Comprehensive Study Guide to Liquid Solutions and Notes on Liquid Solutions

Introduction to Solutions and Their Importance

• Definition of Solutions: Solutions are homogeneous mixtures of two or more than two components. A homogeneous mixture is defined as having a composition and properties that are uniform throughout the mixture.

• Solvent vs. Solute:

  • Solvent: The component present in the largest quantity. It determines the physical state in which the solution exists (solid, liquid, or gas).

  • Solute: One or more components present in the solution other than the solvent.

• Binary Solutions: Solutions consisting of only two components. This Unit focuses primarily on binary liquid solutions.

• Significance of Composition: The utility of mixtures depends on their specific composition.

  • Alloys: The properties of brass (copper + zinc) differ from German silver (copper + zinc + nickel) or bronze (copper + tin).

  • Fluoride Concentrations:

  • $1.0\,ppm$ (part per million) of fluoride ions in water prevents tooth decay.

  • $1.5\,ppm$ causes mottled teeth.

  • High concentrations are poisonous (e.g., sodium fluoride used in rat poison).

  • Medical Applications: Intravenous injections must match the salt concentration of blood plasma.

Types of Solutions

• Solutions are categorized by the physical state of the solute and solvent (Table 1.1):

  • Gaseous Solutions:

  • Gas in Gas: Mixture of oxygen ($O_2$) and nitrogen ($N_2$).

  • Liquid in Gas: Chloroform ($CHCl_3$) mixed with nitrogen gas.

  • Solid in Gas: Camphor in nitrogen gas.

  • Liquid Solutions:

  • Gas in Liquid: Oxygen ($O_2$) dissolved in water.

  • Liquid in Liquid: Ethanol dissolved in water.

  • Solid in Liquid: Glucose dissolved in water.

  • Solid Solutions:

  • Gas in Solid: Solution of hydrogen in palladium ($Pd$).

  • Liquid in Solid: Amalgam of mercury ($Hg$) with sodium ($Na$).

  • Solid in Solid: Copper dissolved in gold ($Au$).

Quantitative Expressions of Concentration

• Mass Percentage (w/w): Defined as the mass of the component in solution per $100\,g$ of solution.

  • Formula: \text{Mass % of component} = \frac{\text{Mass of component}}{\text{Total mass of solution}} \times 100

  • Example: $10\%$ glucose in water by mass means $10\,g$ glucose in $90\,g$ water.

  • Common Application: Commercial bleaching solution contains $3.62\%$ mass percentage of sodium hypochlorite ($NaOCl$).

• Volume Percentage (V/V): Defined as the volume of a component per $100\,mL$ of solution.

  • Formula: \text{Volume % of component} = \frac{\text{Volume of component}}{\text{Total volume of solution}} \times 100

  • Example: $35\%\,(v/v)$ ethylene glycol is used as car antifreeze; it lowers the freezing point of water to $255.4\,K$ ($-17.6\,^{\circ}C$).

• Mass by Volume Percentage (w/V): The mass of solute dissolved in $100\,mL$ of solution; common in medicine and pharmacy.

• Parts Per Million (ppm): Used for solutes present in trace quantities.

  • Formula: $\text{ppm} = \frac{\text{Number of parts of component}}{\text{Total number of parts of all components}} \times 10^6$

  • Example: A litre of sea water ($1030\,g$) contains $6 \times 10^{-3}\,g$ of dissolved $O_2$, expressed as $5.8\,ppm$.

• Mole Fraction ($x$): The ratio of moles of a component to the total moles of all components.

  • Formula for component A: $x_A = \frac{n_A}{n_A + n_B}$

  • The sum of mole fractions of all components in a solution is always unity: $x_1 + x_2 + ... + x_i = 1$.

  • Example 1.1: In a $20\%$ ethylene glycol ($C_2H_6O_2$) solution by mass, the mole fraction ($x_{glycol}$) is calculated as follows:

  • $20\,g\,C_2H_6O_2$ ($0.322\,mol$) and $80\,g\,H_2O$ ($4.444\,mol$).

  • $x_{glycol} = \frac{0.322}{0.322 + 4.444} = 0.068$.

• Molarity (M): Moles of solute per litre of solution.

  • Formula: $M = \frac{\text{Moles of solute}}{\text{Volume of solution in litres}}$

  • Unit: $mol\,L^{-1}$ or $mol\,dm^{-3}$.

  • Molarity is a function of temperature because volume depends on temperature.

• Molality (m): Moles of solute per kilogram of solvent.

  • Formula: $m = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}$

  • Molality is independent of temperature as mass does not change with temperature.

Solubility of Solids and Gases in Liquids

• Solubility Definition: The maximum amount of a substance that can be dissolved in a specified amount of solvent at a specific temperature.

• Nature of Solute and Solvent: Follows the rule "like dissolves like."

  • Polar solutes (e.g., $NaCl$, sugar) dissolve in polar solvents (water).

  • Non-polar solutes (e.g., naphthalene, anthracene) dissolve in non-polar solvents (benzene).

• Equilibrium in Solubility:

  • Dissolution: Solute particles go into the solvent, increasing concentration.

  • Crystallization: Solute particles in solution collide with solid solute and separate out.

  • Saturated Solution: A state of dynamic equilibrium where the rate of dissolution equals the rate of crystallization. No more solute can be dissolved at that T and P.

  • Unsaturated Solution: More solute can still be dissolved.

• Solubility of Solids in Liquids:

  • Temperature Effect: If dissolution is endothermic ($\Delta_{sol}H > 0$), solubility increases with T. If exothermic ($\Delta_{sol}H < 0$), solubility decreases.

  • Pressure Effect: Minimal impact because solids and liquids are highly incompressible.

• Solubility of Gases in Liquids:

  • Pressure Effect: Gaseous solubility increases with increased pressure.

  • Henry’s Law: At constant temperature, the solubility of a gas is directly proportional to its partial pressure above the liquid surface.

  • Mathematical form: $p = K_H x$, where $p$ is partial pressure and $K_H$ is Henry’s Law constant.

  • Higher $K_H$ indicates lower solubility. $K_H$ increases with temperature, making gases less soluble as temperature rises. (Reason why aquatic life is more comfortable in cold water).

  • Applications of Henry’s Law:

  • Soft Drinks: Bottles are sealed under high pressure to increase $CO_2$ solubility.

  • Scuba Diving: Increased pressure causes more atmospheric gases (like $N_2$) to dissolve in the blood. Rapid ascent causes nitrogen bubbles ("bends"). Tanks are filled with air diluted with helium ($11.7\%\,He$, $56.2\%\,N_2$, $32.1\%\,O_2$) to avoid this.

  • High Altitude: Low partial pressure of oxygen leads to low blood oxygen concentration, causing "anoxia" (inability to think clearly, weakness).

  • Temperature Effect: Dissolution of gases is exothermic (similar to condensation). Thus, solubility decreases as temperature increases.

Vapour Pressure of Liquid Solutions

• Raoult’s Law for Volatile Liquids: For a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction in the solution.

  • Formulas: $p_1 = x_1 p_1^0$ and $p_2 = x_2 p_2^0$.

  • Total Pressure: $p_{total} = p_1^0 + (p_2^0 - p_1^0)x_2$. (Dalton’s Law of partial pressures applied).

  • Vapour Phase Composition: Mole fractions in the vapour phase ($y_1$, $y_2$) are given by $p_i = y_i p_{total}$. Equilibrium vapour is always richer in the more volatile component.

• Raoult’s Law for Non-Volatile Solutes: Addition of a non-volatile solute lowers the vapour pressure of the solvent because solute particles occupy surface space, reducing the number of escaping solvent molecules.

  • General Rule: The partial vapour pressure of the solvent is $p_1 = x_1 p_1^0$.

Ideal and Non-Ideal Solutions

• Ideal Solutions: Obey Raoult’s law over the entire range of concentration.

  • Properties: $\Delta_{mix}H = 0$ and $\Delta_{mix}V = 0$.

  • Molecular Level: Intermolecular attractions A-B are nearly equal to A-A and B-B interactions.

  • Examples: n-hexane and n-heptane; bromoethane and chloroethane; benzene and toluene.

• Non-Ideal Solutions: Do not obey Raoult’s law.

  • Positive Deviation: $p_{total}$ is higher than predicted. A-B interactions are weaker than A-A or B-B. Molecules escape more easily.

  • Example: Ethanol and acetone (acetone breaks ethanol's hydrogen bonds).

  • Negative Deviation: $p_{total}$ is lower than predicted. A-B interactions are stronger than A-A or B-B.

  • Example: Phenol and aniline (intermolecular H-bonding between phenolic proton and aniline nitrogen); Chloroform and acetone.

• Azeotropes: Binary mixtures that have the same composition in liquid and vapour phase and boil at a constant temperature.

  • Minimum Boiling Azeotrope: Formed by solutions with large positive deviation (e.g., $95\%$ ethanol/water).

  • Maximum Boiling Azeotrope: Formed by solutions with large negative deviation (e.g., $68\%$ nitric acid and $32\%$ water).

Colligative Properties

Colligative properties depend only on the number of solute particles, not their nature.

1. Relative Lowering of Vapour Pressure

• The relative lowering is equal to the mole fraction of the solute: $\frac{p_1^0 - p_1}{p_1^0} = x_2$.

• For dilute solutions ($n_2 \ll n_1$): $\frac{p_1^0 - p_1}{p_1^0} = \frac{w_2 M_1}{M_2 w_1}$.

2. Elevation of Boiling Point ($\Delta T_b$)

• Defined as the increase in boiling point: $\Delta T_b = T_b - T_b^0$.

• Formula: $\Delta T_b = K_b m$.

• $K_b$ (Ebullioscopic Constant): Depend on the nature of the solvent. Unit: $K\,kg\,mol^{-1}$.

• Calculating Molar Mass ($M_2$): $M_2 = \frac{1000 \times K_b \times w_2}{\Delta T_b \times w_1}$.

3. Depression of Freezing Point ($\Delta T_f$)

• Freezing point is where the vapour pressure of liquid equals the vapour pressure of the solid phase.

• Formula: $\Delta T_f = K_f m$.

• $K_f$ (Cryoscopic Constant): Depend on the nature of the solvent. Unit: $K\,kg\,mol^{-1}$.

• Calculating Molar Mass ($M_2$): $M_2 = \frac{1000 \times K_f \times w_2}{\Delta T_f \times w_1}$.

• Thermodynamic relations for $K_b$ and $K_f$:

  • $K_f = \frac{R \times M_1 \times T_f^2}{1000 \times \Delta_{fus}H}$

  • $K_b = \frac{R \times M_1 \times T_b^2}{1000 \times \Delta_{vap}H}$

4. Osmosis and Osmotic Pressure ($\Pi$)

• Semipermeable Membrane (SPM): Allows only small solvent molecules (e.g., water) to pass through, hindering larger solute molecules.

• Osmosis: The flow of solvent from pure solvent to solution (or lower concentration to higher concentration) across an SPM.

• Osmotic Pressure: The excess pressure applied to the solution side to stop osmosis.

• Formula: $\Pi = CRT$

  • Since $C = n_2/V$, $\Pi V = \frac{w_2 RT}{M_2}$.

• Advantages: Pressure measurement is at room temperature; molarity is used; magnitude is large even for dilute solutions; suitable for biomolecules (proteins/polymers) sensitive to heat.

• Types of Solutions:

  • Isotonic: Same osmotic pressure. (e.g., $0.9\%\,w/V\,NaCl$ is isotonic with blood cells).

  • Hypertonic: Higher salt concentration than cell fluid; cells shrink.

  • Hypotonic: Lower salt concentration than cell fluid; cells swell.

• Reverse Osmosis: If applied pressure exceeds osmotic pressure, solvent flows from solution to solvent. Used in desalination of sea water using cellulose acetate membranes.

Abnormal Molar Masses and van’t Hoff Factor

• Abnormal Molar Mass: Experimentally determined molar mass that is different from the theoretical value due to association or dissociation.

  • Dissociation: Molecules split into ions (e.g., $KCl$). Particles increase, colligative properties increase, calculated molar mass decreases.

  • Association: Molecules combine (e.g., ethanoic acid dimers in benzene). Particles decrease, calculated molar mass increases.

• van’t Hoff Factor ($i$): Accounts for the extent of association/dissociation.

  • $i = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}}$

  • $i = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}}$

  • $i = \frac{\text{Total moles of particles after association/dissociation}}{\text{Moles of particles before}}$

• Modified Colligative Equations:

  • Relative lowering of VP: $\frac{p_1^0 - p_1}{p_1^0} = i \frac{n_2}{n_1}$

  • Elevation of BP: $\Delta T_b = i K_b m$

  • Depression of FP: $\Delta T_f = i K_f m$

  • Osmotic Pressure: $\Pi = i \frac{n_2 RT}{V}$

• Examples of $i$:

  • For $NaCl$, $KCl$, $MgSO_4$: $i$ approaches $2$ for complete dissociation.

  • For $K_2SO_4$: $i$ approaches $3$.

  • For ethanoic acid in benzene: $i$ is approximately $0.5$.

Questions & Discussion

• Intext Question 1.1: Calculate mass % of benzene and $CCl_4$ if $22\,g$ benzene is in $122\,g\,CCl_4$. (Answer: $15.28\%$, $84.72\%$).

• Intext Question 1.3: Calculate molarity for (a) $30\,g\,Co(NO_3)_2 \cdot 6H_2O$ in $4.3\,L$ and (b) $30\,mL$ of $0.5\,M\,H_2SO_4$ diluted to $500\,mL$. (Answer: $0.024\,M$, $0.03\,M$).

• Exercise 1.11: Why do gases always tend to be less soluble in liquids as temperature is raised? (Reason: Dissolution is exothermic; high T shifts equilibrium back to gas phase).

• Exercise 1.12: Scuba diving and "bends." To avoid nitrogen bubbles blocking capillaries, divers use air diluted with helium.

• Exercise 1.31: Arrange acetic acid, trichloroacetic acid, and trifluoroacetic acid in order of increasing FP depression. (Answer: Trifluoroacetic acid has highest dissociation due to electronegative F atoms, hence highest $i$ and highest $\Delta T_f$).

• Calculations involving Reverse Osmosis: Mentioned as a method for potable water requirement in many countries.

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