Top 50 Most Important
Subjective Questions
Solutions. Master Concentration terms, Raoult's Law, Colligative Properties, and the van't Hoff Factor.
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Concentration Terms
A solution is a homogeneous mixture of two or more chemically non-reacting substances whose composition can be varied within certain limits. Its components are the solvent (the component present in the largest quantity, determining the physical state) and the solute (the component present in a lesser quantity).
Molarity ($M$): The number of moles of solute dissolved per liter (or $dm^3$) of the solution. It is temperature-dependent.
Molality ($m$): The number of moles of solute dissolved per kilogram ($1000 \text{ g}$) of the solvent. It is temperature-independent.
Molality is based on the mass of the solvent, and mass does not change with temperature. Molarity is based on the volume of the solution, which expands or contracts with changes in temperature. Therefore, molality remains constant over varying temperatures, making it a more reliable unit.
The mole fraction of a component in a mixture is the ratio of the number of moles of that component to the total number of moles of all components in the mixture.
$x_A = \frac{n_A}{n_A + n_B}$.
It is a dimensionless quantity (a pure ratio) and has no unit. The sum of mole fractions of all components is always 1.
Parts per million ($ppm$) is defined as the parts of a component per million parts ($10^6$) of the solution.
$ppm = \left( \frac{\text{Mass of component}}{\text{Total mass of solution}} \right) \times 10^6$.
It is used exclusively to express the concentration of a solute that is present in trace quantities, such as pollutants in air or water.
Molarity and Molality are nearly equal for very dilute aqueous solutions. In a highly dilute solution, the mass of the solute is negligible, and the density of the solution is approximately $1 \text{ g/mL}$ (same as pure water). Thus, 1 Liter of solution weighs approximately 1 kg, making the denominators equivalent.
It signifies that $10 \text{ grams}$ of glucose is dissolved in $90 \text{ grams}$ of water, resulting in a total solution mass of $100 \text{ grams}$.
No. Mass percentage is a ratio of masses. Since mass is an intrinsic property of matter that does not change with temperature, mass percentage is completely temperature-independent.
Normality is defined as the number of gram equivalents of the solute dissolved per liter of the solution.
$N = \frac{\text{Mass of solute}}{\text{Equivalent mass of solute} \times \text{Volume of solution (L)}}$.
Like molarity, it is temperature-dependent.
When a solution is diluted by adding more solvent, its volume increases while the number of moles of solute remains strictly constant. Since Molarity = Moles / Volume, an increase in the denominator (volume) causes the molarity to decrease.
Solubility & Henry's Law
Solubility is defined as the maximum amount of a solute that can be dissolved in a specified amount of solvent (usually $100 \text{ g}$) at a strictly constant temperature and pressure to form a saturated solution.
It means that a solute will dissolve in a solvent if they have similar intermolecular forces. Polar solutes (like $NaCl$) dissolve in polar solvents (like water) due to ion-dipole interactions. Non-polar solutes (like naphthalene) dissolve in non-polar solvents (like benzene) due to similar London dispersion forces.
According to Le Chatelier's Principle:
1. If the dissolution process is endothermic ($\Delta_{sol} H > 0$), the solubility increases with a rise in temperature (e.g., $KNO_3$ in water).
2. If the dissolution process is exothermic ($\Delta_{sol} H < 0$), the solubility decreases with a rise in temperature (e.g., $Li_2CO_3$ in water).
The dissolution of a gas in a liquid is an inherently exothermic process ($\Delta H < 0$) because gas molecules lose kinetic energy when entering the liquid phase. According to Le Chatelier's Principle, increasing the temperature of an exothermic equilibrium shifts it backward, driving the gas out of the solution.
Henry's Law: $p = K_H \cdot x$
Where $p$ = partial pressure of gas, $x$ = mole fraction of gas in solution, and $K_H$ = Henry's law constant.
Significance: At a given pressure, the higher the value of $K_H$, the lower the solubility of the gas in the liquid.
The solubility of gases (like dissolved oxygen) in water decreases with an increase in temperature. In cold water, there is a significantly higher concentration of dissolved oxygen available, making respiration easier and life more comfortable for aquatic species.
According to Henry's Law, the solubility of a gas in a liquid is directly proportional to its partial pressure above the liquid surface. Sealing bottles of soft drinks under high pressure ensures a large amount of $CO_2$ remains dissolved, giving the drink its characteristic fizz.
At high depths (high pressure), extra nitrogen dissolves in a diver's blood. As they ascend (pressure decreases), this nitrogen suddenly bubbles out, blocking capillaries—a painful and dangerous condition called "the bends" (decompression sickness).
Prevention: Scuba tanks are diluted with Helium (which has very low solubility in blood) to minimize nitrogen uptake.
Anoxia is a medical condition characterized by a severe lack of oxygen in blood and tissues, causing weakness and inability to think clearly. At high altitudes, the partial pressure of oxygen is much lower than at ground level. According to Henry's law, this leads to a dangerously low concentration of dissolved oxygen in the blood of climbers.
Yes. The Henry's Law constant ($K_H$) is not a universal constant. It depends entirely on the chemical nature of the gas, the chemical nature of the solvent, and the temperature. Different gases in the same solvent at the same temperature have vastly different $K_H$ values.
Raoult's Law & Azeotropes
Vapor pressure is the pressure exerted by the vapors of a liquid in thermodynamic equilibrium with its condensed (liquid) phase at a given temperature in a closed system.
Raoult's Law states that for a solution of volatile liquids, the partial vapor pressure of each component in the solution is directly proportional to its mole fraction present in solution.
$p_1 = p_1^0 \cdot x_1$
Where $p_1^0$ is the vapor pressure of the pure component.
According to Raoult's law, $p = p^0 x$. According to Henry's law, $p = K_H x$. If the volatile component is a gas dissolving in a liquid, its behavior is identical in both formulas. Raoult's law becomes a special case of Henry's law when the proportionality constant $K_H$ happens to equal the vapor pressure of the pure state ($p^0$).
- It strictly obeys Raoult's Law over the entire range of concentration ($p_{total} = p_1 + p_2$).
- Enthalpy of mixing is zero ($\Delta_{mix}H = 0$). No heat is absorbed or evolved.
- Volume of mixing is zero ($\Delta_{mix}V = 0$).
- The A-B intermolecular interactions are perfectly identical in strength to A-A and B-B interactions.
Occurs when the newly formed A-B interactions are weaker than the pure A-A and B-B interactions. Molecules escape more easily, causing vapor pressure to be higher than expected by Raoult's law. $\Delta_{mix}H > 0$ and $\Delta_{mix}V > 0$.
Example: Ethanol + Acetone. Acetone breaks the strong hydrogen bonds of ethanol, weakening overall forces.
Occurs when the newly formed A-B interactions are stronger than the pure A-A and B-B interactions. Molecules are held tighter, causing vapor pressure to be lower than expected. $\Delta_{mix}H < 0$ and $\Delta_{mix}V < 0$.
Example: Chloroform + Acetone. A new, strong hydrogen bond forms between the two, limiting vaporization.
Azeotropes are binary mixtures of liquids that have the exact same composition in liquid and vapor phase. Consequently, they boil at a single, constant temperature like a pure liquid. Because the vapor composition matches the liquid, they cannot be separated by fractional distillation.
Solutions showing a large positive deviation from Raoult's law form minimum boiling azeotropes at a specific composition. Their combined vapor pressure is so high that the mixture boils at a temperature lower than either pure component. (e.g., $95.5\%$ Ethanol in water).
Solutions showing a large negative deviation from Raoult's law form maximum boiling azeotropes. Because strong bonds hold the molecules down, the vapor pressure drops severely, forcing the mixture to boil at a temperature higher than either pure component. (e.g., $68\%$ Nitric acid in water).
When a non-volatile solute is added to a volatile solvent, the vapor pressure of the solution is entirely due to the solvent. Thus, the relative lowering of the vapor pressure of the solution is exactly equal to the mole fraction of the non-volatile solute.
Colligative Properties (RLVP, BP, FP)
Colligative properties are properties of dilute solutions that depend strictly on the number of solute particles (moles, molecules, or ions) present in a given volume of solvent, and NOT on the chemical nature, shape, or identity of the solute.
In a pure liquid, the entire surface is occupied by volatile solvent molecules. When a non-volatile solute is added, a fraction of the surface area is blocked by non-volatile solute particles. This directly reduces the number of solvent molecules escaping into the vapor phase, lowering the total vapor pressure.
The RLVP is equal to the mole fraction of the solute ($x_2$).
$\frac{p_1^0 - p_1}{p_1^0} = x_2 = \frac{n_2}{n_1 + n_2}$
For very dilute solutions, $n_1 \gg n_2$, so it approximates to $\frac{n_2}{n_1}$.
A liquid boils when its vapor pressure equals atmospheric pressure. Because adding a non-volatile solute lowers the vapor pressure, the solution must now be heated to a higher temperature for its vapor pressure to catch up to atmospheric pressure. Thus, boiling point elevates.
The Ebullioscopic constant (Molal elevation constant) is defined as the elevation in boiling point produced when 1 mole of a non-volatile solute is dissolved in $1 \text{ kg}$ of solvent (i.e., when molality = 1).
Unit: $\text{K kg mol}^{-1}$.
For a dilute solution, the elevation of boiling point ($\Delta T_b$) is directly proportional to the molal concentration ($m$) of the solute.
$\Delta T_b = K_b \cdot m \quad \text{where } m = \frac{W_2 \times 1000}{M_2 \times W_1}$
Freezing occurs when the vapor pressure of the liquid phase equals the vapor pressure of the solid phase. Because a solute lowers the vapor pressure of the liquid, the liquid-vapor pressure curve intersects the solid-vapor pressure curve at a lower temperature. Thus, the solution freezes at a depressed temperature.
The Cryoscopic constant (Molal depression constant) is the depression in freezing point observed when 1 mole of solute is dissolved in $1 \text{ kg}$ of solvent. $\Delta T_f = K_f \cdot m$.
$K_f$ depends exclusively on the nature of the solvent (like its heat of fusion), not on the solute.
Ethylene glycol acts as an anti-freeze. By utilizing the principle of depression of freezing point, adding it to water lowers the freezing point below $0^\circ\text{C}$, preventing the radiator water from freezing and bursting the engine pipes in cold winter climates.
Osmotic Pressure is strictly preferred.
Reasons: 1. It provides a measurable large magnitude even for very dilute solutions of massive polymers. 2. It is measured at room temperature, which prevents biomolecules (like proteins) from denaturing (which would happen at elevated boiling points).
Osmotic Pressure & van't Hoff Factor
Osmosis: The spontaneous flow of only solvent molecules through a Semi-Permeable Membrane (SPM) from a region of lower solute concentration to higher solute concentration.
Diffusion: The movement of both solute and solvent molecules from their respective regions of higher concentration to lower concentration. No SPM is required.
Osmotic pressure is the excess external mechanical pressure that must be applied to the solution side (the side with higher concentration) to just stop the process of osmosis (the influx of solvent across the SPM).
Formula: $\pi = C R T$ (where C is Molarity).
Two solutions having the exact same osmotic pressure at a given temperature are called isotonic. When separated by a semi-permeable membrane, no net osmosis occurs between them. This implies they have the same molar concentration ($\pi_1 = \pi_2 \implies C_1 = C_2$).
- Hypertonic (High salt): Water flows out of the RBCs into the solution via osmosis. The cells shrink (plasmolysis).
- Hypotonic (Low salt/pure water): Water flows into the RBCs. The cells swell and may eventually burst (hemolysis).
If a pressure greater than the osmotic pressure is applied to the solution side, the direction of osmosis is reversed. Pure solvent is forced out of the solution through the SPM into the pure solvent side.
Application: Desalination of seawater to obtain pure drinking water.
Abnormal molar mass occurs when the solute undergoes either dissociation (splitting into ions, e.g., $NaCl$) or association (joining of molecules, e.g., Acetic acid in benzene) in the solution. This changes the total number of particles, altering the colligative properties and leading to a calculated molar mass that is lower (dissociation) or higher (association) than the actual value.
The van't Hoff factor ($i$) corrects for abnormal molar masses. It is defined as the ratio of the observed (experimental) colligative property to the normal (calculated) colligative property.
$i = \frac{\text{Normal Molar Mass}}{\text{Abnormal Molar Mass}} = \frac{\text{Observed Colligative Property}}{\text{Calculated Colligative Property}}$
- For Dissociation (e.g., $NaCl, KCl$): $i > 1$ (particles increase).
- For Association (e.g., Acetic acid in benzene): $i < 1$ (particles decrease).
- For Non-electrolytes (e.g., Glucose, Urea): $i = 1$ (no change in particles).
For a solute undergoing dissociation into '$n$' ions per molecule:
$\alpha = \frac{i - 1}{n - 1}$
For example, for $BaCl_2 \rightarrow Ba^{2+} + 2Cl^-$, $n = 3$.
For a solute undergoing association where '$n$' molecules associate to form a single macromolecule (e.g., $n=2$ for a dimer):
$\alpha = \frac{1 - i}{1 - \frac{1}{n}}$
For example, Acetic acid forms a dimer in benzene, so $n = 2$.
Chapter 1 Mastered!
You have just conquered the 50 most critical subjective questions for Class 12 Chemistry, Chapter 1: Solutions. You are fully equipped for your Board Exams.
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