Problem 13 - Chemistry: The Central Science

Question

Which of these statements about the common-ion effect is most correct? (a) The solubility of a salt MA is decreased in a solution that already contains either \(\mathrm{M}^{+}\)or \(A^{-}\). (b) Common ions alter the equilibrium constant for the reaction of an ionic

Step-by-Step Solution

Answer

The most correct statement about the common-ion effect is statement (a): The solubility of a salt MA is decreased in a solution that already contains either \(\mathrm{M}^{+}\) or \(A^{-}\) ions. This is because adding a common ion shifts the position of the equilibrium and decreases solubility, in accordance with Le Châtelier's principle. Statement (b) is incorrect, as the equilibrium constant is not altered when a common ion is added.

Step 1: The common-ion effect is a phenomenon that occurs when the solubility of a sparingly soluble salt is reduced in the presence of a common ion (an ion that is already present in the solution). This effect is a result of Le Châtelier's principle, which states that if a system at equilibrium is disturbed, the equilibrium will shift to minimize the disturbance. When a common ion is added to a saturated solution, the position of the equilibrium is shifted, causing the solubility to decrease. #Step 2: Analyzing statement (a)#

Statement (a) says that the solubility of a salt MA is decreased in a solution that already contains either \(\mathrm{M}^{+}\) or \(A^{-}\) ions. This statement follows the definition of the common-ion effect, as adding either a cation (\(\mathrm{M}^{+}\)) or an anion (\(A^{-}\)) that is already present in the saturated solution will shift the position of the equilibrium and decrease solubility. #Step 3: Analyzing statement (b)#

Step 2: Statement (b) says that common ions alter the equilibrium constant for the reaction of an ionic compound. This statement is not correct because the equilibrium constant (K) is not altered when a common ion is added. Instead, the common-ion effect causes the reaction to shift its position towards the side with fewer ions to minimize the disturbance, but the equilibrium constant remains unchanged. #Step 4: Comparing the statements and choosing the most correct one#

Comparing both statements, statement (a) accurately describes the common-ion effect, whereas statement (b) incorrectly implies that the equilibrium constant is altered when a common ion is introduced. Therefore, the most correct statement about the common-ion effect is statement (a).

Key Concepts

Solubility of Salts

Understanding the solubility of salts is crucial when navigating the realms of chemistry. Solubility refers to the maximum amount of a solute, such as a salt, that can dissolve in a solvent at a given temperature to form a saturated solution.

• Water-soluble salts, such as sodium chloride, dissolve easily because the attraction between the water molecules and the ions in the salt is strong enough to separate the ions from their crystal lattice.
• Sparingly soluble salts, conversely, have limited solubility due to weaker interactions with the solvent. An example of such a salt is calcium sulfate.
• The solubility of a salt is an equilibrium condition where the rate of dissolving salt equals the rate at which the ions rejoin to form solid salt.

When examining the solubility of salts, it's important to note variables that affect solubility, such as temperature and the presence of other ions in the solution, which is specifically showcased in the 'common-ion effect'.

Le Châtelier's Principle

Le Châtelier's principle is a foundational concept in chemistry that helps predict the behavior of a system at equilibrium upon experiencing external changes.

Put simply, the principle states that if an external stress, such as a change in concentration, pressure, or temperature, is applied to a system that's in equilibrium, the system will adjust itself to counteract the effect of the applied stress and restore a new balance.

• If you add more reactant to a system, the system will 'shift' to produce more product.
• If you remove product from a system, the system will 'shift' to produce more product to replace what was removed.
• If you increase the pressure by decreasing the volume of a gaseous system, the system will shift toward the side with fewer gas molecules.
• If you increase the temperature, the system will shift in the direction that absorbs heat (endothermic direction).

Through this principle, we gain insights into the behavior of soluble salts when they are part of an equilibrium system.

Equilibrium Shift

An equilibrium shift is the movement of a reaction's position as it establishes a new equilibrium state in response to a change in conditions. This shift happens in accord with Le Châtelier's principle which aims to maintain a system's equilibrium.

For instance, when dealing with the solubility of salts, if a common ion is present in excess, the equilibrium shifts to re-solidify some of the salt to reduce the effect of that excess. Here's how it plays out:

• In a saturated solution of a salt, both dissolving and re-formation of the solid are happening at equal rates.
• When an additional quantity of one of the ions is introduced (the common ion), the system is no longer at equilibrium.
• The shift will occur to reduce the concentration of the added ion, which often results in the precipitation of the salt.
• This shift is evidence that the solubility of the salt has decreased due to the increase in the concentration of the common ion.

Equilibrium Constant

The equilibrium constant (K) is a number that quantifies the ratio of concentrations of products to reactants at equilibrium for a particular reaction at a given temperature. It provides a way to understand the position of equilibrium and the extent to which a reaction occurs.

Key points include:

• The value of the equilibrium constant is derived from the law of mass action, which relates the concentrations of products and reactants to the rate at which they form and decompose.
• A large K value indicates a greater concentration of products at equilibrium, suggesting the reaction proceeds nearly to completion.
• A small K value implies a higher concentration of reactants, indicating the reaction only happens to a limited extent.
• Crucially, the value of K remains unchanged with the addition of a common ion – only the position of equilibrium changes as the system reacts to minimize the disturbance and maintain the established K value.

Understanding the equilibrium constant is therefore central to predicting how changes, such as the addition of a common ion, will affect a system's equilibrium without altering the inherent ratio that K represents.