The osmotic pressure of a saturated solution of strontium sulfate at \(25^{\circ} \mathrm{C}\) is 21 torr. What is the solubility product of this salt at \(25^{\circ} \mathrm{C} ?\)

Osmotic pressure is a key concept when studying solutions and their properties. It's the pressure required to prevent the flow of a solvent into a solution through a semipermeable membrane, which occurs due to osmosis—the movement of solvent molecules from a region of lower solute concentration to one of higher solute concentration.

The formula given in the exercise, \(\pi = MRT\), illustrates the direct proportionality between osmotic pressure (\(\pi\)), molar concentration (\(M\)) of the solute, the gas constant (\(R\)), and the absolute temperature (\(T\)).

Understanding this concept is crucial for grasping how solubility product relates to osmotic pressure. In the exercise, the conversion of osmotic pressure from torr to atmospheres was necessary to use standard units, which is important for the consistency and accuracy of calculations in chemistry.

The quantity known as molar concentration, denoted by \(M\), is a measure of the amount of a solute present in a given volume of solution, typically expressed in moles per liter (mol/L). It is a fundamental concept for understanding the concentration of particles in a solution and plays a vital role in chemical reactions and solution dynamics.

In the provided exercise, the molar concentration of strontium sulfate was calculated using the osmotic pressure formula where molar concentration can be rearranged to be \(M = \frac{\pi}{RT}\). This calculation shows the inverse relationship between molar concentration and both the temperature and the ideal gas constant. Comprehending how to find molar concentration is essential for students aiming to determine the solubility product, as it directly affects the values used in the dissolution equation.

The dissolution equation represents the process by which a solid solute dissolves in a solvent to form a solution. It involves the breaking down of a substance into its constituent ions or molecules when it is dissolved in a solvent.

In the exercise, the dissolution equation for strontium sulfate (\(SrSO_4\)) is depicted by the equilibrium reaction: \(SrSO_{4(s)} \rightleftharpoons Sr^{2+}_{(aq)} + SO^{2-}_{4(aq)}\). This equation is necessary to understanding how to further calculate the solubility product (\(K_{sp}\)). The solubility product itself is an equilibrium constant that applies to the saturated solution of an ionic compound, as seen with strontium sulfate.

Knowing each ion's concentration in the solution allows us to calculate \(K_{sp}\), by simply multiplying the concentrations of the ions as shown in the solution step: \(K_{sp} = [Sr^{2+}][SO^{2-}_{4}]\). The dissolution equation is imperative in predicting the solubility of compounds and understanding the dynamics of ionic substances in solution.