Complex Ions: Formation Constant: Videos & Practice Problems

In chemistry, a complex ion forms when a metal cation, acting as a Lewis acid (electron pair acceptor), bonds with a ligand, which is a molecule or ion that acts as a Lewis base (electron pair donor). An example is when ammonia molecules, each with a lone pair of electrons, bond to a cadmium ion, resulting in a complex ion with a net charge that reflects the metal cation's charge. The stability of such complex ions in solution is quantified by the formation constant (K_f), an equilibrium constant that expresses the ratio of the concentration of products to reactants, excluding solids and liquids. Understanding the concept of complex ions and the formation constant is crucial for predicting the behavior of metals in various chemical environments.

Complex Ions and Formation Constant

A complex ion is a structure that consists of a metal cation, which functions as a Lewis acid, bonded to one or more ligands. A Lewis acid is defined as an electron pair acceptor, while a ligand acts as a Lewis base by donating a lone pair of electrons to the metal cation. For instance, in the case of ammonia (NH₃), it possesses a lone pair that can be donated to a cadmium ion (Cd²⁺). In this interaction, ammonia serves as the Lewis base, and the cadmium ion acts as the Lewis acid by accepting the electron pair.

In practice, multiple ammonia molecules can coordinate with a single cadmium ion. In this example, four ammonia molecules are connected to the cadmium ion, forming a complex ion. Although ammonia is neutral and carries no charge, the cadmium ion has a +2 charge, resulting in the overall complex ion having a +2 charge as well. This structure can be referred to as a complex ion, which is a term that encompasses the interaction of the Lewis acid and Lewis base.

Additionally, the concept of complex ions is linked to the formation constant, denoted as K_f. The formation constant is an equilibrium constant that quantifies the stability of the complex ion in solution. It is calculated as the ratio of the concentrations of the products (the complex ion) to the concentrations of the reactants (the free metal cation and ligands), while excluding the phases of solids and liquids from the expression. Thus, the formation constant provides insight into the extent of the reaction between the Lewis acid and Lewis base, highlighting the significance of complex ions in coordination chemistry.

Complex Ions and Formation Constant Example

The formation of a complex ion occurs when a silver ion combines with cyanide ions, specifically represented by the reaction where 1 mole of silver ion reacts with 2 moles of cyanide ion to form a complex ion. The formation constant (K_f) for this reaction is 1.0 × 10²¹, indicating a strong tendency for the complex to form.

To determine the concentration of silver ion at equilibrium after mixing 100 mL of 0.010 M silver perchlorate with 220 mL of 0.25 M cyanide, we first calculate the initial moles of each reactant. The moles of silver ion can be calculated using the formula:

moles = liters × molarity

For silver perchlorate:

moles of silver ion = 0.100 L × 0.010 M = 0.0012 moles

For cyanide ion:

moles of cyanide ion = 0.220 L × 0.25 M = 0.055 moles

Next, we find the initial concentrations by dividing the moles by the total volume of the solution, which is 320 mL (or 0.320 L):

Initial concentration of silver ion = 0.0012 moles / 0.320 L = 0.00375 M

Initial concentration of cyanide ion = 0.055 moles / 0.320 L = 0.171875 M

Using an ICE (Initial, Change, Equilibrium) chart, we denote the initial concentrations of silver ion and cyanide ion, with the product concentration starting at zero. The change in concentration for the reactants is determined by the limiting reactant, which in this case is the silver ion. The change for silver ion is -x, and for cyanide ion, it is -2x, where x is the amount reacted.

At equilibrium, the concentrations are:

• Silver ion: x
• Cyanide ion: 0.171875 - 2x
• Complex ion: 0.00375

Applying the equilibrium expression for the formation constant:

K_f = [Complex ion] / ([Silver ion] × [Cyanide ion]²)

Substituting the known values into the equation:

1.0 × 10²¹ = 0.00375 / (x × (0.171875 - 2x)²)

Rearranging to isolate the silver ion concentration gives:

[Silver ion] = [Complex ion] / (K_f × [Cyanide ion]²)

Plugging in the values:

[Silver ion] = 0.00375 / (1.0 × 10²¹ × (0.171875)²)

Calculating this results in a silver ion concentration of approximately 1.39 × 10^-22 M, indicating that at equilibrium, the concentration of free silver ions is extremely low due to the strong formation of the complex ion.

If your equilibrium constant K is equal to the product of K_sp and K_f, find the solubility of AgCl in 2.0 M NH₃. K_sp of AgCl = 1.77 × 10⁻¹⁰; K_f of Ag(NH₃)₂⁺ = 1.7 × 10⁷.

• A. 1.04 × 10⁻¹⁷ M
• B. 9.78 × 10⁻³ M
• C. 9.89 × 10⁻² M
• D. 3.01 × 10⁻³ M

Answer: (C)

A solution is composed of 3.20 × 10⁻⁴ M Co(NO₃)₃ mixed with 0.200 M NH₃. Determine the [Co³⁺] that remains once the solution reaches equilibrium in the formation of Co(NH₃)₆³⁺.

• A. 2.30 × 10⁻³³ M
• B. 7.03 × 10⁻³⁷ M
• C. 2.76 × 10⁻³⁸ M
• D. 8.40 × 10⁻⁴² M

Answer: (A)

Here’s what students ask on this topic:

What is the formation constant, K_f?

The formation constant, often denoted as K_f, is an equilibrium constant that measures the propensity of a complex ion to form from its constituent ions in solution. In other words, it quantifies the stability of a complex in a solution. The larger the value of K_f, the more stable the complex ion is.

For example, if you have a metal ion M and ligands L that bind to it to form a complex ML_n, the formation constant is defined by the equilibrium reaction:

M + nL → ML_n

The formation constant, K_f, for this reaction would be expressed as:

$K{f}_{}=\frac{\left[{\mathrm{ML}}_n\right]}{\left[M\right]\left[L\right]n^{}}$

Here, [ML_n] is the concentration of the complex ion, and [M] and [L] are the concentrations of the metal and ligand, respectively. The brackets denote the concentration of each species in moles per liter (M). A high K_f value indicates a complex that is heavily favored to form, while a low K_f suggests that the complex is less favored and may dissociate more readily back into its components.

How do you calculate the formation constant K_f?

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The formation constant (K<sub>f</sub>) is a specific type of equilibrium constant that measures the stability of a complex in solution. To calculate K<sub>f</sub>, you need to consider the balanced chemical equation for the formation of the complex from its constituent ions.

For example, if you have a complex ion formation represented as:

$aM+bL\rightleftharpoons {\mathrm{ML}}_{ab}$

where M is the metal ion, L is the ligand, and ML<sub>ab</sub> is the complex ion, the formation constant K<sub>f</sub> would be calculated using the following expression:

$K{f}_{}=\frac{\left[{\mathrm{ML}}_{ab}\right]}{\left(\right[M]{)}^a*(\left[L\right]{)}^b}$