Revision: Std XII >> Solutions MAH-MHT CET (PCM/PCB) Solutions

A solution is a homogeneous mixture of two or more substances in the same or different physical phases. The substances that form the solution are called its components.

Solute + Solvent = Solution

Homogeneous mixtures of two or more than two components are known as solutions.

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.

A solution which contains more solute than would be necessary to saturate it at a given temperature is called a supersaturated solution.

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.

A solution in which more solute can be dissolved without raising the temperature is called an unsaturated solution.

A solution in which no solute can be dissolved further at a given temperature is called a saturated solution.

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.

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.

or

Osmosis is a flow of solvent through a semipermeable membrane into the solution. The direction of osmosis can be reversed by applying a pressure larger than the osmotic pressure. This is called reverse osmosis.

Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.

\[\pi=\frac{n_2RT}{V}=\mathrm{CRT}\]

\[\pi=\frac{w_2RT}{\mathrm{M}_2V}\]

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.

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

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.

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.

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.

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

or

When a solution and pure solvent or two solutions of different concentrations are separated by a semipermeable membrane, the solvent molecules pass through the membrane this is called osmosis.

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.

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.

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).

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.

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

A solution is a homogeneous mixture of two or more components whose concentration can be varied within certain limits.

• Solute — the component present in a smaller amount (dissolved)
• Solvent — the component present in a larger amount (dissolving medium)
• A binary solution contains only two components: one solute + one solvent.

Classification of Mixtures

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:

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

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

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

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