Question

What is the common ion effect? How does Le Châtelier's principle explain it? Use the solubility equilibrium for \(\mathrm{AgCl}\) and the addition of \(\mathrm{NaCl}\) to the solution to illustrate the common ion effect.

Short answer

The common ion effect is the decrease in solubility of a salt when another salt with a common ion is added. Le Châtelier's principle explains this by stating the system will counteract the increase in concentration of the common ion by shifting the equilibrium to reduce its solubility, as demonstrated with \(AgCl\) and \(NaCl\).

Step-by-step solution

Understanding the Common Ion Effect

The common ion effect refers to the reduction in solubility of a salt when another salt with a common ion is added to the solution. This occurs because the increase in the concentration of the common ion shifts the equilibrium, according to Le Châtelier's principle.

Describing Le Châtelier's Principle

Le Châtelier's principle states that if a change is made to a system at equilibrium, the system responds to counteract the change and re-establish equilibrium. In the context of solubility, adding a salt with a common ion is such a change.

Considering the Solubility of AgCl

The solubility product (\(K_{sp}\) of silver chloride (\(AgCl\) can be represented by the equation: \[\mathrm{AgCl (s) \rightleftharpoons Ag^+ (aq) + Cl^- (aq)}\], \[K_{sp} = [\mathrm{Ag^+}][\mathrm{Cl^-}]\].

Applying the Common Ion Effect with Addition of NaCl

When sodium chloride (\(NaCl\) is added to the solution, the concentration of chloride ions (\(Cl^-\) increases. According to Le Châtelier's principle, the system will shift the equilibrium to the left, decreasing the solubility of \(AgCl\).

Key concepts

Le Châtelier's Principle Explained

When you're trying to understand how systems in chemistry find balance, Le Châtelier's principle is your best friend. Imagine a seesaw that's nicely level. This is like a chemical equation in equilibrium. But if someone jumps onto one end, it tilts, right? Well, Le Châtelier's principle tells us that the seesaw – or our chemical system – wants to get back to level again.
In scientific terms, it states that if there's a change in concentration, temperature, or pressure, the equilibrium will shift to minimize that change. Take the seesaw as an example again: If a weight is added on one side, the other side might push up harder or the weight might spread out to balance again. In chemistry, this could mean making more reactants or products to get back to equilibrium.
Let's talk about when you add more of one reactant, like what happens with the common ion effect. If we add more of an ion that's already in the solution, Le Châtelier's tells us that the equilibrium will shift to use up that extra ion, often by making less of a product that contains it. This helps keep everything balanced, so the concentration of the added ion doesn't just keep increasing.

Understanding Solubility Equilibrium

Solubility equilibrium is like a dance between solid and dissolved ions. A substance's solubility is basically how well it can dissolve in water, and the equilibrium part is about how the solid and dissolved parts reach a standstill.
Imagine sugar dissolving in water. At first, lots of sugar grains dissolve, but as time goes on, the process slows down until the amount of sugar dissolving is the same as the amount coming back out of the solution. That's the solubility equilibrium.
Now, in a water solution, for our AgCl example, the silver ions (\(Ag^+\)) and chloride ions (\(Cl^-\)) are in a delicate balance. Looking at it through Le Châtelier's lens, if we already have plenty of chloride ions in there and we try to add more AgCl, the equilibrium will be disturbed. The water will refuse to dissolve as much AgCl as before, because it's trying to keep the seesaw balanced with the extra \(Cl^-\) ions we just introduced. This quirky behavior is the core of the common ion effect.

Decoding the Solubility Product (Ksp)

If solubility equilibrium is the dance, then the solubility product (\(K_{sp}\)) is the music that guides the moves. It's a special number that tells us how well a salt can dissolve in water at a specific temperature. This number doesn't change unless the temperature does, so it's pretty reliable.
Here's how it works: For our buddy silver chloride (\(AgCl\)), we have the dance between the solid and the ions it breaks into – silver (\(Ag^+\)) and chloride (\(Cl^-\)). The \(K_{sp}\) for \(AgCl\) is just the concentrations of these ions multiplied together when everything's in balance.
When we mess with the music by bringing more chloride ions to the party from NaCl, the dance has to change. To keep the \(K_{sp}\) the same (because it's stubborn and doesn't like to change), the amount of silver ions in the water will reduce, meaning less \(AgCl\) dissolving. This shifting around just to keep the \(K_{sp}\) constant is a brilliant demonstration of Le Châtelier's principle in action with the solubility product.