Question

Silver bromide is "insoluble." What does this mean about the concentrations of \(\mathrm{Ag}^{+}\) and \(\mathrm{Br}^{-}\) in a saturated solution of AgBr? What makes it possible for a precipitate of \(\mathrm{AgBr}\) to form when solutions of the soluble salts \(\mathrm{AgNO}_{3}\) and \(\mathrm{NaBr}\) are mixed?

Short answer

Silver bromide being 'insoluble' means \(\mathrm{Ag}^{+}\) and \(\mathrm{Br}^{-}\) concentrations in a saturated solution are very low. A precipitate of AgBr forms when \(\mathrm{AgNO}_{3}\) and \(\mathrm{NaBr}\) are mixed because their ionic products exceed the solubility product, causing solid AgBr to precipitate.

Step-by-step solution

Understanding the term 'insoluble'

When a substance is termed 'insoluble,' it means that it has a very low solubility in water. This implies that only a very small amount of the substance can dissolve in water to form a solution at a given temperature.

Interpreting the concentrations of ions

For an 'insoluble' salt like silver bromide (AgBr), the concentrations of the ions \(\mathrm{Ag}^{+}\) and \(\mathrm{Br}^{-}\) in a saturated solution will be very low because very little of the salt can dissolve in the solution to release these ions.

Understanding the formation of a precipitate

A precipitate of AgBr can form when solutions of soluble salts, such as \(\mathrm{AgNO}_{3}\) and \(\mathrm{NaBr}\), are mixed together because \(\mathrm{Ag}^{+}\) and \(\mathrm{Br}^{-}\) ions from these salts come into contact. Since AgBr has a very low solubility product, the product of the concentrations of \(\mathrm{Ag}^{+}\) and \(\mathrm{Br}^{-}\) ions exceeds the solubility product, leading to the formation of a solid precipitate.

Key concepts

Solubility Product

The solubility product, often represented as Ksp, is a constant that provides a measure of the solubility of an ionic compound. It is defined as the product of the concentrations of the ions that constitute the compound, each raised to the power of their respective stoichiometric coefficients in the balanced equation for its dissolution. For silver bromide (AgBr), which dissociates into \(\mathrm{Ag}^{+}\) and \(\mathrm{Br}^{-}\) ions in water, the solubility product equation would be expressed as: \[ K_{\text{sp}} = [\mathrm{Ag}^{+}][\mathrm{Br}^{-}] \
\]In the case of AgBr, Ksp is a very small number, reflecting its low solubility. Only a tiny amount of AgBr will dissolve to reach a state of equilibrium where the ionic product of \(\mathrm{Ag}^{+}\) and \(\mathrm{Br}^{-}\) is equal to the Ksp. If the ionic product exceeds the Ksp, precipitation will occur, resulting in fewer ions in solution until equilibrium is re-established.

Precipitation Reactions

Precipitation reactions involve the formation of a solid, known as a precipitate, from the mixture of two solutions containing soluble salts. The reaction takes place when the product of the concentrations of the reacting ions exceeds the solubility product (Ksp) of the compound they form upon combination. Following the example of silver bromide:\
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• When aqueous solutions of AgNO3 and NaBr are mixed,
• \(\mathrm{Ag}^{+}\) from AgNO3 and \(\mathrm{Br}^{-}\) from NaBr interact,
• If their ionic product is greater than the Ksp of AgBr, a precipitation reaction occurs,
• AgBr, a solid precipitate, forms and separates from the solution.

\
\The physical sign of a precipitation reaction is the appearance of a cloudy or solid material in the solution, which indicates that a new substance has formed that is not soluble in the mixture.

Ionic Concentration

The ionic concentration refers to the amount of an ion present in a unit volume of solution. In the context of solubility, it's the concentration of each ion that results from the dissolution of an ionic compound in a solvent. For poorly soluble compounds like AgBr, ionic concentrations of \(\mathrm{Ag}^{+}\) and \(\mathrm{Br}^{-}\) are extremely low in a saturated solution, as the compound only dissociates into its ions to a very small extent. The solubility product, Ksp, of AgBr dictates these concentrations:\
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• The solubility of AgBr is minimal, hence, the ionic concentrations are low,
• Any change in these ionic concentrations can lead to either more solid dissolving or precipitating to maintain the constant Ksp.

\
\Monitoring ionic concentrations is crucial in predicting whether precipitation will occur or in determining the amount of a substance that can dissolve before the solution becomes saturated.

Saturated Solution

A saturated solution exists when a solvent holds the maximum possible amount of a dissolved solute under equilibrium at a given temperature and pressure. For a solution of AgBr in water, this state is achieved when the dissolved ions \(\mathrm{Ag}^{+}\) and \(\mathrm{Br}^{-}\) reach a concentration at which the product is equal to the solubility product, Ksp. Any additional AgBr added to the solution will not dissolve and will remain as a precipitate:\
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• The saturated solution of AgBr has a very low concentration of \(\mathrm{Ag}^{+}\) and \(\mathrm{Br}^{-}\), showing its low solubility,
• If either \(\mathrm{Ag}^{+}\) or \(\mathrm{Br}^{-}\) is introduced in excess to a saturated solution, AgBr will precipitate out,
• A saturated solution represents a dynamic equilibrium between the dissolved ions and the undissolved excess solid.

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\Such solutions are important for understanding various phenomena in chemistry, ranging from the formation of natural mineral deposits to the principles behind various industrial processes.