Solutions

Depression in freezing point is a colligative property. Higher the value of i, higher will be depression in freezing point and lowest will be the freezing point of solution. For � � � � � � � � � � � � � � � � � � � � � � � � � �

Now,
Normality =
Hence, mass of oxalic acid in 500 cc of solution can be calculated as

Normality = N Volume= Now, � �

van't Hoff factor,

Glucose does not undergo dissociation or association hence, .

An azeotrope is a mixture of two or more liquids that has the same composition in both the liquid and vapor phases, making it impossible to separate them by simple distillation. The correct azeotrope here is formed by carbon tetrachloride ( ) and chloroform ( ), which forms an azeotropic mixture. This mixture has a constant boiling point, unlike most mixtures that boil at different points. - Chlorobenzene + Bromobenzene and + do not form azeotropes.
- + are alkane hydrocarbons that do not form an azeotropic mixture.
Therefore, the correct answer is + , as they form a true azeotrope.

Step 1: Solubility of gases in liquids is influenced by several factors:
• Nature of solute and solvent: Polar gases dissolve better in polar solvents (like water), and non-polar in non-polar solvents.
• Pressure (Henry’s Law): Solubility is directly proportional to pressure exerted on the surface of the liquid. Higher pressure = greater solubility.
• Temperature: Increasing temperature generally decreases the solubility of gases in liquids due to exothermic dissolution.
Step 2: Concentration of the solution does not affect the intrinsic solubility of a gas in a liquid. It affects the amount already dissolved but not the capacity for dissolution. Hence, it’s not a factor influencing solubility.

Azeotropes are mixtures of two or more liquids that boil at a constant temperature and cannot be separated by distillation. - Heptane and Octane (both hydrocarbons) do not form a minimum boiling azeotrope because they have similar boiling points.
- Water and Nitric acid form a minimum boiling azeotrope at 68.5°C.
- Ethanol and Water form a minimum boiling azeotrope at 78.2°C.
- Acetone and Carbon dioxide also form a minimum boiling azeotrope. Thus, the correct answer is (i), (iii), and (iv).

Azeotropes are mixtures with constant boiling points that cannot be separated by distillation.
Maximum boiling azeotropes form when strong hydrogen bonding or interactions between components reduce their vapor pressure.
Acetone and chloroform form such a mixture due to H-bonding.

Given:
- Molar mass of PbCl = 278 g/mol
- Mass of PbCl = 0.2 g
- K of PbCl = 3.2 10

Step 1: Calculate the number of moles of PbCl :

Step 2: Write the dissociation equation for PbCl :

Step 3: Use the K expression:
Let the concentration of Pb ions be . Then, the concentration of Cl ions will be .
Thus, we have: Substituting the given value: Solving for :
Step 4: Find the volume of water required:
We know the moles of PbCl is mol, and the concentration of Pb is mol/L.
Using the formula for concentration: Solving for :

We are given a 5 m aqueous solution, meaning there are 5 moles of solute dissolved in 1 kg of solvent (water). To calculate the mole fraction of solute, we use the following formula: For 1 kg of water, the number of moles of solvent (water) is: Now, the mole fraction of solute is: Thus, the mole fraction of the solute is 0.082.

The (Henry’s Law constant) is defined as the ratio of the partial pressure of a gas to its concentration in a solution, i.e., where is the partial pressure and is the concentration of the gas in solution. - Statement A is incorrect because Henry’s Law constant, , increases with decreasing solubility. This means that a higher corresponds to lower solubility, not higher. - Statement B is correct because depends on the nature of the solvent and solute. - Statement C is correct since the value of changes with temperature. As temperature increases, the solubility of gases typically decreases, which leads to a change in . - Statement D is correct because according to Henry’s Law, the concentration of gas in the solution is directly proportional to the partial pressure, so the value changes with changes in partial pressure.

To find the relationship between the osmotic pressures of X and Y, we use the formula for osmotic pressure: Where: - is the osmotic pressure, - is the van’t Hoff factor (which is 2 for , as it dissociates into two ions: ), - is the molarity of the solution, - is the gas constant, - is the temperature in Kelvin. For the electrolyte , the van't Hoff factor . For the non-electrolyte solution Y, , since it does not dissociate. Now, let’s calculate the osmotic pressures for both solutions: - For (electrolyte): - For Y (non-electrolyte): We are given that the osmotic pressure of Y is , so . Now, comparing and : Thus, .

The amount of substance reacted can be calculated using Faraday's law of electrolysis: Where: - is the mass of Cu deposited (in grams), - is the molar mass of Cu (63.5 g/mol), - is the current in amperes (3.0 A), - is the time in seconds (2 hours = 7200 s), - is the current efficiency (90% = 0.9), - is the number of electrons involved in the reaction (2 for Cu), - is the Faraday constant ( ). Now, the amount of CuSO₄ that reacts can be calculated by converting the mass of Cu deposited into moles: The change in molarity of CuSO₄ can then be determined by using the initial volume of the solution: Finally, the final molarity of CuSO₄ will be: First, calculate the moles of Cu deposited: Now, calculate the moles of Cu: Now, calculate the change in molarity: Finally, calculate the final molarity:
Thus, the final molarity of the CuSO₄ solution is approximately .

The elevation in boiling point ( ) is related to the molality (m) of the solution by the formula: Where: - is the ebullioscopic constant of the solvent, - is the molality of the solution, - is the van't Hoff factor, which represents the number of particles the solute dissociates into. For dimerization, , where is the degree of association. Given: Substituting into the equation: Simplifying: Since the degree of dissociation ( ) can range from 0 to 1, the actual dimerization factor ( ) corresponds to 100% association.
Thus, the percentage association of X is 100%.