Question

Explain why (a) the freezing point of \(0.10 \mathrm{~m} \mathrm{CaCl}_{2}\) is lower than the freezing point of \(0.10 \mathrm{~m} \mathrm{CaSO}_{4}\) (b) the solubility of solids in water usually increases as the temperature increases. (c) pressure must be applied to cause reverse osmosis to occur. (d) \(0.10 \mathrm{M} \mathrm{BaCl}_{2}\) has a higher osmotic pressure than \(0.10 \mathrm{M}\) glucose. (e) molarity and molality are nearly the same in dilute solutions.

Short answer

#Answer#: (a) \(0.10 \mathrm{~m} \mathrm{CaCl}_{2}\) has a lower freezing point than \(0.10 \mathrm{~m} \mathrm{CaSO}_{4}\) because it dissociates into more ions, resulting in a greater freezing point depression. (b) Solubility of solids in water generally increases with temperature because increased temperature and kinetic energy allow more solid particles to dissolve in the solvent. (c) Pressure must be applied to cause reverse osmosis to occur, as it overcomes the osmotic pressure and drives water against its natural tendency. (d) \(0.10 \mathrm{M} \mathrm{BaCl}_{2}\) has a higher osmotic pressure than \(0.10 \mathrm{M}\) glucose because it dissociates into more solute particles. (e) Molarity and molality are nearly the same in dilute solutions because the mass and volume of solute are negligible compared to those of the solvent, making the volume of the solution and mass of the solvent almost equal.

Step-by-step solution

(a) Comparing freezing points of \(0.10 \mathrm{~m} \mathrm{CaCl}_{2}\) and \(0.10 \mathrm{~m} \mathrm{CaSO}_{4}\)

Freezing point depression is a colligative property, which depends on the number of solute particles in the solution. When a salt dissolves in water, it dissociates into its ions. \(\mathrm{CaCl}_{2}\) dissociates into 3 ions: one \(\mathrm{Ca}^{2+}\) ion and two \(\mathrm{Cl}^{-}\) ions, while \(\mathrm{CaSO}_{4}\) dissociates into 2 ions: one \(\mathrm{Ca}^{2+}\) ion and one \(\mathrm{SO}_{4}^{2-}\) ion. Since \(\mathrm{CaCl}_{2}\) produces 3 ions, the freezing point depression will be greater than \(\mathrm{CaSO}_{4}\), which produces only 2 ions. Thus, \(0.10 \mathrm{~m} \mathrm{CaCl}_{2}\) has a lower freezing point than \(0.10 \mathrm{~m} \mathrm{CaSO}_{4}\).

(b) Solubility and temperature relationship

The solubility of a solid in water generally increases with temperature. This is because solubility is an equilibrium process and is driven by the energy balance between the lattice energy of the solid and the energy released by solvation of the solid particles. As temperature increases, the average kinetic energy of the water molecules also increases. This increased kinetic energy breaks the bonds between the solid particles more effectively, allowing more solid particles to dissolve in the solvent. Therefore, the solubility of solids usually increases as the temperature increases.

(c) Pressure and reverse osmosis

Osmosis is the process in which water passes through a semi-permeable membrane from a region of lower solute concentration to a region of higher solute concentration. In reverse osmosis, water is forced to move from a region of higher solute concentration to a region of lower solute concentration, against its natural tendency. To achieve reverse osmosis, pressure must be applied to the solution with higher solute concentration. This pressure overcomes the osmotic pressure and drives the water to flow in the opposite direction. Therefore, pressure must be applied to cause reverse osmosis to occur.

(d) Osmotic pressure of \(0.10 \mathrm{M} \mathrm{BaCl}_{2}\) and \(0.10 \mathrm{M}\) glucose

Osmotic pressure is directly proportional to the molar concentration of solute particles in a solution. When \(0.10 \mathrm{M} \mathrm{BaCl}_{2}\) dissolves in water, it dissociates into 3 ions: one \(\mathrm{Ba}^{2+}\) ion and two \(\mathrm{Cl}^{-}\) ions. Thus, the total concentration of solute particles is \(0.10\times 3 = 0.30 \mathrm{M}\). In contrast, glucose is a non-electrolyte which does not dissociate in water, and its molar concentration remains \(0.10 \mathrm{M}\). Since the concentration of solute particles in the \(\mathrm{BaCl}_{2}\) solution is higher, its osmotic pressure is also higher. Therefore, \(0.10 \mathrm{M} \mathrm{BaCl}_{2}\) has a higher osmotic pressure than \(0.10 \mathrm{M}\) glucose.

(e) Molarity and molality in dilute solutions

Molarity, represented as M, is defined as the number of moles of solute per liter of solution, while molality, represented as m, is defined as the number of moles of solute per kilogram of solvent. Since dilute solutions have a small amount of solute, the mass and volume of the solute are negligible compared to the mass and volume of the solvent. In such cases, the volume of the solution and the mass of the solvent are almost equal. Therefore, the values of molarity and molality become essentially the same for dilute solutions.

Key concepts

Freezing Point Depression

Understanding freezing point depression begins with the concept that adding a solute to a solvent decreases the temperature at which the liquid becomes solid—its freezing point. This phenomenon is pivotal not just in scientific inquiries, but also in day-to-day applications such as using salt to melt ice on roads. The underlying principle involves the effect of solute particles on the solvent's ability to form a solid structure; in other words, the added particles disrupt the orderly patterns necessary for solidification.

Why does this matter? For students examining the behavior of solutions, it’s important to recognize that the degree to which the freezing point is lowered is directly related to the amount of solute particles in the solution. This is irrespective of the chemical nature of the solute itself. Remember, a more concentrated solution means more particles interfering with the freezing process, and thus a lower freezing point. This is why a calcium chloride solution, which dissociates into three ions, will have a lower freezing point than a calcium sulfate solution with only two ions, assuming both have the same molality.

Osmotic Pressure

Moving on to osmotic pressure, it is essential to comprehend how substances move through a semipermeable membrane—a membrane that allows certain particles to pass while blocking others. Osmosis, the movement of a solvent (like water) into a region with a higher concentration of solute, attempts to balance solute concentrations on both sides of the membrane. The pressure that needs to be applied to prevent this natural flow of water is termed osmotic pressure.

Why is this significant in a learning context? Because osmotic pressure is a foundational concept in understanding many biological and environmental processes; for example, it is used by our kidneys to filter blood. Educators often stress the real-world importance of such properties in medical treatments, like dialysis. Students learn that in solutions where solute particles fully dissociate, like barium chloride, osmotic pressure is decidedly more pronounced than in solutions of non-dissociative substances like glucose, reflecting the greater number of particles exerting force on the membrane.

Solubility and Temperature

When discussing solubility and temperature, warmth usually equates to a more welcoming environment for substances to dissipate into solution. This relationship is particularly evident with solid solutes in liquids; as temperature ascends, the kinetic energy of the solvent molecules increases correspondingly. This additional energy aids the solvent molecules in breaking down the solute’s crystalline structure, allowing more solute to dissolve.

Why does this inform our understanding of chemical solutions? It's a critical aspect for a variety of applications from cooking to industrial processes, where control over solubility can affect the outcome significantly. It also serves as a pivotal lesson in thermodynamics and chemistry, illuminating the delicate balance between endothermic and exothermic processes and the role of entropy in dissolving solids.

Reverse Osmosis

The concept of reverse osmosis is not just academically fascinating but also practically useful, particularly in water purification systems. Reverse osmosis requires external pressure to be applied to a solution to force water molecules through a semipermeable membrane, counteracting natural osmotic pressure and enabling the movement of water from a higher to a lower solute concentration. This artificial imposition is essentially 'reversing' the expected direction of water flow.

Why must pressure be exerted? Without this pressure, water would naturally move towards the area of higher concentration, attempting to equalize solute levels. Therefore, reverse osmosis systems are designed to ensure that the applied pressure is greater than the natural osmotic pressure. This understanding is pivotal when exploring water treatment technology and is instrumental in producing clean water in areas where it's not readily available, showcasing the real-world significance of colligative properties.