Introduction
In chemistry, a solution is a homogeneous mixture composed of two or more substances. In a solution, a solute is dissolved in a solvent. The study of solutions is crucial for understanding various chemical processes and reactions. This document will cover the fundamental concepts of solutions, their properties, and the calculations associated with them as per the JEE Main Chemistry syllabus.
Components of a Solution
Solute and Solvent
- Solute: The substance that is dissolved in a solution. It is usually present in a smaller amount.
- Solvent: The substance in which the solute is dissolved. It is usually present in a larger amount.
For example, in a saltwater solution, salt (NaCl) is the solute, and water (H₂O) is the solvent.
Types of Solutions
Based on the Physical State
- Gaseous Solutions: Both solute and solvent are in the gaseous state.
- Example: Air (O₂ in N₂)
- Liquid Solutions: Solute can be a gas, liquid, or solid, and the solvent is in the liquid state.
- Example: Carbonated water (CO₂ in H₂O)
- Solid Solutions: Both solute and solvent are in the solid state.
- Example: Alloys (Brass, which is Cu and Zn)
Based on Concentration
- Dilute Solution: Contains a small amount of solute relative to the solvent.
- Concentrated Solution: Contains a large amount of solute relative to the solvent.
- Saturated Solution: Contains the maximum amount of solute that can dissolve at a given temperature.
- Unsaturated Solution: Can dissolve more solute at a given temperature.
- Supersaturated Solution: Contains more solute than can theoretically dissolve at a given temperature.
Concentration Terms
Molarity (M)
Molarity is defined as the number of moles of solute per liter of solution. $$ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} $$
If 2 moles of NaCl are dissolved in 1 liter of water, the molarity of the solution is: $$ M = \frac{2 \text{ moles}}{1 \text{ liter}} = 2 \text{ M} $$
Molality (m)
Molality is defined as the number of moles of solute per kilogram of solvent. $$ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} $$
Molality is temperature-independent because it is based on the mass of the solvent.
Normality (N)
Normality is defined as the number of gram equivalents of solute per liter of solution. $$ N = \frac{\text{gram equivalents of solute}}{\text{volume of solution in liters}} $$
Mole Fraction (χ)
Mole fraction is the ratio of the number of moles of a component to the total number of moles of all components in the solution. $$ \chi_A = \frac{\text{moles of component A}}{\text{total moles of all components}} $$
Mass Percent
Mass percent is the mass of the solute divided by the total mass of the solution, multiplied by 100. $$ \text{Mass Percent} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100 $$
Parts per Million (ppm)
Parts per million is a way of expressing very dilute concentrations of substances. It is the number of parts of solute per million parts of the solution. $$ \text{ppm} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 10^6 $$
Confusing molarity with molality. Remember, molarity is per liter of solution, while molality is per kilogram of solvent.
Colligative Properties
Colligative properties depend on the number of solute particles in a solution, not on the nature of the solute. These include:
Relative Lowering of Vapor Pressure
The vapor pressure of a solvent decreases when a non-volatile solute is added. $$ \frac{\Delta P}{P_0} = \chi_B $$ where $\Delta P$ is the lowering of vapor pressure, $P_0$ is the vapor pressure of the pure solvent, and $\chi_B$ is the mole fraction of the solute.
Boiling Point Elevation
The boiling point of a solution is higher than that of the pure solvent. $$ \Delta T_b = K_b \cdot m $$ where $\Delta T_b$ is the elevation in boiling point, $K_b$ is the ebullioscopic constant, and $m$ is the molality.
Freezing Point Depression
The freezing point of a solution is lower than that of the pure solvent. $$ \Delta T_f = K_f \cdot m $$ where $\Delta T_f$ is the depression in freezing point, $K_f$ is the cryoscopic constant, and $m$ is the molality.
Osmotic Pressure
Osmotic pressure is the pressure required to stop the flow of solvent into the solution through a semipermeable membrane. $$ \Pi = MRT $$ where $\Pi$ is the osmotic pressure, $M$ is the molarity, $R$ is the gas constant, and $T$ is the temperature in Kelvin.
Use colligative properties to determine molar masses of solutes by measuring changes in boiling point, freezing point, or osmotic pressure.
Raoult's Law
Raoult's Law states that the partial vapor pressure of each volatile component in a solution is directly proportional to its mole fraction. $$ P_A = \chi_A P_A^0 $$ where $P_A$ is the partial vapor pressure of component A, $\chi_A$ is the mole fraction of A, and $P_A^0$ is the vapor pressure of pure A.
If the vapor pressure of pure water at 25°C is 23.8 mm Hg and the mole fraction of water in a solution is 0.9, then the vapor pressure of water in the solution is: $$ P_{\text{H}_2\text{O}} = 0.9 \times 23.8 \text{ mm Hg} = 21.42 \text{ mm Hg} $$
Ideal and Non-Ideal Solutions
Ideal Solutions
Ideal solutions obey Raoult's Law over the entire range of concentration. The enthalpy change of mixing is zero, and the volume change of mixing is also zero.
Non-Ideal Solutions
Non-ideal solutions do not obey Raoult's Law. They exhibit either positive or negative deviations.
- Positive Deviation: The vapor pressure is higher than predicted by Raoult's Law.
- Negative Deviation: The vapor pressure is lower than predicted by Raoult's Law.
Non-ideal behavior is often due to differences in intermolecular forces between solute and solvent molecules.
Henry's Law
Henry's Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. $$ C = k_H P $$ where $C$ is the concentration of the gas, $k_H$ is Henry's law constant, and $P$ is the partial pressure of the gas.
If the Henry's law constant for CO₂ in water at 25°C is 3.3 × 10⁻² mol/L·atm, and the partial pressure of CO₂ is 1 atm, the solubility of CO₂ is: $$ C = 3.3 \times 10^{-2} \text{ mol/L·atm} \times 1 \text{ atm} = 3.3 \times 10^{-2} \text{ mol/L} $$
Conclusion
Understanding the properties and behavior of solutions is essential for solving various problems in chemistry. This comprehensive study note has covered the key concepts, including types of solutions, concentration terms, colligative properties, Raoult's Law, and Henry's Law. Mastery of these topics will provide a strong foundation for tackling solution-related questions in the JEE Main Chemistry exam.
Practice solving numerical problems related to molarity, molality, and colligative properties to strengthen your understanding and speed.
