Solutions – NEET UG ChemistryPractice Questions & PYQs

The depression in freezing point is related to the molality of a solution through the cryoscopic constant using the expression $\Delta T_f = K_f m.$ Substituting the given values of 5.12 for the constant and 0.078 for the molality results in a value of 0.399 K. Expressing this result to two decimal places yields 0.40 K.

Deviations from ideal solution behavior arise when intermolecular attractive forces between unlike molecules differ from those between like molecules. In positive deviations, the original intermolecular forces between identical molecules are stronger than the newly formed interactions between different molecules, causing the molecules to escape into the vapor phase more readily. Consequently, this weaker attraction results in a higher total vapor pressure than predicted by Raoult's law alongside positive enthalpy and volume changes upon mixing.

Solutions that exhibit large negative deviations from Raoult's law feature strong attractive interactions between dissimilar molecules, causing them to boil at a higher temperature than either pure component. Water and nitric acid form a classic example of this behavior because strong interactions between nitric acid and water molecules create a system with exceptionally low vapour pressure. Consequently, this mixture requires a higher boiling point than its individual constituents, forming a maximum boiling azeotrope.

The partial pressure of an individual gas in a mixture is determined by the equation $P = P_{\text{total}} \times X$, where total pressure and mole fraction are related proportionally. The mole fraction of dry air is found by subtracting the water vapour mole fraction from one, giving 0.98. Multiplying this value by the total pressure of 1.2 atm directly gives the partial pressure of dry air as 1.176 atm.

An ideal solution is characterized by thermodynamic conditions where intermolecular forces between different molecules match those of pure components, resulting in an enthalpy change of mixing equal to zero ($\Delta_{\text{mix}} H = 0$). This zero enthalpy change occurs alongside a zero volume change, a positive entropy change, and a negative Gibbs free energy change.

Concentration terms that rely on the volume of the solution are inherently temperature-dependent because liquid volume expands or contracts with changes in temperature. Molarity is defined as the number of moles of solute per litre of solution, making it sensitive to thermal fluctuations. In contrast, mass-based concentration units remain completely unaffected by temperature variations.

The molal depression constant is an intrinsic property determined solely by the thermodynamic characteristics of the solvent, such as its latent heat of fusion and freezing point. Because $K_f$ depends exclusively on the nature of the solvent rather than the solute concentration, altering the molality of the solution has zero effect on its value. Therefore, doubling the molality leaves the molal depression constant completely unchanged.

The molar mass of the solute is first determined using the relative lowering of vapor pressure formula, substituting standard atmospheric pressure alongside the given solution pressure and mass quantities to obtain the molecular weight. This calculated molar mass is then used to find the molality of the solution. Multiplying this molality by the given ebullioscopic constant yields the boiling point elevation, which, when added to the normal boiling point of water, gives the final solution temperature of $101^\circ\text{C}$.

Strong electrolytes dissociate completely in aqueous solution according to the equation $\text{Ba(OH)}_2 \rightarrow \text{Ba}^{2+} + 2\text{OH}^-$. Counting the resulting species shows that one formula unit yields one barium ion and two hydroxide ions, giving a total of three particles. Because the van't Hoff factor represents the total number of particles produced per formula unit, its value is 3.

According to Raoult's law, the partial vapor pressure of a volatile component in a mixture depends directly on its pure component vapor pressure and its mole fraction in the liquid phase. Since benzene possesses a substantially higher pure vapor pressure than toluene at the same temperature, it exerts a greater partial pressure in the equimolar liquid mixture. Consequently, applying Dalton's law of partial pressures shows that the vapor phase is richer in the more volatile component, resulting in a higher percentage of benzene above the solution.

The formation of an ideal solution is a spontaneous process, which inherently requires the Gibbs free energy of mixing to be negative rather than zero. While enthalpy change, internal energy change, and deviation in vapor pressure from Raoult's law all equal zero due to identical intermolecular forces, the entropy increase drives the process forward. Consequently, stating that $\Delta G_{mix}=0$ violates the fundamental thermodynamic condition for solution formation.

The van't Hoff factor ($i$) for a completely ionized electrolyte equals the total number of ions ($n$) produced per formula unit. Aluminium sulfate dissociates into two aluminium ions and three sulfate ions, giving a total of five ions, so its value of $i$ is $5$. Potassium hexacyanoferrate(II), $\mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6]$, dissociates into four potassium ions and one hexacyanoferrate complex ion, also yielding a total of five ions. Therefore, both electrolytes share an identical van't Hoff factor.

The elevation in boiling point is directly proportional to the product of the molality, the ebullioscopic constant, and the van't Hoff factor, expressed as $\Delta T_b = i K_b m$. Since both solutions share the same solvent and molality, a higher boiling point elevation for substance X directly indicates a larger van't Hoff factor compared to substance Y. A larger van't Hoff factor implies that the solute particles multiply in solution through dissociation, meaning substance X undergoes dissociation in water while substance Y does not.

A molal concentration of $1.00 \text{ m}$ indicates that exactly one mole of solute is dissolved in $1000 \text{ g}$ of water. The number of moles of water is calculated by dividing this mass by the molar mass of water, resulting in approximately $55.56 \text{ moles}$. The mole fraction of the solute is then found by dividing the moles of solute by the total moles of both components, yielding the final value.

The formation of a solution involves the spontaneous mixing of components, which inherently increases the overall disorder and randomness of the system. Consequently, the entropy of mixing ($\Delta S_{\text{mix}}$) for an ideal solution is always positive rather than zero. Other thermodynamic parameters such as enthalpy and volume changes upon mixing, as well as deviations from Raoult's law, remain strictly zero due to uniform intermolecular interactions.

Freezing point depression is a colligative property governed by the formula $\Delta T_f = i K_f m$, where the magnitude of depression depends directly on the van't Hoff factor ($i$) of the solute. Among the given options, $\mathrm{Al}_2(\mathrm{SO}_4)_3$ dissociates completely to yield the highest number of discrete particles per formula unit, producing a van't Hoff factor of $5$. Because a larger particle count intensifies the colligative effect, this solution experiences the most significant lowering of its freezing point.

Molarity is defined by the relation $M = \frac{W \times 1000}{M_w \times V}$ where $W$ is the mass of the solute \in grams and $M_w$ is its molar mass. For a 250 mL solution at 2.0 M, the required mass of pure nitric acid is calculated using its molar mass of $63\text{ g mol}^{-1}$, yielding $31.5\text{ g}$ of pure $\mathrm{HNO}_3$. Since the concentrated acid is only 70% pure by mass, dividing this pure mass by $0.70$ determines that $45\text{ g}$ of the concentrated nitric acid solution must be used.

Raoult's law states that the total vapour pressure of an ideal binary solution is the sum of the partial vapour pressures of its components, given by $P_{\text{total}} = P^\circ_1 X_1 + P^\circ_2 X_2$. First, determine the number of moles for each component by dividing their given masses by their respective molar masses, resulting \in $0.213\text{ moles}$ for chloroform and $0.470\text{ moles}$ for dichloromethane. Next, compute the mole fraction for each liquid and substitute these values along with the respective pure component vapour pressures into Raoult's equation to obtain a total solution vapour pressure of $90.63\text{ mm Hg}$.

Raoult's law dictates that the total vapor pressure of an ideal binary solution is given by the sum of the individual component pressures, expressed mathematically as $P = x_A P_A + x_B P_B$. Since the sum of mole fractions in a binary mixture equals one, substituting $x_B = 1 - x_A$ into the initial pressure expression yields $P = x_A P_A + (1 - x_A) P_B$. Expanding and rearranging this equation by grouping the terms containing $x_A$ isolates the pure component pressures, resulting in the final expression $P = P_B + x_A(P_A - P_B)$.

The van't Hoff factor quantifies the actual number of particles present in solution relative to the number of formula units dissolved. When a solute undergoes dissociation, it splits into multiple ions or particles, which increases the total particle count and yields a van't Hoff factor greater than one. Conversely, when solute molecules undergo association, they combine to form larger aggregates, thereby reducing the total number of particles and resulting in a van't Hoff factor less than one.