18 g glucose ₍C₆H₁₂O₆ ) is added to 178.2 g water. The vapor pressure of water (in torr) for this aqueous solution is:

• 76.0

• 752.4

• 759.0

• 759.0

Molarity is defined as the number of moles of solute dissolved per liter of solution. 

 Molality of a solution is defined as the number of moles of solute dissolved in 1000 grams of solvent. 

While molarity decreases with an increase in temperature, molality is independent of temperature. This happens because molality involves mass, which does not change with a change in temperature, while molarity involves volume, which is temperature dependent.

b) Given 

 w₂ = 10.50 g 

w₁ = 200 g 

Molar mass of MgBr₂ (M₂) = 184 g 

 Using the formula, 

(a) Osmosis: The process of flow of solvent molecules from pure solvent to a solution or from a solution of lower concentration to a solution of higher concentration through a semi-permeable membrane is called osmosis. 

Osmotic Pressure: The pressure required to just stop the flow of solvent due to osmosis is called osmotic pressure (π) of the solution. 

 Yes, the osmotic pressure of a solution is a colligative property. The osmotic pressure is expressed as. 

 
Where,  

π  = osmotic pressure 

n = number of moles of solute 

V = volume of solution 

T = temperature 

From the equation, it is clear that osmotic pressure depends on upon the number of moles of solute ‘n’ irrespective of the nature of the solute. 

Hence, osmotic pressure is a colligative property. 

(b) Given

 K_b = 0.512 k kg mol^-1

w₂ = 15.00 g 

w₁ = 250.0 g 

M₂ = 58.44 g 

Using the formula, 

(a) Let p₁, p₂ = Partial vapour pressure of two volatile components 1 and 2 of a mixture 

= Vapour pressure of pure components 1 and 2

x₁, x₂ = Mole fractions of the components 1 and 2

p_total = Total vapour pressure of the mixture then Raoult’s law can be stated as: For a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction.

That is, for component 1,

p₁      x₁

And, p₁ = x₁

For component 2,

P₂ = x₂

According to Dalton’s law of partial pressures,

 The plot of vapour pressure and mole fraction of an ideal solution at constant temperature is shown below.

Raoult’s Law as a Special Case of Henry’s Law

According to Raoult’s law, the vapour pressure of a volatile component in a given solution is p₁ = x₁

According to Henry’s law, the partial vapour pressure of a gas (the component is so volatile that it exists as gas) in a liquid is

p = K_H x

It can be observed that in both the equations, the partial vapour pressure of the volatile component varies directly with its mole fraction. Only the proportionality constants K_H and are different. Thus, Raoult’s law becomes a special case of Henry’s law in which K_H is equal to .

(b) Given: w₂ = 1g (weight of solute)

w₁ = 50 g (weight of solvent)

T_f = 0.40 K

k_f = 5.12 K Kg mol^-1

M₂ =? (Molar mass of solute)

Using the equation,

T_f = K_fm (where m is molality)

0.40 = 5.12 x m

(a)

(i) Ideal Solution:

Solutions which obey Raoult’s law over the entire range of concentrations are known as the ideal solution. Along with that for ideal solution:

Enthalpy of mixing of the pure components to form the solution i.e _mix H = 0 and volume of mixing, _mix V = 0.

An ideal solution will be formed when intermolecular forces of attraction between the molecules of solute (A - A) and those between the molecules of solvent (B -B) are nearly equal to those between solute and solvent molecules (A - B).

For Example n-Hexane and n-heptane

(ii) Azeotropes

Binary mixtures which have the same composition in liquid and vapour phase, and have constant boiling points are known as azeotropes. It is not possible to separate its components by fractional distillation .There are two types of azeotropes:

Minimum boiling azeotrope, example: Ethanol-water mixture containing ethanol approximately 95% by volume.

Maximum boiling azeotrope, example: Nitric acid-water mixture containing 68% nitric acid and 32% water by mass.

(iii) Osmotic Pressure

The process of flow of solvent molecules from pure solvent to a solution or from a solution of lower concentration to a solution of higher concentration through a semi-permeable membrane is called osmosis. The pressure required to prevent the flow of solvent due to osmosis is called osmotic pressure (Ï€) of the solution.

Osmotic pressure is directly proportional to the molarity C of the solution at a given temperature T.

Where,

n₂ = Number of moles of solute

V= Volume of the solution in litres

(b) Assume that 100 g of solution contains 10 g of glucose and 90 g of water as our glucose solution is 10% by weight

Where w₂ = weight is solute in 'g'

w₁ = weight of solvent in 'g'

M₂ = Molecular mass of solute.

So,