Solutions Class 12 – Notes, NCERT Solutions, Formulas & CBSE PYQs | Chemistry Unit 2 Guide
Solutions Class 12 – Notes, NCERT Solutions, Formulas & CBSE PYQs | Chemistry Unit 2 Guide
Unit 2 – Solutions
2.1 Types of Solutions
2.2 Expressing Concentration of
Solutions
2.3 Solubility
2.4 Vapour Pressure of Liquid
Solutions
2.5 Ideal and Non-ideal Solutions
2.6 Colligative Properties and
Determination of Molar Mass
2.7 Abnormal Molar Masses
1. Introduction to Solutions
In everyday life, we rarely encounter pure substances, as most are mixtures of two or more pure substances. A solution is defined as a homogeneous mixture of two or more components. Homogeneous means that the solution's composition and properties are uniform throughout.
- Components of a Solution:
- Solvent: The component present in the largest quantity, which determines the physical state of the solution.
- Solute(s): One or more components present in the solution other than the solvent.
- Binary Solutions: In this unit, primarily binary solutions are considered, meaning they consist of two components.
- Utility and Importance: The usefulness of mixtures depends on their composition. For instance, the properties of brass (copper and zinc mixture) differ from German silver (copper, zinc, and nickel) or bronze (copper and tin). In practical applications, specific concentrations are crucial; for example, 1 part per million (ppm) of fluoride ions in water prevents tooth decay, while 1.5 ppm can cause mottled teeth, and higher concentrations are poisonous. Intravenous injections require specific ionic concentrations that match blood plasma. Many biological processes in the body occur within liquid solutions.
2. Types of Solutions
Solutions can be classified based on the physical state of the solute and solvent. The solvent determines the overall physical state of the solution.
- Gaseous Solutions:
- Gas in Gas: Mixture of oxygen and nitrogen gases.
- Liquid in Gas: Chloroform mixed with nitrogen gas.
- Solid in Gas: Camphor in nitrogen gas.
- Liquid Solutions: These are primarily discussed in the source.
- Gas in Liquid: Oxygen dissolved in water (essential for aquatic life).
- Liquid in Liquid: Ethanol dissolved in water.
- Solid in Liquid: Glucose dissolved in water.
- Solid Solutions:
- Gas in Solid: Solution of hydrogen in palladium.
- Liquid in Solid: Amalgam of mercury with sodium.
- Solid in Solid: Copper dissolved in gold (e.g., alloys like brass, German silver, bronze).
3. Expressing Concentration of Solutions (Quantitative Methods)
While solutions can be described qualitatively (e.g., dilute or concentrated), a quantitative description is essential for clarity and precision. There are several ways to express the concentration of a solution quantitatively:
- Mass Percentage (w/w):
- Definition: The mass of a component divided by the total mass of the solution, multiplied by 100.
- Formula: Mass % of a component = (Mass of the component in the solution / Total mass of the solution) × 100.
- Example: 10% glucose in water by mass means 10 g of glucose is dissolved in 90 g of water, making a 100 g solution.
- Application: Commonly used in industrial chemical applications, like commercial bleaching solutions containing 3.62% sodium hypochlorite by mass.
- Volume Percentage (V/V):
- Definition: The volume of a component divided by the total volume of the solution, multiplied by 100.
- Formula: Volume % of a component = (Volume of the component / Total volume of solution) × 100.
- Example: 10% ethanol solution in water means 10 mL of ethanol in 100 mL total solution.
- Application: Commonly used for solutions containing liquids, such as a 35% (v/v) ethylene glycol solution used as antifreeze, which lowers water's freezing point to 255.4 K (–17.6°C).
- Mass by Volume Percentage (w/V):
- Definition: The mass of solute dissolved in 100 mL of the solution.
- Application: Commonly used in medicine and pharmacy.
- Parts Per Million (ppm):
- Definition: Used for trace quantities of solute, defined as the number of parts of the component per million parts of all components in the solution.
- Formula: Parts per million = (Number of parts of the component / Total number of parts of all components of the solution) × 10⁶.
- Forms: Can be expressed as mass to mass, volume to volume, or mass to volume.
- Example: Sea water containing 6 × 10⁻³ g of dissolved oxygen in 1030 g of water is expressed as 5.8 ppm. Concentrations of pollutants in water or the atmosphere are often given in ppm.
- Mole Fraction (x):
- Definition: The number of moles of a component divided by the total number of moles of all components in the solution.
- Formula for binary mixture: For components A and B with moles nA and nB, xA = nA / (nA + nB).
- Formula for 'i' components: xᵢ = nᵢ / Σnᵢ.
- Property: The sum of all mole fractions in a given solution is always unity (x₁ + x₂ + ... + xᵢ = 1).
- Application: Very useful for relating physical properties of solutions, like vapour pressure, and in calculations involving gas mixtures.
- Example 1.1: Calculating the mole fraction of ethylene glycol (C₂H₆O₂) in water.
- Molarity (M):
- Definition: The number of moles of solute dissolved in one litre (or one cubic decimetre) of solution.
- Formula: Molarity = Moles of solute / Volume of solution in litre.
- Units: mol L⁻¹ or M, also mol dm⁻³.
- Example: 0.25 mol L⁻¹ NaOH solution means 0.25 mol of NaOH in one litre of solution.
- Example 1.2: Calculating the molarity of 5 g NaOH in 450 mL solution.
- Molality (m):
- Definition: The number of moles of the solute per kilogram (kg) of the solvent.
- Formula: Molality (m) = Moles of solute / Mass of solvent in kg.
- Example: 1.00 mol kg⁻¹ KCl solution means 1 mol (74.5 g) of KCl dissolved in 1 kg of water.
- Example 1.3: Calculating the molality of 2.5 g ethanoic acid in 75 g of benzene.
- Temperature Dependence of Concentration Units:
- Independent of Temperature: Mass percentage, parts per million (ppm), mole fraction, and molality are independent of temperature. This is because these units are based on mass or number of moles, which do not change with temperature.
- Dependent on Temperature: Molarity is a function of temperature because the volume of the solution changes with temperature, while the mass does not.
4. Solubility
Solubility refers to the maximum amount of a substance that can be dissolved in a specified amount of solvent at a specific temperature. It is influenced by the nature of the solute and solvent, as well as temperature and pressure.
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Solubility of a Solid in a Liquid:
- "Like Dissolves Like": A general rule stating that polar solutes dissolve in polar solvents, and non-polar solutes dissolve in non-polar solvents. This means a solute dissolves in a solvent if their intermolecular interactions are similar.
- Example: Sodium chloride and sugar dissolve in water (polar-polar), while naphthalene and anthracene do not. Conversely, naphthalene and anthracene dissolve in benzene (non-polar-non-polar), but sodium chloride and sugar do not.
- Saturated Solution: A solution in which no more solute can be dissolved at the given temperature and pressure. It exists in dynamic equilibrium with the undissolved solute, and the concentration of solute in it is its solubility.
- Unsaturated Solution: A solution in which more solute can be dissolved at the same temperature.
- Effect of Pressure: Pressure has no significant effect on the solubility of solids in liquids because solids and liquids are highly incompressible.
- "Like Dissolves Like": A general rule stating that polar solutes dissolve in polar solvents, and non-polar solutes dissolve in non-polar solvents. This means a solute dissolves in a solvent if their intermolecular interactions are similar.
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Solubility of a Gas in a Liquid:
- Many gases dissolve in water, though to varying extents (e.g., oxygen dissolves slightly, sustaining aquatic life; hydrogen chloride gas is highly soluble).
- Effect of Pressure: The solubility of gases in liquids is greatly affected by pressure, increasing with an increase in pressure.
- Mechanism: Increasing pressure over the solution increases the number of gas particles per unit volume, leading to more particles striking and entering the solution until a new equilibrium is reached.
- Effect of Temperature: Solubility of gases in liquids decreases with a rise in temperature. This is because the dissolution of a gas in a liquid is generally an exothermic process (heat is evolved), and according to Le Chatelier's Principle, increasing temperature shifts the equilibrium to favor the reverse process (gas coming out of solution).
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Henry's Law:
- Statement: 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.
- Alternative (mole fraction form): The mole fraction of gas in the solution is proportional to the partial pressure of the gas over the solution.
- Formula: p = K_H x.
- p: Partial pressure of the gas in the vapor phase.
- K_H: Henry's law constant.
- x: Mole fraction of the gas in the solution.
- Henry's Law Constant (K_H): This constant depends on the nature of the gas and the temperature. A higher K_H value at a given pressure indicates lower solubility of the gas in the liquid.
- Applications of Henry's Law:
- Soft Drinks and Soda Water: Bottles are sealed under high pressure to increase the solubility of CO₂, making them fizzy.
- Scuba Diving: Divers breathe air at high pressures underwater, which increases the solubility of atmospheric gases (like nitrogen) in their blood. Rapid ascent reduces pressure, releasing dissolved gases and forming nitrogen bubbles in the blood, causing bends (painful and dangerous). To prevent this and anoxia (low oxygen at high altitudes), scuba tanks are filled with air diluted with helium (11.7% helium, 56.2% nitrogen, 32.1% oxygen).
- High Altitudes: Lower partial pressure of oxygen at high altitudes leads to lower oxygen concentration in the blood and tissues of climbers, causing anoxia (weakness, impaired thinking).
- Example 1.4: Calculating the millimoles of N₂ gas dissolved in 1 liter of water using Henry's Law.
5. Vapour Pressure of Liquid Solutions
Liquids at a given temperature vaporize, and at equilibrium, the pressure exerted by the vapors over the liquid phase is called vapor pressure.
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Effect of Non-Volatile Solute: When a non-volatile solute is added to a solvent, the vapor pressure of the solution is lower than that of the pure solvent at the same temperature.
- Reason: In a pure liquid, the entire surface is occupied by solvent molecules. When a non-volatile solute is added, the solute particles also occupy part of the surface area, reducing the fraction of the surface available for solvent molecules to escape into the vapor phase. This reduction in escaping solvent molecules leads to a lower vapor pressure.
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Raoult's Law:
- Statement for Volatile Liquids: For a solution of volatile liquids, the partial vapor pressure of each component in the solution is directly proportional to its mole fraction in the solution.
- Formula: p₁ = x₁ p₁⁰.
- p₁: Partial vapor pressure of component 1 in the solution.
- x₁: Mole fraction of component 1 in the solution.
- p₁⁰: Vapor pressure of pure component 1.
- Dalton's Law of Partial Pressures Applied: The total vapor pressure (p_total) over the solution is the sum of the partial pressures of its components:
- p_total = p₁ + p₂.
- Substituting Raoult's law for each component: p_total = x₁ p₁⁰ + x₂ p₂⁰.
- Conclusions from Total Vapor Pressure Equation:
- Total vapor pressure can be related to the mole fraction of any one component.
- Total vapor pressure varies linearly with the mole fraction of component 2.
- The total vapor pressure either decreases or increases with the increase of the mole fraction of component 1, depending on the pure components' vapor pressures.
- Composition of Vapour Phase: If y₁ and y₂ are the mole fractions of components 1 and 2 in the vapor phase, then according to Dalton's law of partial pressures:
- p₁ = y₁ p_total.
- p₂ = y₂ p_total.
- In general: pᵢ = yᵢ p_total.
- Example 1.5: Calculating the vapor pressure and vapor phase composition for a solution of chloroform (CHCl₃) and dichloromethane (CH₂Cl₂). The more volatile component will be richer in the vapor phase at equilibrium.
- Raoult's Law as a Special Case of Henry's Law:
- Both laws state that the partial pressure of a volatile component or gas is directly proportional to its mole fraction in the solution. The difference lies in the proportionality constant.
- Raoult's law constant is the vapor pressure of the pure component (p₁⁰), while Henry's law constant is K_H.
- Thus, Raoult's law is a special case of Henry's law where K_H becomes equal to p₁⁰.
6. Ideal and Non-ideal Solutions
Liquid-liquid solutions are classified as ideal or non-ideal based on their adherence to Raoult's law.
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Ideal Solutions:
- Definition: Solutions that obey Raoult's law over the entire range of concentration.
- Key Properties:
- Enthalpy of mixing (Δ_mix_H) is zero: No heat is absorbed or evolved when components are mixed.
- Volume of mixing (Δ_mix_V) is zero: The volume of the solution is equal to the sum of the volumes of its pure components.
- Molecular Interactions: In an ideal solution, the intermolecular attractive forces between A-A molecules and B-B molecules are nearly equal to those between A-B molecules in the mixture.
- Examples: Solution of n-hexane and n-heptane, bromoethane and chloroethane, benzene and toluene are nearly ideal.
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Non-Ideal Solutions:
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Definition: Solutions that do not obey Raoult's law over the entire range of concentration.
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Their vapor pressure is either higher or lower than that predicted by Raoult's law.
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Positive Deviation from Raoult's Law:
- Observation: The total vapor pressure is higher than predicted by Raoult's law [39, 42(a)].
- Cause: The intermolecular attractive forces between solute-solvent molecules (A-B) are weaker than those between solute-solute (A-A) or solvent-solvent (B-B) molecules.
- Effect: Molecules find it easier to escape from the solution than from their pure state, leading to an increase in vapor pressure.
- Mixing Properties:
- Δ_mix_H > 0 (Endothermic): Heat is absorbed upon mixing.
- Δ_mix_V > 0: The volume of the solution is greater than the sum of the volumes of the pure components (expansion occurs).
- Examples:
- Ethanol and Acetone: In pure ethanol, molecules are hydrogen bonded. Adding acetone breaks some of these hydrogen bonds, weakening interactions and increasing vapor pressure.
- Carbon Disulphide and Acetone: Dipolar interactions between solute-solvent molecules are weaker than interactions among pure solute and solvent molecules.
- Azeotropes: Solutions showing a large positive deviation form minimum boiling azeotropes at a specific composition. These cannot be separated by fractional distillation because the liquid and vapor phases have the same composition and boil at a constant temperature.
- Example: Ethanol-water mixture, which forms an azeotrope with approximately 95% ethanol by volume.
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Negative Deviation from Raoult's Law:
- Observation: The total vapor pressure is lower than predicted by Raoult's law [39, 42(b)].
- Cause: The intermolecular attractive forces between solute-solvent molecules (A-B) are stronger than those between solute-solute (A-A) or solvent-solvent (B-B) molecules.
- Effect: This stronger interaction decreases the escaping tendency of molecules, consequently decreasing the vapor pressure.
- Mixing Properties:
- Δ_mix_H < 0 (Exothermic): Heat is evolved upon mixing.
- Δ_mix_V < 0: The volume of the solution is less than the sum of the volumes of the pure components (contraction occurs).
- Example: Nitric acid and water form a maximum boiling azeotrope with approximately 68% nitric acid by mass, boiling at 393.5 K.
- Azeotropes: Solutions showing a large negative deviation form maximum boiling azeotropes at a specific composition.
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7. Colligative Properties and Determination of Molar Mass
Colligative properties are properties of solutions that depend on the number of solute particles, regardless of their chemical identity or nature, relative to the total number of particles in the solution. These properties are often used to determine the molar masses of solutes.
The four main colligative properties are:
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Relative Lowering of Vapour Pressure:
- The vapor pressure of a solvent in a solution is less than that of the pure solvent. Raoult's law quantifies this, showing that the lowering depends only on the concentration of solute particles.
- Formula: The reduction in vapor pressure (Δp₁) is given by Δp₁ = x₂ p₁⁰, where x₂ is the mole fraction of the solute and p₁⁰ is the vapor pressure of the pure solvent.
- Relative Lowering: The ratio of the lowering of vapor pressure to the vapor pressure of the pure solvent is equal to the mole fraction of the solute: (p₁⁰ - p₁) / p₁⁰ = x₂.
- Molar Mass Determination: For a dilute solution, this can be expressed as **(p₁⁰ - p₁) / p₁⁰ = (w₂ M₁) / (w₁ M₂) **, where w and M are mass and molar mass, and subscripts 1 and 2 refer to solvent and solute, respectively. This equation allows the calculation of the solute's molar mass (M₂).
- Example 1.6: Calculating the molar mass of a non-volatile solid based on the vapor pressure lowering in benzene.
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Elevation of Boiling Point (ΔT_b):
- The boiling point of a solution is always higher than that of the pure solvent. This is because the vapor pressure of the solution is lowered by the non-volatile solute, so a higher temperature is needed to make its vapor pressure equal to the atmospheric pressure.
- Definition: The increase in boiling point, ΔT_b = T_b - T_b⁰, where T_b is the boiling point of the solution and T_b⁰ is the boiling point of the pure solvent.
- Relationship: For dilute solutions, the elevation of boiling point is directly proportional to the molal concentration (m) of the solute: ΔT_b = K_b m.
- K_b: The constant of proportionality is called the Boiling Point Elevation Constant, Molal Elevation Constant, or Ebullioscopic Constant, with units of K kg mol⁻¹.
- Molar Mass Determination: If w₂ grams of solute with molar mass M₂ are dissolved in w₁ grams of solvent, the molar mass can be calculated using: M₂ = (K_b w₂ 1000) / (ΔT_b w₁).
- Example 1.8: Calculating the molar mass of a non-volatile solute given the boiling point elevation in benzene.
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Depression of Freezing Point (ΔT_f):
- The freezing point of a solution is lower than that of the pure solvent when a non-volatile solute is dissolved.
- Definition: The decrease in freezing point, ΔT_f = T_f⁰ - T_f, where T_f⁰ is the freezing point of the pure solvent and T_f is the freezing point of the solution.
- Relationship: For dilute solutions, the depression of freezing point is directly proportional to the molality (m) of the solution: ΔT_f = K_f m.
- K_f: The proportionality constant is called the Freezing Point Depression Constant, Molal Depression Constant, or Cryoscopic Constant, which depends on the nature of the solvent.
- Molar Mass Determination: The molar mass of the solute (M₂) can be determined using: M₂ = (K_f w₂ 1000) / (ΔT_f w₁).
- Table 1.3 provides K_b and K_f values for common solvents.
- Example 1.9: Calculating the freezing point depression and freezing point of a solution of ethylene glycol in water.
- Example 1.10: An example of determining molar mass from freezing point depression (calculation partially obscured in sources).
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Osmosis and Osmotic Pressure (Π or P):
- Semipermeable Membranes (SPM): These are membranes (natural like pig's bladder, parchment, or synthetic like cellophane) that contain submicroscopic pores. They allow small solvent molecules (e.g., water) to pass through but hinder larger solute molecules.
- Osmosis: The process of flow of solvent molecules through a semipermeable membrane. This flow occurs spontaneously from the pure solvent side to the solution side, or from a more dilute solution to a more concentrated solution. The solvent molecules always flow from a region of lower solute concentration to higher solute concentration.
- Natural Examples: Raw mangoes shrivel in brine (lose water to salt solution), wilted flowers revive in fresh water (gain water), and blood cells collapse in saline water (lose water if saline is hypertonic).
- Osmotic Pressure: This is the excess pressure that must be applied to the solution side to prevent osmosis (to stop the net flow of solvent molecules into the solution through the SPM).
- Colligative Property: Osmotic pressure is a colligative property because it depends on the number of solute molecules, not their identity.
- Relationship: For dilute solutions, osmotic pressure (Π or P) is proportional to the molarity (C) of the solution and the temperature (T):
- Π = C R T (Equation 1.39).
- C = n₂/V, where n₂ is moles of solute and V is volume of solution in liters. So, Π = (n₂/V) R T (Equation 1.40).
- Molar Mass Determination: This method is widely used for determining molar masses of proteins, polymers, and other macromolecules due to its suitability for large molecular masses at room temperature. If w₂ grams of solute with molar mass M₂ are present in volume V of solution, then:
- M₂ = (w₂ R T) / (Π V) (Equation 1.42).
- Types of Solutions based on Osmotic Pressure:
- Isotonic Solutions: Solutions having the same osmotic pressure. For example, a 0.9% (mass/volume) NaCl solution is isotonic with blood plasma, so intravenous injections are dissolved in water with similar ionic concentrations.
- Hypertonic Solutions: Solutions with a higher salt concentration (e.g., > 0.9% mass/volume NaCl) compared to blood cells. If cells are placed in such a solution, water flows out of the cells by osmosis, causing them to shrink.
- Hypotonic Solutions: Solutions with a lower salt concentration (e.g., < 0.9% mass/volume NaCl). If cells are placed in such a solution, water flows into the cells by osmosis, causing them to swell.
- Example 1.11: Calculating the molar mass of a protein based on its osmotic pressure.
- Reverse Osmosis and Water Purification:
- Process: If a pressure greater than the osmotic pressure is applied to the solution side of a semipermeable membrane, the direction of osmosis can be reversed. Pure solvent (water) is forced out of the solution through the membrane.
- Application: This phenomenon is used in desalination of sea water to obtain potable water.
- Membranes: Cellulose acetate films are common porous membranes used, as they are permeable to water but impermeable to impurities and ions present in sea water. High pressure is typically required.
8. Abnormal Molar Masses
The colligative properties are based on the assumption that the solute is non-volatile and does not undergo dissociation or association in the solution. However, some solutes can exhibit abnormal molar masses when they either dissociate or associate in the solvent.
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Dissociation:
- When an ionic compound like KCl dissolves in water, it dissociates into ions (e.g., K⁺ and Cl⁻), increasing the total number of particles in the solution.
- If a solute dissociates, the observed colligative property will be higher than expected, leading to a calculated molar mass that is lower than the actual (normal) molar mass.
- Example: One mole of KCl in 1 kg of water is expected to increase the boiling point by 2 × 0.52 K = 1.04 K, as it produces two moles of particles (K⁺ and Cl⁻).
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Association:
- Some solutes, like ethanoic acid in benzene, can associate to form larger molecules (e.g., dimers).
- If a solute associates, the observed colligative property will be lower than expected, leading to a calculated molar mass that is higher than the actual (normal) molar mass.
- Example: If ethanoic acid forms a dimer, the number of particles in solution is effectively halved, meaning the boiling point elevation or freezing point depression will be half the normal value. Consequently, the calculated molar mass will be twice the expected value.
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Van't Hoff Factor (i):
- Introduced by van't Hoff in 1880, this factor accounts for the extent of dissociation or association of a solute in solution.
- Definitions:
- i = Normal molar mass / Abnormal (experimental) molar mass.
- i = Observed colligative property / Calculated colligative property.
- i = Total number of moles of particles after association/dissociation / Number of moles of particles before association/dissociation.
- Interpretation of 'i':
- For association: i < 1 (fewer particles than initial moles).
- For dissociation: i > 1 (more particles than initial moles).
- For solutes that neither associate nor dissociate (ideal behavior): i = 1.
- Example 1.12: Calculation of the percentage association of benzoic acid in benzene, which forms a dimer, demonstrating how 'i' is used to find the degree of association.
- Example: Calculation of the van't Hoff factor and dissociation constant for acetic acid in water, illustrating how 'i' can be used to determine the degree of dissociation for weak electrolytes. For strong electrolytes like KCl, NaCl, and MgSO₄, the 'i' values approach their theoretical number of ions (e.g., 2 for KCl) as the solution becomes more dilute.
In essence, understanding solutions is like understanding a well-orchestrated dance. The solvent sets the stage and the rhythm, while the solute particles are the dancers. Their concentration describes how crowded the dance floor is, and solubility tells us how many dancers can join before it's too full. If the dancers (solute) start breaking apart or holding hands (dissociation or association), the "molar mass" you calculate from their performance on the dance floor might seem abnormal, requiring the van't Hoff factor to correct your count. Meanwhile, colligative properties are like observing the overall impact of the dance on the environment, such as how much the stage vibrates (vapor pressure lowering) or how much hotter the room gets (boiling point elevation), effects that depend only on the number of dancers, not who they are.
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