Question

I was reading the paper Relaxation Kinetics of Ferric Thiocyanate (Goodall et. al, 1972) and I came across a passage which read

Reaction (1) is the simplest representation of the equilibrium between ferric and thiocyanate ions and their complex. The ratio k12/k21
is the equilibrium constant Kc
, which has the value 1391mole−1
at 298°K and ionic strength 0.5 mole kg−1
(8
)
[Fe(H2O)6]3++SCN−⇌k12k21[Fe(H2O)5SCN]2++H2O (1)

However, the paper later makes clear that reaction (1) cannot be single step

Reaction (1) is insufficient to explain the mechanism of the equilibration, since the relaxation rate decreases with increase in the concentration of hydrogen ion in the solution. This is explained by introducing eqns. (2)-(4). Most of the reaction proceeds through the hydroxo complex, which is present in amount determined by the pH and the acid dissociation constant of the hexaquo complex, KOH=1.89×10−3mole−1
at 298 ∘
K and ionic strength 0.5 mole kg−1
(10
).
[Fe(H2O)6]3+⇌fast[Fe(H2O)5OH]2++H+ (2)
[Fe(H2O)5OH]2++SCN−⇌k34k43[Fe(H2O)4(OH)SCN]+ (3)
H++[Fe(H2O)4(OH)SCN]+⇌fast[Fe(H2O)5SCN]2+ (4)

How then can it be possible that Kc=k12/k21
for reaction (1), since it is not elementary?

Answer 1

The equilibrium constant (Kc) applies to the overall reaction for ferric thiocyanate formation, despite it being non-elementary and involving intermediate steps. Kc remains consistent even with multi-step mechanisms as it reflects the ratio of product to reactant concentrations at equilibrium. Concepts like Le Chatelier's principle and solubility products (Ksp) are essential for understanding reactions involving equilibria.

Step-by-step explanation:

The question relates to the equilibrium constant (Kc) for ferric thiocyanate and why it is considered constant when the reaction is not elementary. The initial representation of the formation of the ferric thiocyanate complex is given by the reaction [Fe(H2O)6]3+ + SCN− ⇌ [Fe(H2O)5SCN]2+ + H2O. However, changes in the concentration of hydronium ions suggest additional steps in the mechanism, involving the intermediate formation of a hydroxo complex. This detail is accounted for by subsequent reactions in the mechanism.

Despite the multi-step nature of the reaction, the equilibrium constant Kc for the overall reaction still applies. It represents the ratio of the product of concentrations of the products to the reactants at equilibrium, regardless of the complexity of the mechanism leading to that equilibrium. In subsequent steps (2)-(4), which involve the hydroxo complex, they contribute to the overall equilibrium but do not change the expression or the value for Kc of the net reaction.

To understand the behavior of such systems, it's important to recognize concepts like Le Chatelier's principle and solubility product constants (Ksp). Le Chatelier's principle predicts how a system at equilibrium will respond to disturbances, such as concentration changes. Solubility products, on the other hand, provide crucial information on the point at which a precipitate will form when product concentrations exceed the Ksp value.