A solution contains 1.0 \(\times 10^{-5}\) mol of KBr and 0.10 mol of KCl per liter. AgNO \(_{3}\) is gradually added to this solution. Which forms first, solid AgBr or solid AgCl?

In the context of solubility, chemical equilibrium refers to a state where the rate of dissolution (the process of a substance dissolving) of a substance is equal to the rate of precipitation (the process of a substance coming out of solution as a solid). This equilibrium is significant in the solubility product constant (K_sp) exercises, such as determining whether AgBr or AgCl will precipitate first.

The K_sp is a reflection of the equilibrium state for a sparingly soluble compound and is specific for any given compound at a particular temperature. The calculation of ionic concentrations at equilibrium is central to predicting the point at which a solid will begin to form in a solution containing multiple ions.

Understanding chemical equilibrium allows us to apply Le Chatelier's Principle. This principle posits that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. In our exercise, this means that adding silver ions (Ag⁺) will shift the equilibrium to form more solid product if it surpasses the equilibrium concentration governed by K_sp.

Ionic concentration is a measure of how many ions of a particular type are present in a solution, typically expressed in moles per liter (Molarity, M). In our example involving KBr, KCl, and AgNO₃, ion concentrations are pivotal to solving for which salt will precipitate first. We need to know the initial concentrations of bromide (Br⁻) and chloride (Cl⁻) ions to understand how much Ag⁺ can be added before reaching the solubility limit, as represented by the K_sp value.

When we talk about ionic concentration in a solubility context, we are often referring to the ions that come from a salt dissociating in water. Considering the equation for the solubility product constant, knowing the ionic concentrations of either reactant or product will allow us to calculate the concentration of the other in equilibrium conditions. The exact molarity values give us the tool to predict and calculate when and which compounds will precipitate out of the solution.

Precipitation reactions occur when two soluble salts react in solution to form one or more insoluble products. This reaction is essential for determining which compound, AgBr or AgCl, precipitates first. Typically, a precipitate will form when the product of the concentrations of the ions exceeds the solubility product constant (K_sp).

For example, when AgNO₃ is added to the solution containing KBr and KCl, silver ions combine with bromide and chloride ions. If the product of these ionic concentrations surpasses the respective K_sp value, it indicates that the system has exceeded the maximum concentration of ions that can stay dissolved, and thus a precipitate will form.

To predict the outcome of precipitation reactions, one must compare the relative solubility (K_sp) of the potential precipitates. In our scenario, we compare the ion concentrations at which AgBr and AgCl will begin to precipitate. The one that forms a solid at the lower concentration of silver ions is the one that will precipitate first when Ag⁺ is added to the solution.