Solutions

Given,
Weight of non-volatile solute,
Weight of solvent,
Lowering of vapour pressure,

Vapour pressure of pure solvent,

Molecular weight of solvent

Molecular weight of solute,
According to Raoult's law

Sodiummetaaluminate, thus formed, is soluble in water and changes into the complex , in which coordination
number of is

Equal weight


Molarity

To calculate the freezing point of a solution, we can use the formula:
ΔT_f = K_f x m
Given: K_f = 1.86 (in units of molal per degree Celsius)
m = 0.05 molal
Substituting the given values into the formula, we get:
ΔT_f = 1.86 x 0.05
ΔTf = 0.093^oC
The freezing point depression (ΔT_f) is 0.093^oC
Freezing point of the solution = Freezing point of water - ΔT_f
Freezing point of the solution = 0^oC - 0.093^oC = -0.093^oC
Freezing point of the 0.05 molal solution of the non-electrolyte in water is approximately -0.093^oC.
freezing point (ΔTf​) can be calculated using the formula ΔTf​=kf​×m, where kf​ is the cryoscopic constant and m is the molality. For the given values kf =1.86 and m=0.05, the calculation yields ΔTf​=0.093.
Thus, the final freezing point (Tf​) is found by subtracting 0.0930.093 from the initial temperature,

Step 1: Define colligative properties
Colligative properties include:
- Osmotic pressure: Pressure required to prevent osmosis, proportional to solute concentration.
- Depression of freezing point: Lowering of freezing point, proportional to molality.
- Elevation of boiling point: Increase in boiling point, proportional to molality.
- Vapor pressure lowering: Decrease in vapor pressure due to solute particles.

Step 2: Analyze each option
- Osmotic pressure: Depends on the number of solute particles (van’t Hoff factor times concentration). Colligative.
- Depression of freezing point: Depends on molality and the number of solute particles. Colligative.
- Elevation of boiling point: Depends on molality and solute particle concentration. Colligative.
- Refractive index: Measures how light bends in a medium. It depends on the chemical nature of both solute and solvent, not just the number of particles. Not colligative.

Step 3: Conclusion
Refractive index is not a colligative property.

The pH is calculated as:
Given : Thus, option (1) is correct.

Step 1: Use the dilution formula where
,
,
,
final volume after dilution in liters.
Step 2: Calculate final volume Step 3: Calculate volume of water to be added