Revision: Solutions Chemistry HSC Science (General) 12th Standard Board Exam Maharashtra State Board

A homogeneous mixture of two or more substances, whose relative amounts may be changed within certain limits, is called a solution.

It is characterised as a solution that adheres to Raoult's Law, with no interactions between the molecules and no volume or heat change during mixing.

For an ideal solution, Enthalpy of mixing of the pure components to form the solution is Δ_mix H = 0 and the volume of mixing is Δ_mix V = 0.

Two or more solutions exerting the same osmotic pressure are called isotonic solutions.

When two solutions are separated by a semipermeable membrane and no osmosis occurs, i.e., there is no net flow of water on either side through the membrane, the solutions are said to be isotonic solutions. If the membrane is perfectly semipermeable, the two solutions possess the same osmotic pressure and are also referred to as iso-osmotic solutions.

It is defined as the amount of solute that can be dissolved in 100 g of the solvent at the given conditions. It is also expressed as the maximum quantity of solute moles that can be dissolved in solvent to form 1 dm³ of solution.

Ebullioscopic constant or molal elevation constant, is the elevation in the boiling point produced when one mole of the solute is dissolved in one kilogram of solvent. 

ΔT_b = K_b × m

ΔT_b = K_b if m = 1 molal

Where K_b = Molal elevation constant

ΔT_b = Elevation in boiling point.

Two or more solutions exerting the same osmotic pressure are called an isotonic solution.

The process of moving a solvent from a solution to a pure solvent through a semipermeable membrane while applying excessive pressure on the solution side is known as reverse osmosis.

The net spontaneous flow of solvent molecules into the solution or from more dilute solution to more concentrated solution through a semipermeable membrane is called osmosis.

It is a thin film, such as cellophane, which has pores large enough to allow the solvent molecules to pass through them.

It is the net spontaneous flow of solvent molecules into the solution or from a more dilute solution to a more concentrated solution through a semipermeable membrane.

If a pressure larger than the osmotic pressure is applied to the solution side, then pure solvent from the solution passes into the pure solvent side through the semipermeable membrane. This phenomenon is called reverse osmosis.

Osmotic pressure may be defined as the external pressure which should be applied to the solution in order to stop the phenomenon of osmosis, i.e., to stop the flow of solvent into the solution when the two are separated by a semipermeable membrane.

The solution having lower osmotic pressure as compared to some other solution is referred to as a hypotonic solution.

Semipermeable membrane: It is a membrane which allows the solvent molecules, but not the solute molecules, to pass through it.

Semipermeable membrane is a film such as cellophane which has pores large enough to allow the solvent molecules to pass through them.

The process in which solvent flows from solution into pure solvent through a semipermeable membrane by applying pressure greater than osmotic pressure is called reverse osmosis.

The fraction of total number of molecules that dissociate into ions is called degree of dissociation.

A homogeneous mixture of two or more chemically non-reacting substances is called a solution.

The component of a solution which is present in smaller quantity and gets dissolved is called solute.

The component of a solution which is present in larger quantity and dissolves the solute is called solvent.

The maximum amount of solute that can be dissolved in a given amount of solvent at a specific temperature is called solubility.

A solution that contains the maximum amount of solute at a given temperature is called a saturated solution.

A solution that contains less solute than the maximum amount that can be dissolved at a given temperature is called an unsaturated solution.

A solution that contains more solute than required for saturation at a given temperature is called a supersaturated solution.

The pressure required to stop the flow of solvent through a semipermeable membrane during osmosis is called osmotic pressure.

The flow of solvent molecules through a semipermeable membrane from pure solvent or dilute solution to concentrated solution is called osmosis.

Two solutions having the same osmotic pressure at a given temperature are called isotonic solutions.

A solution having higher osmotic pressure than another solution is called a hypertonic solution.

A solution having lower osmotic pressure than another solution is called a hypotonic solution.

The physical properties of dilute solutions that depend only on the number of solute particles and not on their nature are called colligative properties.

\[i=\frac{\text{Colligative property of electrolyte solution}}{\text{Colligative property of nonelectrolyte solution}}\]

\[i=\frac{\text{Actual moles of particles after dissociation}}{\text{Moles of formula units dissolved}}\]

Relation with degree of dissociation:

i = 1 + α(n − 1)

\[\alpha=\frac{i-1}{n-1}\]

Statement: The solubility of a gas in a liquid is directly proportional to the pressure of the gas over the solution.

S = K_H⋅P

Where S = solubility (mol L⁻¹), P = pressure (bar), K_H = Henry's law constant (mol L⁻¹ bar⁻¹).

Gases like NH₃ and CO₂ do NOT obey Henry's law (they react with water).

Henry’s law states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas over the solution.

For a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction.

If p_i is the partial vapour pressure of i^th component in a solution and χ_i is its mole fraction in the solution, then according to Raoult’s law,

p_i ∝ χ_i

or p_i = constant × χ_i    ...(i)

If we consider the component in its pure state, then 

`p_i = p_i^circ` and

χ_i = 1

Where P_i is the vapour pressure of the i^th component in the pure state. In the case of the pure i^th component, we shall have a 100% pure component, and χ_i will be equal to 1. Substituting the values in Eq. (i), we have

p_i = constant × 1

or constant = `p_i^circ`

Again putting the value of the constant in Eq. (i), we have

`p_i = p_i^circ* chi_i`

Raoult’s law states that the partial vapour pressure of any volatile component of a solution is equal to the vapour pressure of the pure component multiplied by its mole fraction in the solution. 

For a solution of volatile liquids, the partial vapour pressure of each component in the solution at a particular temperature is equal to the product of the vapour pressure of the component in the pure state and its mole fraction in the solution.

Mathematically, for a binary solution:

\[\ce{P_A = P{^{\circ}_{A}}\chi_A}\] and 

\[\ce{P_B = P{^{\circ}_{B}}\chi_B}\]

The total vapour pressure is:

\[\ce{P_{total} = P_A + P_B = P{^{\circ}_{A}}\chi_A + P{^{\circ}_{B}}\chi_B}\]

Statement: The partial vapour pressure of any volatile component of a solution is equal to the vapour pressure ofthe pure component multiplied by its mole fraction in the solution.

For a binary solution of two volatile components:

\[\mathrm{P}_{1}=\mathrm{P}_{1}^{0}x_{1}\quad\mathrm{and}\quad\mathrm{P}_{2}=\mathrm{P}_{2}^{0}x_{2}\]

Raoult's law Using Dalton's law of partial pressures, Total vapour pressure (P) is given by:

\[\mathrm{P}=\mathrm{P}_{1}+\mathrm{P}_{2}=\mathrm{P}_{1}^{0}x_{1}+\mathrm{P}_{2}^{0}x_{2}=\left(\mathrm{P}_{2}^{0}-\mathrm{P}_{1}^{0}\right)x_{2}+\mathrm{P}_{1}^{0}\]

Composition of vapour phase: If y₁ and y₂ are the mole fractions of the components 1 and 2, respectively, in the vapour phase; then using Dalton's law of partial pressures: P₁ = y₁P and P₂ = y₂P

The vapour pressure of a solution containing a non-volatile solute at a particular temperature is directly proportional to the mole fraction of the solvent in the solution.

According to Raoult’s law,

`P = P_"solvent" = P^circ * chi_"solvent"`    ...(i)

For a binary mixture,

`chi_"solute" + chi_"solvent" = 1`

∴ `chi_"solvent" = 1 - chi_"solute"`

Putting this value in the equation (i), we have

`P = P^circ xx (1 - chi_"solute")`

or `P/P^circ = 1 - chi_"solute"`

or `1 - P/P^circ = chi_"solute"`

or `(P^circ - P)/P^circ = chi_"solute"`

In the above equation, the term (P° − P) represents the lowering of vapour pressure in the formation of the solution. The term `(P^circ - P)/P^circ`is called the relative lowering of vapour pressure of the solution.

Statement:
The depression in freezing point of a solvent is directly proportional to the molality of the solution.

Mathematical Expression:

ΔT_f = K_f m

Where:
K_f​ = Cryoscopic constant

Statement:
The osmotic pressure of a dilute solution is directly proportional to its molar concentration at constant temperature.

Mathematical Expression:

π = MRT

Where:
π = Osmotic pressure
M = Molarity
R = Gas constant
T = Temperature in Kelvin

Statement:
At constant temperature, the solubility of a gas in a liquid is directly proportional to the pressure of the gas above the solution.

Mathematical Expression:

S ∝ P

S = K_HP

Where:
S = Solubility of gas
P = Pressure of gas
K_H = Henry’s law constant

Statement:
The total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases.

Mathematical Expression:

P = P₁ + P₂​

Statement:
At constant temperature, the partial vapour pressure of a volatile component in a solution is equal to the product of its mole fraction and vapour pressure in pure state.

Mathematical Expression:

P₁ = P₁⁰ x₁​

For binary solution:

P = P₁ + P₂​

Statement:
For dilute solutions, the relative lowering of vapour pressure is equal to the mole fraction of the solute.

Mathematical Expression:

\[\frac{\Delta P}{P^0}=x_2\]

Statement:
The elevation in boiling point of a solvent is directly proportional to the molality of the solution.

Mathematical Expression:

ΔT_b = K_bm

Where:
K_b​ = Ebullioscopic constant

Based on the physical states of solute and solvent, there are 9 types of solutions:

Based on the amount of solute dissolved at a given temperature:

Factors Affecting Solubility

Electrolytes dissociate in solution → produce more particles → colligative properties are greater than expected. Observed molar masses are less than formula mass.

van't Hoff factor (i):

\[i=\frac{\text{Colligative property of electrolyte solution}}{\text{Colligative property of non-clectrolyte solution of same concentration}}\]

\[i=\frac{(\Delta T_f)_o}{(\Delta T_f)_t}=\frac{(\Delta T_b)_o}{(\Delta T_b)_t}=\frac{(\Delta P)_o}{(\Delta P)_t}=\frac{\pi_o}{\pi_t}=\frac{M_{\text{theoretical}}}{M_{\mathrm{observed}}}\]

Modified Colligative Expressions:

\[\Delta P=i\cdot P_1^0\cdot x_2\]

\[\Delta T_{b}=iK_{b}m=\frac{i1000K_{b}w_{2}}{M_{2}W_{1}}\]

\[\Delta T_{f}=iK_{f}m=\frac{i1000\times K_{f}\times w_{2}}{M_{2}W_{1}}\]

\[\pi=i\cdot MRT=\frac{i\cdot W_{2}RT}{M_{2}V}\]

• Solutions of electrolytes exhibit colligative properties, but they do not obey the same quantitative relations as nonelectrolyte solutions.
• The observed colligative properties of electrolyte solutions are greater than those of nonelectrolyte solutions of the same concentration.
• The molar masses of electrolytes determined from colligative property measurements are found to be lower than their expected formula masses.
• The abnormal behaviour of electrolytes is due to their dissociation into two or more ions in aqueous solution, which increases the number of solute particles.