Complex Ions: Formation Constant - Online Tutor, Practice Problems & Exam Prep

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 Ion and Ligand

Now a complex ion is a structure containing a metal cation that acts as a Lewis acid and covalently bonded to a ligand. Now remember a Lewis acid is an electron pair acceptor. Now a ligand is a molecule or ion that acts as a Lewis base and donates a lone pair to the metal cation.

Here in this example we have the ammonia molecule with its lone pair and we have the cadmium ion. Ammonium. Ammonium with its lone pair can donate this lone pair to the cadmium iron. Ammonia is acting as our Lewis base. Cadmium ion is accepting the electron pair, so it's acting as our Lewis acid. Now in reality, more than one of these ammonias can connect with the cadmium ion. Here we have four of them connecting to the cadmium ion.

Now you don't need to be able to figure out how many would attach, you'll learn that much later on in a later chapter. But for right now in this example we have 4 ammonium molecules connecting to the cadmium ion. Ammonia itself is neutral, has no charge, but cadmium here has A²⁺ charge. So overall the structure has A²⁺ chart. Now in the past we've talked about Lewis acid base chemistry. In the past we'd have called this an adduct because we added them together, but in this case we can also call it a complex ion. This would represent our complex ion structure.

Now, connected to the idea of complex ions is the equilibrium constant of the formation constant. Here we're going to say the formation constant is capital K_f. It is another equilibrium constant. Like other equilibrium constants, it is a ratio of product to reactive concentrations. But now they deal with complex ions. Here we're going to say like other equilibrium constants, it can be calculated by setting up an expression and ignoring the phases of solids and liquids. So just remember we have a Lewis acid Lewis space reacting together, adding together to create a complex ion. Associated with this complex ion is a K_f value, known as our formation constant.

Complex Ions: Formation Constant Example

Here it says the formation of the complex ion created by the combining of silver ion and cyanide is given below. Here we have one mole of silver ion reacting with two moles of cyanide ion to give us our complex ion. Here it has a formation constant of 1.0×1021.

Now if 100 M LS of 0.010 molar of silver per chlorine is mixed with 220 M LS of 0.25 molar cyanide, what is the concentration of silver ion once equilibrium has been reached? Alright, so the setup is we set up our ice chart with the given formation equation. Here we have to remember that there's two moles of cyanide ion. Here we're dealing with a nice chart which stands for initial change equilibrium.

We're going to say here Step 2. We're going to determine the moles of the metal cation and the ligand anion and divide them by the total volume using the chemical reaction to determine their initial concentrations. Remember ice charts use molarity as one of its units. Moles equals liters times molarity. If I divide this by 1000 and divide this by 1000 and multiply by their molarities will have the moles of our reactants.

So here I'd have 0.100 liters times 0.010 molar. Here silver perchlorate is in the same ratio as silver ion, so the moles of silver perchlorate equal the moles of silver ion. So liters times molarity gives me an initial amount equal to 0.0012 moles of silver ions, so 0.0012 moles of silver ion here. We need the molarity of it so we divide it by the total volume used. We have 100 MLS here and 220ML here, so that's a total of 320 M LS. Dividing that by 1000 gives me my liters. This comes out to be 0.00375 molar for my silver ion, so that's your initial amount, the cyanide ion.

Divide the MLS by 1000 to get liters and multiply by the molarity. That'll give me initially 0.055 moles of cyanide ion. Again, divide by total volume used, which is 0.320 liters. So my molarity here is 0.171875 molar. Take those molarities and plug them in. Now here using the initial rows, place the initial concentrations of the metal cation and the ligand anion. And here we don't have any information on our product. So initially it's zero.

Now using the change row, looking at the reactants subtract from their initial amounts by the smaller mole amount. So what do I mean by that? Well, out of the two, well, two molarity amounts that we've got, we're going to subtract by the smaller ones, we're going to do subtract 0.00375 and then here there's a 2 here, so it's 2X or 2 * 0.00375 molarity moles. Remember we're using molarity here, so we can say the same thing will be applied to molarity as they would have been with molts.

Now using the law of conservation of mass, whatever you lose as a reactant, you gain or you add that amount to products. So here we add 0.00375 molar here. Now this is important because this is quite different from your customers seeing with ICE charts. Using the equilibrium row, set up the equilibrium expression and solve for X. Here we're going to say the amount of the metal cation in reality will never reach 0, so set it to the X variable. So here, although it looks like these are subtracting each other to give me a 0 total at the end, we never quite get there. So this is X at equilibrium.

Here when we subtract points 171875 by two times this 0.00375, I have a remainder of 0.164375 molar. Here we just bring this down 0.00375 molar so we have everyone at equilibrium except for the ion we need to find. Here They gave us a formation constant for this equation. So we're going to say KF, which is an equilibrium constant, is equal to products overreactants, just like all other equilibrium constants. We know what KF is, we know what the product is at equilibrium, and we know what this ion is at equilibrium. The only variable missing is the silver island, so just isolate it.

Rearranging my equation, I'm going to see that silver ion concentration equals the product concentration divided by KF times the cyanide ion concentration squared. Here, plug in the values that we know. So silver ion concentration equals 0.00375 divided by the KF, which in this question was 10×1021 and then CN minus was 0.164375. And don't forget that it's squared punch. Punch that all into your calculator, you'll see the silver ion concentration at the end is 1.39×10−22 molar. So this would represent the molarity of my silver 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

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

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:

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