Calculate the molar solubility of AgBr in \(0.035 M \mathrm{NaBr}\left(K_{\mathrm{sp}}=5 \times 10^{-13}\right)\).

The solubility product constant, symbolized as Ksp, is a numerical representation of the solubility of a sparingly soluble salt in water. It indicates the product of the concentrations of the ions that are produced when the salt dissolves in water, each raised to the power of their stoichiometric coefficients. In essence, the Ksp provides us with information on the extent to which a compound can dissolve, under the assumption that the solution is at equilibrium.

For example, when we consider silver bromide (AgBr), the Ksp expression is given by the equation: \[ K_{\mathrm{sp}} = [\mathrm{Ag}^+][\mathrm{Br}^-] \].

This equilibrium constant is specific for each salt at a given temperature. When the ionic product of a salt's constituents in solution (Q) is less than Ksp, the salt can further dissolve, but if Q exceeds Ksp, the solution becomes supersaturated and the salt will precipitate. Therefore, knowing the Ksp allows us to calculate how much of the salt can dissolve to form a saturated solution.

The common ion effect refers to the decrease in solubility of an ionic compound when another compound with a common ion is present in the solution. This is a result of Le Chatelier's principle, which states that if an equilibrium system is disturbed, the system will adjust itself to counteract the change and re-establish equilibrium.

For instance, in the exercise, sodium bromide (NaBr) introduces additional Br- ions to the system. Since Br- is a product of the dissociation of AgBr, the system will shift to counter this by reducing the dissociation of AgBr, thus decreasing its solubility. This effect is crucial when calculating molar solubility in a solution that already contains a common ion. The presence of NaBr means there is a higher initial concentration of Br- ions in the solution, which influences the solubility calculation of AgBr.

The dissociation equation represents the process by which an ionic compound breaks apart into its individual ions when it dissolves in water. It's crucial for understanding how a compound dissociates and which ions are present in the solution.

For AgBr, the dissociation equation is simply: \[ \mathrm{AgBr(s)} \rightleftharpoons \mathrm{Ag}^+(\mathrm{aq}) + \mathrm{Br}^-(\mathrm{aq}) \].

This indicates that silver ions (Ag+) and bromide ions (Br-) are produced when AgBr dissolves. Writing out the dissociation equation helps in understanding how the salt dissociates in water and is essential for setting up the Ksp expression.

The ionic product, often referred to as Q, is similar to the solubility product constant (Ksp) but is used to describe the product of the concentrations of ions in a solution at any given moment, not necessarily at equilibrium. The ionic product helps in determining the direction in which the equilibrium will shift to achieve solubility equilibrium.

The equation to calculate Q is the same as the equation for Ksp, but it does not assume the solution is at equilibrium. For AgBr, Q is given by the equation: \[ Q = [\mathrm{Ag}^+][\mathrm{Br}^-] \].

By comparing the value of Q with Ksp, one can ascertain if the salt will continue to dissolve (QKsp), or if the system is at equilibrium (Q=Ksp). In the context of the exercise, analyzing Q allows us to understand the influence of additional Br- ions from NaBr on the solubility of AgBr.