Revision: Solutions Chemistry Science (English Medium) Class 12 CBSE

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

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.

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 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.

Molality (m) is defined as the number of moles of the solute dissolved in one kilogram (kg) of the solvent. The units of molality are moles per kilogram, i.e., mole kg⁻¹. The molality is preferred over molarity if the volume of the solution is either expanding or contracting with temperature.

Molality (m) = `"Number of mole of solute"/"Mass of solvent (in kg)"`

The mass percentage of a component of a solution is defined as the mass of the solute in grams present in 100 g of the solution.

Mole fraction of a constituent is the fraction obtained by dividing the number of moles of that constituent by the total number of moles of all the constituents present in the solution.

\[x_{1}=\frac{n_{1}}{n_{1}+n_{2}+n_{3}+...+n_{i}}\]

Normality (N) of a solution is defined as the number of gram equivalents of the solute present in one liter of the solution. Normality is used in acid-based redox titrations.

Normality (N) = `"Number of gram equivalents of solute"/"Volume of solution in litre"`

The mole fraction of a particular component in a solution is the ratio of the number of moles of that component to the total number of moles of all the components present in the solution.

Molarity (M) is defined as the number of moles of solute dissolved in one litre (or one cubic decimetre) of 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.

The elevation in boiling point of a solution is directly proportional to the molal concentration (molality) of the solute in the solution.

ΔT_b = K_b m

Where

ΔT_b = Elevation in boiling point

K_b = Molal elevation constant (ebullioscopic constant)

m = Molality of the solution

Azeotropes are the binary mixtures of solutions that have the same composition in liquid and vapour phases and that have constant boiling points.

Colligative Properties: Colligative properties are the properties of the solutions which depend upon the number of solute particles present in the solution, irrespective of their nature, relative to the total number of particles present in the solution.

Examples: Relative lowering of vapour pressure of the solvent, depression of freezing point of the solvent, elevation of boiling point of the solvent, osmotic pressure of the solution

Molal elevation constant (K_b) is defined as the elevation in boiling point of a solution when one mole of a non-volatile solute is dissolved in one kilogram of a volatile solvent.

The temperature at which the liquid and solid forms of a substance can exist together in equilibrium is called the freezing point of that substance.

Cryoscopic constant or the Molal depression constant is defined as the depression in freezing point when one mole of non-volatile solute is dissolved in one kilogram of solvent. Its unit is K Kg mol⁻¹.

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.

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.

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.

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

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

When the molar mass calculated using colligative properties differs from the theoretical molar mass, it is called an abnormal molar mass.

The ratio of the observed (experimental) value of a colligative property to the normal (calculated) value of the same property is termed as van’t Hoff factor, i.

A solution in which more solute can be dissolved at the same temperature is called an unsaturated solution.

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

The pressure exerted by vapours of a liquid over the liquid surface in equilibrium at a given temperature is called vapour pressure.

A solution is a homogeneous mixture of two or more components whose composition and properties are uniform throughout.

The component present in larger quantity in a solution is called the solvent.

The component present in smaller quantity in a solution is called the solute.

A solution which contains the maximum amount of solute dissolved at a given temperature and pressure is called a saturated solution.

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 hypertonic solution.

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

The flow of solvent from solution to pure solvent through a semipermeable membrane when pressure greater than osmotic pressure is applied is called reverse osmosis.

The experimentally determined molar mass of a solute which is different from its expected (normal) molar mass is called abnormal molar mass.

The composition of a solution expressed quantitatively is called its concentration.

A solution which obeys Raoult’s law over the entire range of concentration is called an ideal solution.

For an ideal solution:

ΔH_mix = 0

$\Delta Vmix=0$

A solution which does not obey Raoult’s law over the entire range of concentration is called a non-ideal solution.

A binary liquid mixture which boils at a constant temperature with fixed composition is called an azeotrope.

• Large positive deviation → Minimum boiling azeotrope
• Large negative deviation → Maximum boiling azeotrope

 The properties of solutions which depend only on the number of solute particles present and not on their nature are called colligative properties.

The decrease in vapour pressure of a solvent on adding a non-volatile solute is called lowering of vapour pressure.

\[\Delta p=p_1^0-p_1\]

Relative lowering:

\[\frac{p_1^0-p_1}{p_1^0}=x_2\]

For dilute solution:

\[\frac{p_1^0-p_1}{p_1^0}=\frac{n_2}{n_1}\]

\[=\frac{w_2M_1}{w_1M_2}\]

The increase in boiling point of a solvent on addition of a non-volatile solute is called elevation of boiling point.

\[\Delta T_b=iK_bm\]

A membrane which allows only solvent molecules to pass through it but not solute molecules is called a semipermeable membrane.

The flow of solvent molecules through a semipermeable membrane from lower concentration to higher concentration is called osmosis.

The excess pressure that must be applied to a solution to stop the flow of solvent through a semipermeable membrane is called osmotic pressure.

\[\mathrm{Molarity}=\frac{\text{Number of moles of solute}}{\text{Volume of solution in litres}}\]

\[=\frac{w}{\mathrm{Molar~Mass}}\times\frac{1000}{V}\]

\[\mathrm{Normality}=\frac{\text{Number of gram equivalents of solute}}{\text{Volume of solution of litres}}\]

Normality of a solution = Molarity × n_f

\[\mathrm{Molality~}=\frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}}=\frac{W_{\mathrm{B}}}{M_{\mathrm{B}}}\times\frac{1000}{W_{\mathrm{A}}}\]

where A = solvent, B = solute

\[\mathrm{Volume}\%=\frac{\text{Volume of component}}{\text{Total volume of solution}}\times100\]

\[x_i=\frac{n_i}{n_1+n_2+\cdots+n_i}\]

For binary solution:

\[x_A=\frac{n_A}{n_A+n_B}\]

x_A ​+ x_B​ = 1

\[m=\frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}\]

\[M=\frac{\text{Moles of solute}}{\text{Volume of solution in litre}}\]

\[\mathrm{Mass}\%=\frac{\text{Mass of component in solution}}{\text{Total mass of solution}}\times100\]

\[\mathrm{ppm}=\frac{\text{Number of parts of component}}{\text{Total number of parts of all components}}\times10^6\]

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 at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.

1. Henry was the first to give a quantitative relationship between the pressure and solubility of a gas in a solvent, which is known as Henry’s law. The law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of the liquid or solution.
2. Dalton, a contemporary of Henry, also concluded independently that the solubility of a gas in a liquid solution is a function of the partial pressure of the gas. If we use the mole fraction of a gas in the solution as a measure of its solubility, then it can be said that the mole fraction of gas in the solution is proportional to the partial pressure of the gas over the solution.
3. The most commonly used form of Henry’s law states that “the partial pressure of the gas in the vapour phase (p) is proportional to the mole fraction of the gas (x) in the solution” and is expressed as:
   p ∝ x
   p = K_H . x
4. Here, K_H is Henry’s law constant. When a mixture of more than one gas is brought into contact with a solvent, each gaseous component dissolves in proportion to its partial pressure. That is why Henry’s law is applied to every gas, independent of the presence of other gases.

Statement:

At constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of the liquid.

Mathematical Form:

p = K_H x

Where
p = partial pressure of gas
x = mole fraction of gas
K_H = Henry’s law constant

Raoult’s Law (For Volatile Liquids):

Statement:

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

Mathematical Form:

\[p_1=p_1^0x_1\]

\[p_2=p_2^0x_2\]

Total Vapour Pressure (Dalton’s Law):

\[P_{total}=p_1+p_2\]

\[P_{total}=p_1^0x_1+p_2^0x_2\]

Raoult’s Law (For Non-Volatile Solute):

\[p=p^0x_{solvent}\]

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:

Factors Affecting Solubility

Vapour Pressure of Liquid:

Vapour pressure of a liquid = pressure exerted by the vapour in equilibrium with the liquid at a given temperature.

Raoult's Law — Vapour Pressure of Liquid-Liquid Solutions:

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 vapour pressure of the component in pure state and its mole fraction in solution.

Total vapour pressure of solution:

where P°_A and P°_B are the vapour pressures of pure components at the same temperature.

Composition of Vapour Phase:

The composition of the vapour phase in equilibrium with the solution is determined by the partial pressures of the components:

\[P_A=Y_AP_T\quad\Rightarrow\quad Y_A=\frac{P_A}{P_T}\]

\[P_B=Y_BP_T\quad\Rightarrow\quad Y_B=\frac{P_B}{P_T}\]

where Y_A and Y_B are mole fractions of A and B in the vapour phase.

For a solution of gas dissolved in liquid (A = solvent, B = gas):

• If the gas perfectly obeys Raoult's Law: P_B = P°_B · X_B
• If it obeys Henry's Law: P_B = K_H · X_B

When K_H = P°_B (i.e., vapour pressure of pure gas equals Henry's constant), Raoult's Law becomes a special case of Henry's Law.

Henry's Law applies when the solute is a gas; Raoult's Law applies when the solute is a volatile liquid.

For ideal solution: ΔH_mix = 0, ΔV_mix = 0

For non-ideal solution: ΔH_mix ≠ 0, ΔV_mix ≠ 0 

• Positive deviation: A-B interaction < A-A or B-B interactions 
• Negative deviation: A-B interaction > A-A or B-B interactions

Plots for Ideal and Non-Ideal Solutions: Formation of ideal solutions can also be represented graphically.

Formation of non-ideal solutions with negative deviation can be represented as:

Azeotropic Mixtures:

A type of liquid mixture having a definite composition and boiling like a pure liquid (i.e., constant boiling mixture).

The relative lowering of vapour pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute in the solution.

\[\frac{p^\circ-p_{\mathrm{solution}}}{p^\circ}=\frac{n_2}{n_1+n_2}\]

Boiling point of solution is greater than that of pure solvent and is given by

ΔT_b = K_b × m

• K_b = Metal elevation constant or Ebullioscopic constant
• M = molality

where, 

\[\Delta T_{\mathbf{b}}=T_{\mathbf{b}}-T_{\mathbf{b}}^{\circ}\]

\[\Delta T_{\mathrm{b}}=\frac{K_{\mathrm{b}}\times W_{2}\times1000}{M_{2}\times W_{1}}\]

Freezing point of solution is smaller than that of pure solvent and is given by

ΔT_f = K_f × m

K_f = Metal depression constant or cryoscopic constant

where, \[\Delta T_{\mathbf{f}}=T_{\mathbf{f}}^{\circ}-T_{\mathbf{f}}\]

\[\Delta T_\mathrm{f}=\frac{\mathrm{K}_f\times W_2\times1000}{M_2\times W_1}\]

The factor used to account for the extent of association or dissociation of solute particles in solution is called van’t Hoff factor.

\[i=\frac{\text{Normal molar mass}}{\text{Abnormal molar mass}}\]

\[i=\frac{\text{Observed colligative property}}{\text{Calculated colligative property}}\]

\[i=\frac{\text{Total moles of particles after dissociation/association}}{\text{Total moles of particles before dissociation/association}}\]

Value of i

• For dissociation → i > 1
• For association → i < 1
• For no association/dissociation → i = 1