7: Abnormal Molecular Mass

In water, one NaCl formula unit dissociates ideally as NaCl → Na⁺ + Cl⁻. Therefore, one solute unit produces two particles. The ideal van’t Hoff factor is the number of particles formed per original unit, so i = 2. In real solutions, ion interactions can make the measured value slightly different, but the ideal complete-dissociation value is 2.

One formula unit of calcium chloride dissociates completely as CaCl₂ → Ca²⁺ + 2Cl⁻. This produces one calcium ion and two chloride ions, giving three particles in total from one original unit. Therefore, the ideal van’t Hoff factor is i = 3. The subscript 2 on chlorine must be included; counting only the types of ions would incorrectly give 2.

Aluminium chloride dissociates completely according to AlCl₃ → Al³⁺ + 3Cl⁻. Thus, one formula unit produces one aluminium ion and three chloride ions, for a total of four particles. The ideal van’t Hoff factor is therefore i = 4. The ionic charges identify the ions but are not added; the number of particles, including the coefficient 3, determines i.

In complete dimerization, every two original molecules become one effective particle. Thus the particle number becomes one-half of the number expected without association. Since i is the ratio of effective to expected particles, i = 1/2 = 0.5. This also causes the observed molar mass to become twice the normal value.

In complete trimerization, three original solute molecules combine to form one larger particle: 3A → A₃. Thus the number of effective particles becomes one-third of the original number. Since the van’t Hoff factor is the ratio of actual to expected particle number, i = 1/3. In general, complete association of n molecules gives i = 1/n.

Colligative properties depend on the number of dissolved particles, not simply on the chemical formula of the solute. Association reduces the number and dissociation increases it. The van’t Hoff factor i incorporates this change by multiplying the ideal colligative expression, so the calculated effect matches the actual particle population.

Molar mass is commonly determined from osmotic pressure, elevation of boiling point, or depression of freezing point. These are colligative properties and depend on the number of solute particles. Association or dissociation changes that number, so using such measurements without the van’t Hoff correction can produce an abnormal molar mass.

A van’t Hoff factor greater than 1 means that the solution contains more effective particles than expected from the undissociated formula unit. This occurs when molecules or formula units split into smaller particles, which is dissociation. Association would give i less than 1, while i = 1 would indicate no change in particle number.

A van’t Hoff factor below 1 means that the effective number of solute particles has decreased. This is caused by association, in which two or more molecules combine. Since i = 0.65 is greater than the complete-dimerization limit of 0.5 but less than 1, it is consistent with partial dimerization under a simple model. It does not indicate dissociation or ideal behaviour.

The observed molar mass is lower when i is greater than 1. Dissociation of a salt in water increases the number of particles because each formula unit can produce several ions, so the colligative effect is larger and the calculated molar mass becomes smaller. All other options describe association, which gives i less than 1.

A value i less than 1 means that the effective number of solute particles has decreased. Benzoic acid can form hydrogen-bonded dimers in benzene, so two molecules behave as one particle. The aqueous salts listed generally dissociate into ions and therefore tend to give i greater than 1, not less than 1.

Complete dissociation of AB2 gives one A ion and two B ions, for example A2+ + 2B−. Thus one original formula unit produces three particles. Under the ideal complete-dissociation assumption, the van’t Hoff factor is the number of particles formed, so i = 3. The subscripts must be included when counting ions.

The stated dissociation is A₂B → 2A⁺ + B²⁻. One formula unit therefore produces two A⁺ ions and one B²⁻ ion, making three particles in total. For complete dissociation, the ideal van’t Hoff factor equals this number of product particles per original unit, so i = 3. Ionic charge magnitudes are not added; only the number of particles is counted.

Abnormal molar mass arises because association or dissociation changes the effective number of solute particles. The van’t Hoff factor i measures this change and enters the colligative-property equations directly. Values below 1 indicate association, values above 1 indicate dissociation, and i = 1 indicates no change in particle number.

Association joins two or more solute particles, so the total number of particles decreases. Colligative effects then become smaller than expected, and the molar mass calculated from that effect appears higher than the normal molar mass. Therefore, the association–higher observed molar mass pair is correct; dissociation gives i > 1 and a lower observed molar mass.

The van’t Hoff factor i represents the number of particles formed from one formula unit, relative to the undissociated solute. On complete dissociation, CaCl₂ produces one Ca²⁺ ion and two Cl⁻ ions, giving three particles; therefore i = 3. NaCl gives only two ions, while glucose is a non-electrolyte and benzoic acid in benzene commonly associates.

Glucose is a molecular, non-electrolyte solute in ordinary dilute solution. It dissolves as whole glucose molecules rather than splitting into ions, and it does not normally form dimers or larger associated particles under these conditions. Thus the number of solute particles remains unchanged, so the van’t Hoff factor is i = 1. Values above one indicate dissociation, whereas values below one indicate association.

Osmotic pressure depends on the number of solute particles and is represented by π = iCRT. Association combines particles, so i becomes less than one and the effective particle concentration decreases. Consequently, the observed osmotic pressure is lower than the value calculated for unchanged solute molecules. Dissociation or ionization would instead increase it.

For a solute that neither associates nor dissociates, i is approximately 1. Here i = 1.25, which is greater than one, so the number of particles has increased. Because the value is well below the ideal value for complete dissociation into several particles, partial or slight dissociation is the suitable interpretation. Association would instead give i less than one.

For an abnormal solution, the measured colligative effect equals i times the value calculated for an ideal, non-associating and non-dissociating solute. With i = 0.9, the effect is 0.9 of the normal value, so it is slightly smaller, not zero. A value below one usually reflects association, which reduces the number of solute particles.

Abnormal molar mass arises when the number of solute particles differs from the number expected from the formula. The main causes in this chapter are association, which reduces particles, and dissociation, which increases them. Therefore, first check whether either process can occur; then use i and the appropriate colligative-property relation. Colour, vessel shape, and shaking are irrelevant.

A larger number of particles produces a larger colligative effect at the same amount of solute. If that effect is interpreted using the unchanged-molecule formula, the calculated molar mass must appear smaller, because the effect is inversely related to molar mass in such calculations. Thus dissociation generally lowers observed molecular mass; it does not make it zero.

Association combines separate solute molecules into larger units, so fewer particles are present than the formula suggests. The resulting colligative effect is smaller. When the smaller effect is used to calculate molar mass, the value appears larger than the normal molar mass. Therefore association gives a higher observed molecular mass, while dissociation gives a lower one.

The van't Hoff factor compares the actual number of solute particles with the number expected if each formula unit remained intact. When i > 1, more particles are present than expected. The usual cause is dissociation into ions or smaller species. Association would reduce the particle count and give i < 1, so option A is the only suitable conclusion.

The van’t Hoff factor compares the actual number of dissolved particles with the number expected from the formula units. When i is less than one, fewer particles are present than expected. This occurs when two or more solute molecules combine to form larger associated species, such as dimers. Dissociation would increase particles and give i greater than one.