5: Colligative Properties

A hypertonic solution has a higher effective solute concentration outside the red blood cell than inside it. Water therefore moves out of the cell through its selectively permeable membrane by osmosis, causing the cell to lose volume and shrink; this is called crenation. In an isotonic solution there is no net water movement, while a hypotonic solution or pure water drives water into the cell and may cause swelling or haemolysis.

The van’t Hoff factor compares the actual number of solute particles in solution with the number expected from the undissociated formula units. If the solute neither dissociates into smaller particles nor associates into larger particles, the particle number remains unchanged. Consequently, i remains approximately 1. Complete ionisation or formation of dimers changes the particle number and therefore changes i.

Osmotic pressure is measured by considering the pressure required to stop the movement of solvent through a semipermeable membrane. It therefore specifically requires a membrane that permits solvent molecules to pass but restricts solute particles. Elevation of boiling point, depression of freezing point, and lowering of vapour pressure are studied through temperature or vapour-pressure relationships and do not require a membrane for their basic definition.

For an ideal solution containing a non-volatile solute, Raoult’s law gives the relative lowering of vapour pressure as (p° − p)/p° = Xsolute. Therefore, Xsolute = 0.10. Since the mole fractions of solute and solvent add to one, Xsolvent = 1 − 0.10 = 0.90. Hence option C is correct; a mole fraction cannot exceed one.

For a dilute solution, osmotic pressure is expressed as π = iCRT. When temperature T and van’t Hoff factor i are unchanged, π is directly proportional to concentration C. Consequently, if the osmotic pressure changes from π to 2π, the concentration must change from C to 2C. It cannot become half or four times, because those changes would produce π/2 or 4π under the stated constant conditions.

A hypertonic solution has a greater concentration of osmotically active particles than the fluid inside the blood cell. Consequently, its osmotic pressure is higher. Across a selectively permeable membrane, water moves from the region of lower effective solute concentration toward the region of higher effective solute concentration. Therefore water leaves the cell, and option A is correct.

A hypotonic solution has a lower concentration of effective solute particles and therefore a lower osmotic pressure than the cell interior. The cell membrane permits water movement more readily than solute movement. Water consequently enters the cell from the outside, where effective particle concentration is lower, toward the cell fluid, where it is higher. This influx can make the cell swell.

Colligative properties depend primarily on the number of solute particles present in a given amount of solvent, rather than on the chemical identity of those particles. Examples include relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure. If dissociation or association occurs, the effective particle number changes, so the van’t Hoff factor is used.

A non-volatile solute does not itself contribute appreciably to the vapour phase. Its presence lowers the mole fraction and escaping tendency of the solvent, so the solution has a lower vapour pressure than the pure solvent. Increasing the amount of solute lowers the solvent mole fraction further and produces a further decrease in vapour pressure. It does not necessarily become exactly zero.

The actual molarity is C = n/V = 0.010 mol/1.00 L = 0.010 M. For an electrolyte or any solute represented by a van’t Hoff factor, osmotic pressure is π = iCRT. Thus the concentration of effective particles is iC = 2.0 × 0.010 M = 0.020 M. This effective concentration, rather than the analytical molarity alone, must be used in the osmotic-pressure expression.

Freezing-point depression is a colligative property. In a sufficiently dilute solution, its value depends on the number of dissolved particles, represented by molality and the van’t Hoff factor, rather than on the identity of the solute. Viscosity, surface tension, and refractive index depend strongly on molecular interactions and chemical nature.

The elevation in boiling point is the difference between the boiling point of the solution and that of the pure solvent: \(\Delta T_b=T_b(\text{solution})-T_b^0(\text{solvent})\). Hence \(\Delta T_b=100.78-100.00=0.78^\circ C\). A temperature difference has the same numerical value in kelvin, so the answer is 0.78 K.

For a solution containing a non-volatile solute, Raoult’s law gives the relative lowering of vapour pressure as (p° − p)/p° = X_solute, where p° is the vapour pressure of the pure solvent and p is that of the solution. Since X_solute = 0.03, the relative lowering is 0.03, or 3%. The solvent mole fraction, 0.97, is not the requested quantity.

The constants \(K_b\) and \(K_f\) are characteristic properties of the solvent. They depend on quantities such as the solvent’s enthalpy of vaporisation or fusion, molar mass, and boiling or freezing temperature. They do not depend on the chemical identity of a dilute, non-electrolyte solute, although the observed change also depends on molality.

Blood-cell membranes are selectively permeable, so water can move across them while many solutes cannot. In a hypotonic medium, water enters the cell and it may swell or burst; in a hypertonic medium, water leaves and the cell shrinks. These effects are explained by osmosis and differences in osmotic pressure, so option D is correct.

For a solution containing a non-volatile solute, Raoult’s law states that the relative lowering of vapour pressure is equal to the mole fraction of the solute: (P° − P)/P° = Xsolute. Therefore, when the relative lowering is 0.02, Xsolute is approximately 0.02. This relation is especially applicable to dilute solutions, where the solvent mole fraction is close to one and the ideal-solution approximation is valid. Hence, option B is correct.

For a non-electrolyte at a fixed molality, the depression in freezing point is ΔT_f = K_fm. If the solvent’s cryoscopic constant K_f is larger while m remains unchanged, the product K_fm becomes larger. Thus the solution shows a greater freezing-point depression. This conclusion concerns freezing behavior, not a decrease in boiling point or an increase in vapour pressure.

Colligative properties depend primarily on the number of dissolved particles, rather than on their chemical identity. Osmotic pressure, depression in freezing point, elevation in boiling point, and relative lowering of vapour pressure are colligative properties. Viscosity is not colligative because it depends on the nature of the solute and solvent, molecular interactions, and temperature. Hence, viscosity is the correct answer.

For a dilute solution, osmotic pressure is expressed as π = iCRT. If concentration C and the van’t Hoff factor i remain constant, osmotic pressure is directly proportional to the absolute temperature T. Thus, increasing temperature increases the osmotic pressure. It does not become zero or remain unchanged, so option B is correct.

The depression in freezing point is the decrease in the freezing point caused by dissolving a solute. It is calculated as the freezing point of the pure solvent minus the freezing point of the solution: ΔTf = Tf° − Tf = 273.0 K − 271.9 K = 1.1 K. Therefore, option A is correct. The temperature difference in kelvin has the same numerical size as the difference in degrees Celsius.

When a non-volatile solute is added to a solvent, solute particles occupy some positions at the liquid surface and reduce the mole fraction of the solvent. Consequently, fewer solvent molecules can escape from the surface into the vapour phase. According to Raoult’s law, the partial vapour pressure of the solvent becomes lower than its vapour pressure in the pure state. Therefore, option A is correct.

Colligative properties depend primarily on the number of solute particles present in a given amount of solvent, not on the chemical identity of those particles. The important factor is the effective particle count, which can change when an electrolyte dissociates or when molecules associate. Vapour-pressure lowering, boiling-point elevation, freezing-point depression, and osmotic pressure are examples. Therefore, option B gives the correct characteristic.

Osmosis is the movement of solvent through a semipermeable membrane toward the solution with the greater effective solute concentration. The minimum external pressure that must be applied to the solution to just stop this solvent movement is called osmotic pressure. Vapour pressure and partial pressure describe gas-phase or vapour behaviour, while critical pressure is unrelated to osmosis. Therefore, option B is correct.

For a dilute nonelectrolyte solution, the osmotic pressure follows π = CRT because i = 1. At constant temperature, osmotic pressure is directly proportional to molar concentration. The concentration changes from 0.1 M to 0.2 M, so it doubles. Thus the new pressure is 2 × 2.46 = 4.92 atm. Therefore, option C is correct.

The van’t Hoff factor compares the actual number of solute particles in solution with the number expected from the formula units initially dissolved. If i = 1, there is no net change in particle number. This is expected when the solute neither associates into larger units nor dissociates into ions. Complete dissociation or dimerisation would make i greater or less than 1, respectively. Therefore, option A is correct.