC  dD
Note that the equilibrium position is seldom equal parts of A and B on one side and C and D on
the other. The equilibrium position for a strong acid, for example, lies well to the right with little
undissociated acid present, while that for a weak acid may lie more toward the middle, i.e. equal
parts dissociated and undissociated acid.
The general form of the equilibrium constant is written as ‘products over reactants’, i.e.
C    D 
K
a
b
 A  B 
c
d
If, at any time, the system departs from this ratio, concentrations of products and reactants will
adjust until their ratio once again equals K. This is called LeChatelier’s Principle. For
example, in the equation below,
aA  bB  cC  dD
if C is consumed, the reaction will proceed to the right, reducing the quantities of A and B and
adding C and D until the ratio is equal to K; if D is added, the reaction will proceed to the left,
reducing the quantities of C and D and adding A and B until the ratio is equal to K.
Most applications of equilibrium to environmental engineering may be understood on the basis
of the equilibrium position, the equilibrium coefficient and LeChatelier’s Principle. Specific
examples of the application of equilibrium principles to environmental engineering follow.
Volatilization
Here, the equilibrium is between the chemical in its liquid form and the chemical in its gaseous
(vapor) form,
Cl
Cg
and the equilibrium constant, termed the saturation vapor partial pressure, is,
C g 
K 
Cl 
Each chemical has an intrinsic value for the saturation vapor partial pressure, i.e. in a closed
system, at equilibrium, the liquid and gas concentrations will equal a certain ratio, K. The value
of K typically increases with increasing temperature, i.e. more chemical is present in the gas
phase at higher temperatures.
Consider the fate of 50 liters of a volatile organic chemical spilled in a closed room compared
with the fate of 50,000 liters of that same chemical spilled in a tanker wreck. Describe the fate
of the chemical in these two cases on the basis of equilibrium principles, i.e. in terms of the two
equations presented above.
Air-Water Exchange
Here, the equilibrium is between the chemical in an aqueous solution (dissolved in water) and the
chemical in air,
Caq
Cg
and the equilibrium constant, termed the Henry’s Law constant, is,
C g 
K  
Caq 
Each chemical has an intrinsic value for the Henry’s Law constant, i.e. in a closed system, at
equilibrium, the ratio of the concentration in air to the concentration in water will equal K. The
value of K typically increases with increasing temperature, i.e. more chemical is present in air
than in water at higher temperatures.
Consider an attempt to remove (a) oxygen and (b) an organic chemical from water by airstripping. This would work for the volatile organic chemical, but not for oxygen. Explain this
result on the basis of equilibrium principles, i.e. in terms of the two equations presented above.
Acid-Base
Here, the equilibrium is between the chemical in its undissociated form (e.g. HA) and in its
dissociated form (H+ and A-),
HA
H   A
and the equilibrium constant, termed the dissociation constant, is,
 H    A 
K    
 HA
Each acid (and base) has an intrinsic value for the dissociation constant, i.e. in a closed system,
at equilibrium, the ratio of the undissociated acid to the acid in its dissociated form will equal K.
Acids with large values of K (strongly dissociated, equilibrium lying to the right) are called
strong acids, while acids with small values of K (weakly dissociated, equilibrium lying to the
left) are called weak acids.
Consider the case of chlorine dissolved in water, forming hypochlorous acid and hypochlorite
ion
HOCl
H   OCl 
In water treatment, we may adjust the pH to increase the amount of the more effective
disinfectant present. Explain this approach on the basis of equilibrium principles, i.e. in terms of
the three equations presented above.
Precipitation-Dissolution
Here, the equilibrium is between the chemical in the dissolved form and in the solid (precipitate)
form,
AB( s )
A  B
and the equilibrium constant, termed the solubility product, is,
 A   B  
K    
 AB 
and, because the concentration of a solid in a solid is equal to 1, K   A   B  
Each material that may exist in solid form has an intrinsic value for the solubility product. This
means that if the concentration of A+ times the concentration of B- exceeds the value of K, solid
AB will form, reducing the concentrations of A+ and B- in solution.
Iron can be removed from drinking water through aeration, i.e. oxidation of ferrous (Fe2+) iron
to ferric (Fe3+) iron. Comment on what this implies about the solubility products of ferrous
versus ferric iron on the basis of equilibrium principles, i.e. in terms of the two equations
presented above.
Ion Exchange
Here, the equilibrium is between ions dissolved in water and ions attached to a resin,
A  Bresin
Aresin  B
and the equilibrium constant, termed the selectivity coefficient, is, K 
 Aresin  B 
 A Bresin 
Ions are attracted to the resin in proportion to their size and charge.
The classic application of ion exchange is for removal of hardness (Ca2+ and Mg2+) from
drinking water. Initially, the resin holds sodium (Na+) ions. As water is passed through the
resin, Ca2+ and Mg2+ are exchanged (held by the resin), releasing Na+ to the water. Over time,
the resin becomes saturated with Ca2+ and Mg2 and must be recharged. Describe the recharge
process on the basis of equilibrium principles, i.e. in terms of the two equations presented above.
Sorption
Here, the equilibrium is between the chemical in an aqueous solution (dissolved in water) and the
chemical adsorbed to a solid surface,
C( aq )
C( adsorbed )
and the equilibrium constant, termed the sorption coefficient, is,
K
Cadsorbed 
Caqueous 
Each chemical entity has an intrinsic value for the solubility product, i.e. has a tendency to sorb.
In general, we expect hydrophobic chemicals (organic substances) to sorb more strongly than
hydrophilic chemical (inorganic substances).
Consider activated carbon, a strong sorbent, as a means of removing chloride and gasoline
components from a contaminated water supply. Comment on the relative effectiveness of
activated carbon in removing these, on the basis of equilibrium principles, i.e. in terms of the two
equations presented above.