Ch 01 - Solutions12th Chemistry

A solution is a homogeneous mixture of two or more chemically non-reacting substances whose composition can vary within certain limits. The solvent is the component present in the largest quantity, determining the physical state of the solution. The solute is the component(s) present in lesser quantity. A binary solution consists of exactly two components.

Yes, solid solutions can have gas, liquid, or solid solutes dissolved in a solid solvent. Examples include the solution of hydrogen gas in palladium ($H_2$ in Pd), and an amalgam of mercury (liquid) with sodium (Na-Hg). Copper dissolved in gold is an example of a solid in solid solution.

Brass is a mixture of Copper (Cu) and Zinc (Zn). German Silver is a mixture of Copper (Cu), Zinc (Zn), and Nickel (Ni). Bronze is a mixture of Copper (Cu) and Tin (Sn).

Variables & Units:

• Mass of component = Measured in grams (g) or kg.
• Total mass of solution = Mass of solute + Mass of solvent (g or kg).

Conditions/Notes:

• Commonly used in industrial chemical applications (e.g., commercial bleaching solution is 3.62% sodium hypochlorite in water).

A liquid dissolved in a gas can be exemplified by Chloroform ($CHCl_3$) mixed with Nitrogen gas ($N_2$). A solid dissolved in a gas is demonstrated by Camphor vapours in Nitrogen gas ($N_2$).

Variables & Units:

• Volume of component = Measured in mL or L.
• Total volume of solution = Measured in mL or L.

Conditions/Notes:

• Mostly used for liquid-liquid solutions (e.g., 35% v/v ethylene glycol is used as an antifreeze in car engines).

Variables & Units:

• Parts = Can be measured in mass, volume, or moles, as long as numerator and denominator units match.

Conditions/Notes:

• Used exclusively when the solute is present in trace quantities (e.g., fluoride ions in water, pollutants in the air).

Variables & Units:

• $x_i$ = Mole fraction of component $i$ (unitless).
• $n_i$ = Number of moles of component $i$ (mol).
• $\sum n_i$ = Total moles of all components in the solution (mol).

Conditions/Notes:

• The sum of mole fractions of all components in a solution is always exactly 1 ($x_1 + x_2 + ... = 1$).
• Highly useful for relating physical properties (like vapour pressure) to concentration.

Variables & Units:

• Moles of solute = $n$ (mol)
• Volume of solution = $V$ (Liters or $dm^3$)
• M = Molarity ($mol \cdot L^{-1}$)

Conditions/Notes:

• Disadvantage: Molarity depends on volume, which expands/contracts with temperature. Hence, Molarity is temperature-dependent.

Variables & Units:

• Moles of solute = $n$ (mol)
• Mass of solvent = $W$ (kg)
• m = Molality ($mol \cdot kg^{-1}$)

Conditions/Notes:

• Crucial Note: The denominator is strictly the mass of the solvent, not the total solution.
• It is used heavily in colligative properties because it is independent of temperature.

• 1 ppm: Prevents tooth decay.
• 1.5 ppm: Causes teeth to become mottled.
• High Concentrations: Becomes highly poisonous (e.g., sodium fluoride is used in rat poison).

Bonus Fact: Intravenous injections are always dissolved in water containing salts at specific ionic concentrations that exactly match blood plasma concentrations.

Molarity, Volume Percentage (v/v), and Mass by Volume (w/v) are dependent on temperature. Molality, Mole Fraction, Mass Percentage (w/w), and ppm are independent of temperature. The reason is that volume changes due to thermal expansion or contraction, making volume-based terms sensitive to temperature. Mass-based terms remain constant regardless of temperature variations.

• Dynamic Equilibrium: Rate of dissolution (solute going into solution) = Rate of crystallization (solute separating out).
• Effect of Temperature: According to Le Chatelier's Principle, if dissolution is endothermic ($\Delta_{sol}H > 0$), solubility increases with temp. If exothermic ($\Delta_{sol}H < 0$), it decreases.
• Effect of Pressure: Pressure has no significant effect because solids and liquids are highly incompressible.

The guiding principle is that polar solutes dissolve in polar solvents, and non-polar solutes dissolve in non-polar solvents. Water is highly polar, while naphthalene and anthracene are non-polar organic solid compounds. Thus, they do not form strong interactions with water, but readily dissolve in benzene (a non-polar solvent) via London dispersion forces.

Variables & Units:

• $p_i$ = Partial vapour pressure of component $i$ in the solution.
• $p_i^0$ = Vapour pressure of the pure component $i$ at the same temperature.
• $x_i$ = Mole fraction of component $i$ in the liquid phase.

Conditions/Notes:

• The partial vapour pressure of each volatile component is directly proportional to its mole fraction in the solution.

Dissolving a gas in a liquid is similar to condensation, which is an exothermic process ($\Delta_{sol}H < 0$). By Le Chatelier's Principle, increasing the temperature of an exothermic equilibrium shifts the reaction backward. The gas escapes, and solubility decreases. (This is why aquatic species are more comfortable in cold water, which holds more dissolved oxygen).

Variables & Units:

• $p_{\text{total}}$ = Total vapour pressure of the solution.
• $p_1^0$, $p_2^0$ = Vapour pressures of pure components 1 and 2.
• $x_2$ = Mole fraction of component 2 in the liquid phase.

Conditions/Notes:

• This shows that the total vapour pressure over the solution varies linearly with the mole fraction of component 2.

At a given pressure, a higher $K_H$ value means lower solubility of the gas in the liquid, since $x = p / K_H$. For a given gas, $K_H$ increases with an increase in temperature. Therefore, as temperature rises, $K_H$ increases, driving the solubility ($x$) down.

1. Beverages: Soft drink bottles are sealed under high pressure to increase $CO_2$ solubility. 2. Scuba Diving (The Bends): Deep underwater, high pressure increases $N_2$ solubility in blood. Rapid ascent decreases pressure, causing $N_2$ bubbles that block capillaries. Tanks are diluted with Helium to prevent this. 3. High Altitudes (Anoxia): Lower atmospheric pressure at high altitudes leads to low oxygen solubility in the blood, causing weakness and confusion.

Variables & Units:

• $y_i$ = Mole fraction of component $i$ in the vapour phase.
• $p_i$ = Partial pressure of component $i$.
• $p_{\text{total}}$ = Total vapour pressure of the mixture.

Conditions/Notes:

• Derived directly from Dalton's law of partial pressures ($p_i = y_i \cdot p_{\text{total}}$).
• The vapour phase is always richer in the component which is more volatile.

Soft drink and soda water bottles are sealed under high pressure. According to Henry's Law, increasing the partial pressure of a gas above a liquid increases its solubility, thus forcing more $CO_2$ to dissolve in the beverage.

• Deep underwater: High pressure increases the solubility of atmospheric gases (like $N_2$) in the blood.
• Ascent: As the diver surfaces, pressure decreases rapidly, causing the dissolved $N_2$ to bubble out of the blood. This blocks capillaries, a painful and dangerous medical condition known as the bends (decompression sickness).
• Mitigation: Scuba tanks are diluted with Helium (which has very low solubility) to reduce the concentration of nitrogen.

At high altitudes, the partial pressure of oxygen in the atmosphere is much lower than at ground level. Consequently, the solubility of oxygen in the blood decreases. This leads to low concentrations of oxygen in the blood and tissues, causing weakness and loss of clear thinking, a condition known as anoxia.

In a pure liquid, the entire surface is occupied by volatile solvent molecules. When a non-volatile solute is added, solute particles take up part of the surface area. The fraction of the surface covered by solvent molecules reduces, leading to a decreased escaping tendency of the solvent into the vapour phase, thus lowering the overall vapour pressure.

Both laws state that the partial pressure of a volatile component is directly proportional to its mole fraction ($p \propto x$). Henry's Law is $p = K_H \cdot x$ and Raoult's Law is $p = p^0 \cdot x$. Raoult's law becomes a special case of Henry's law when the Henry's law constant ($K_H$) becomes numerically equal to the vapour pressure of the pure component ($p^0$).

Variables & Units:

• $p_1^0$ = Vapour pressure of the pure solvent
• $p_1$ = Vapour pressure of the solution
• $x_2$ = Mole fraction of the non-volatile solute
• $n_1$, $n_2$ = Moles of solvent and solute respectively.

Conditions/Notes:

• The term $(p_1^0 - p_1)$ is the lowering of vapour pressure.
• Dividing by $p_1^0$ gives the relative lowering, which equates precisely to the mole fraction of the solute.

This occurs when solute-solvent (A-B) interactions are weaker than the pure (A-A or B-B) interactions. Molecules escape more easily, causing the vapour pressure to be higher than predicted by Raoult's Law. Thermodynamically, $\Delta_{mix}H > 0$ and $\Delta_{mix}V > 0$. A mixture of ethanol and acetone is an example, where acetone breaks existing hydrogen bonds between ethanol molecules.

An ideal solution obeys Raoult's Law exactly over the entire range of concentrations.

Thermodynamic Conditions:

• $\Delta_{mix}H = 0$: Enthalpy of mixing is zero (no heat absorbed or released).
• $\Delta_{mix}V = 0$: Volume of mixing is zero.

Molecular Level: Intermolecular attractive forces between A-A and B-B are nearly equal to those between A-B.

Examples: n-hexane and n-heptane, benzene and toluene.

Variables & Units:

• $\Delta T_b$ = Elevation of boiling point ($T_b - T_b^0$) in Kelvin (K).
• $K_b$ = Boiling Point Elevation Constant or Ebullioscopic Constant ($K \cdot kg \cdot mol^{-1}$).
• $m$ = Molality of the solution ($mol \cdot kg^{-1}$).

Conditions/Notes:

• The property depends purely on the number of solute particles, strictly valid for dilute, ideal solutions.

• Cause: The solute-solvent (A-B) interactions are stronger than the pure (A-A or B-B) interactions.
• Result: Molecules are held tighter, decreasing the escaping tendency and causing vapour pressure to be lower than predicted by Raoult's law. $\Delta_{mix}H < 0$ and $\Delta_{mix}V < 0$.
• Examples:
  • Chloroform and acetone: They form new, strong hydrogen bonds with each other.
  • Phenol and Aniline: The intermolecular hydrogen bonding between the phenolic proton and the lone pair on the nitrogen atom of aniline is stronger than the respective hydrogen bonds in the pure liquids.

Variables & Units:

• $M_2$ = Molar mass of the solute ($g \cdot mol^{-1}$).
• $w_2$ = Mass of the solute (g).
• $w_1$ = Mass of the solvent (g).
• $K_b$ = Ebullioscopic constant ($K \cdot kg \cdot mol^{-1}$).
• $\Delta T_b$ = Elevation in boiling point (K).

A liquid boils when its vapour pressure equals the external atmospheric pressure. Adding a non-volatile solute lowers the vapour pressure of the solution. Therefore, the solution must be heated to a higher temperature than the pure solvent to make its vapour pressure reach atmospheric pressure, resulting in an elevation of the boiling point.

Azeotropes are binary liquid mixtures having the same composition in the liquid and vapour phase, boiling at a constant temperature. They cannot be separated by fractional distillation.

• Minimum Boiling Azeotrope: Formed by solutions showing a large positive deviation from Raoult's Law (e.g., 95% ethanol in water).
• Maximum Boiling Azeotrope: Formed by solutions showing a large negative deviation from Raoult's Law (e.g., 68% nitric acid in water).

Colligative properties are properties of a solution that depend only on the number of solute particles present, completely independent of their nature or chemical identity.

The four colligative properties are:

1. Relative lowering of vapour pressure
2. Elevation of boiling point
3. Depression of freezing point
4. Osmotic pressure

Variables & Units:

• $\Delta T_f$ = Depression in freezing point ($T_f^0 - T_f$) in Kelvin (K).
• $K_f$ = Freezing Point Depression Constant or Cryoscopic Constant ($K \cdot kg \cdot mol^{-1}$).
• $m$ = Molality of the solution ($mol \cdot kg^{-1}$).

Conditions/Notes:

• Heavily used in calculating molar masses and in anti-freeze applications (e.g., ethylene glycol in car radiators).

At the freezing point, the solid phase is in dynamic equilibrium with the liquid phase, meaning their vapour pressures are equal. Adding a non-volatile solute decreases the vapour pressure of the liquid solvent. The solution's vapour pressure curve will now intersect the solid solvent's vapour pressure curve at a lower temperature, causing freezing point depression.

Variables & Units:

• $M_2$ = Molar mass of the solute ($g \cdot mol^{-1}$).
• $w_2$ = Mass of the solute (g).
• $w_1$ = Mass of the solvent (g).
• $K_f$ = Cryoscopic constant ($K \cdot kg \cdot mol^{-1}$).
• $\Delta T_f$ = Depression in freezing point (K).

Variables & Units:

• R = Universal gas constant ($8.314 \; J \cdot K^{-1} \cdot mol^{-1}$)
• $M_1$ = Molar mass of the solvent ($g \cdot mol^{-1}$)
• $T_f$, $T_b$ = Freezing and boiling points of pure solvent (K)
• $\Delta_{fus}H$ = Enthalpy of fusion ($J \cdot mol^{-1}$)
• $\Delta_{vap}H$ = Enthalpy of vaporisation ($J \cdot mol^{-1}$)

Conditions/Notes:

• These formulas show that $K_f$ and $K_b$ depend exclusively on the physical properties of the pure solvent.

Osmosis is the spontaneous flow of solvent molecules through a semipermeable membrane (SPM). Solvent molecules flow from the pure solvent to the solution, or from a solution of lower concentration to a solution of higher concentration. An SPM (like cellophane or pig's bladder) allows small solvent molecules to pass but completely blocks larger solute molecules.

Variables & Units:

• $\Pi$ = Osmotic pressure (atm or bar)
• $C$ = Molar concentration / Molarity ($mol \cdot L^{-1}$)
• $R$ = Universal gas constant (usually $0.0821 \; L \cdot atm \cdot K^{-1} \cdot mol^{-1}$ or $0.08314 \; L \cdot bar \cdot K^{-1} \cdot mol^{-1}$)
• $T$ = Absolute temperature (K)

Conditions/Notes:

• Since $C = n_2 / V$, the formula can also be written as $\Pi V = n_2 R T$.

Osmotic pressure ($\Pi$) is the excess pressure that must be applied to the solution side to just prevent the passage of solvent molecules through the semipermeable membrane. It is considered a colligative property because its magnitude depends entirely on the number of solute particles present in a given volume, completely independent of their chemical identity.

1. Isotonic: Solutions with the same osmotic pressure; no net osmosis occurs (e.g., 0.9% w/v NaCl is isotonic with fluid inside blood cells). 2. Hypertonic: A solution with a higher osmotic pressure (> 0.9% NaCl). Cells placed in it will lose water and shrink (plasmolysis). 3. Hypotonic: A solution with a lower osmotic pressure (< 0.9% NaCl). Cells placed in it will gain water and swell or burst.

Additional Relation:

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

Conditions/Notes:

• $i = 1$: Neither association nor dissociation (e.g., glucose, urea).
• $i > 1$: Dissociation (e.g., $NaCl$, $K_2SO_4$).
• $i < 1$: Association (e.g., acetic acid in benzene).

Modified Formulas:

1. Relative Lowering of VP: $\frac{p_1^0 - p_1}{p_1^0} = i \cdot \frac{n_2}{n_1}$
2. Elevation of BP: $\Delta T_b = i \cdot K_b \cdot m$
3. Depression of FP: $\Delta T_f = i \cdot K_f \cdot m$
4. Osmotic Pressure: $\Pi = i \cdot \frac{n_2}{V} R T$

Conditions/Notes:

• These must be used for any electrolyte or solute that associates/dissociates in the given solvent.

1. Room Temperature: It is measured at room temperature, crucial because biomolecules (like proteins) are unstable at higher temperatures.
2. Molarity: It uses Molarity instead of molality, which is practically easier to measure for polymers. 3. Large Magnitude: Even for very dilute solutions (which polymers often form due to poor solubility), the magnitude of osmotic pressure is significantly large and easy to accurately measure.

Colligative properties strictly depend on the number of particles.
Dissociation: Ionic compounds (like $KCl$) split into ions. The number of particles doubles, doubling the colligative effect. The calculated molar mass will be lower than the true value. Association: Molecules (like ethanoic acid in benzene) form dimers via hydrogen bonding. The number of particles halves, halving the colligative effect. The calculated molar mass will be higher than the true value.

• Edema: People consuming high amounts of salt experience water retention in tissue cells and intercellular spaces due to osmosis. This resulting puffiness or swelling is called edema.
• Meat Preservation: Salting creates a hypertonic environment. Bacteria on the meat lose water via osmosis, shrivel, and die, protecting the food from bacterial action.

• Definition: If a pressure larger than the osmotic pressure is applied to the solution side, the pure solvent flows out of the solution through the SPM (reversing the natural direction of osmosis).
• Application: Desalination of sea water. High pressure forces pure water out of salty sea water through a polymer membrane (like cellulose acetate).

Definition: It is the mass of the solute (in grams) dissolved in exactly 100 mL of the solution.

Application: This unit is primarily used in the medicine and pharmacy industries.

• Reason: The intermolecular hydrogen bonding between the phenolic proton (from Phenol) and the lone pair on the nitrogen atom (of Aniline) is stronger than the respective hydrogen bonds in pure phenol or pure aniline.
• Result: This stronger A-B interaction significantly decreases the escaping tendency of the molecules, lowering the overall vapour pressure.

Variables:

• $\alpha$ = Degree of dissociation (fraction of total molecules that dissociate)
• $i$ = Van't Hoff factor (Observed / Calculated property)
• $n$ = Total number of ions produced per formula unit (e.g., for $BaCl_2$, $n=3$)

Conditions/Notes:

• Strictly used when an electrolyte partially dissociates (weak acids/bases).
• Often combined with Ostwald's dilution law ($K_a = \frac{c\alpha^2}{1-\alpha}$) to find the dissociation constant.

Variables:

• $\alpha$ = Degree of association (fraction of total molecules that associate)
• $i$ = Van't Hoff factor
• $n$ = Number of molecules associating together (e.g., for a dimer, $n=2$; for a trimer, $n=3$)

Conditions/Notes:

• Used when organic molecules hydrogen-bond in non-polar solvents (e.g., acetic acid forming dimers in benzene).