SOLUTIONS in 2 Hours || BEST for Class 12th Boards || Pure English

A solution is defined as a homogeneous mixture where the solute completely dissolves into a single solvent, ensuring no layers are formed. The concept is illustrated using lemonade, where water acts as the singular solvent and sugar or salt serve as one or more solutes. This explanation emphasizes that every solution maintains one solvent while accommodating multiple solutes, a fundamental aspect of classifying solutions.

Naming Conventions in Multi-Component Solutions Solutions are classified by their components: a binary solution combines one solute and one solvent, a ternary solution includes one solvent with two solutes, and a quaternary solution consists of one solvent with three solutes. The classification underscores that increasing the solute count defines each distinct type. The default assumption remains a binary solution whenever specifics are not provided.

Diverse Expressions of Concentration in Chemical Solutions Concentration quantifies the amount of solute dissolved in a solvent and can be expressed in varied units such as grams, moles, or kilograms, much like height measured in different units. The solvent provides the necessary medium while the solute determines the solution’s reactive properties and taste. Expressing the same concentration in multiple forms highlights the consistency in measurement. Molarity, denoted by a capital 'M', stands as a foundational method for determining concentration.

Fundamentals of Molarity Molarity quantifies the number of moles of solute present in one liter of solution. A solution containing one mole of solute per liter is described as 1 molar, while two moles per liter forms a 2 molar solution. The concept is mathematically expressed by dividing the moles of solute by the solution's volume in liters.

Practical Application of Molarity in Calculations A three molar NaOH solution indicates the presence of three moles of the solute in each liter, which leads to the calculation of its mass using the molar mass of 40 grams per mole, resulting in 120 grams. The method demonstrates how molarity can be used to deduce the mass of solute in a given volume of solution. It also lays the groundwork for tackling problems that include additional factors such as density.

Defining Molality and Its Distinction from Molarity Molality focuses on the ratio of moles of solute to one kilogram of solvent, setting it apart from molarity which uses the total solution volume. By considering only the mass of the solvent, the measurement becomes independent of temperature-related volume changes. The calculation is performed by dividing the moles of solute by the mass of solvent expressed in kilograms.

Understanding Mass by Volume Percentage Mass by volume percentage represents the grams of solute found in 100 milliliters of solution. For instance, if a solution contains 50 grams of solute in 500 milliliters, unitary conversion shows that 10 grams are present per 100 milliliters. This measurement is determined by multiplying the ratio of the solute's mass to the solution's volume (in mL) by 100.

Calculating Mass by Mass and Volume by Volume Percentages Mass by mass percentage is calculated by dividing the solute's mass by the total mass of the solution and multiplying by 100 to express it per 100 grams. Volume by volume percentage similarly measures the milliliters of solute per 100 milliliters of solution. These concise formulas allow for straightforward determination of concentration when mass or volume data is readily available.

Leveraging Mole Fraction in Solution Analysis Mole fraction is defined as the ratio of the moles of one component to the total moles present in a mixture. It is calculated by dividing the moles of a specific substance by the sum of the moles of all constituents, ensuring the combined fractions sum to one. This approach permits the precise analysis of component proportions and facilitates the determination of unknown concentrations in a mixture.

Interpreting Parts Per Million in Dilute Solutions Parts per million (ppm) expresses extremely low concentrations by scaling the mass ratio to one million parts. It is calculated by taking the mass of the solute, dividing it by the mass of the solution, and then multiplying by 10^6. For example, 3 ppm signifies that 3 grams of solute are present in 1,000,000 grams of solution, offering clarity in cases of trace concentrations.

Vapor Pressure as Equilibrium in Sealed Systems Imagine heating water in a sealed bowl where vapor cannot escape into the atmosphere. As the water heats, energized molecules leave the liquid to form vapor that continuously collides with the container walls. A balance is reached when the number of molecules escaping equals the number returning, establishing a constant maximum pressure unique to that temperature.

Molecular Forces Driving Evaporation Within a liquid, molecules in the bulk experience equal forces from all directions, ensuring stability and minimal energy. In contrast, surface molecules lack an upward counter force, making them energetically unbalanced and more likely to escape. This unbalanced force at the boundary propels the molecules into the vapor phase, where their collisions with the container create measurable pressure.

Saturation and Temperature Dependence Equilibrium is attained when evaporation and condensation occur at equal rates, resulting in a saturated vapor state. At this point, the vapor pressure remains constant for a specific temperature regardless of container size or liquid amount. The pressure relies solely on the liquid's nature and the prevailing temperature, increasing as the temperature rises.

Raoult’s Law and Vapor Pressure in Mixtures Mixing two volatile liquids leads each component to contribute a partial vapor pressure that is lower than its pure form. The mutual interference between different molecules reduces each substance’s ability to escape into the vapor phase. The total vapor pressure of the solution is the sum of these diminished partial pressures, exemplifying the principles of Raoult’s Law.

Mole Fractions Govern Partial Vapor Pressures Raoult’s law establishes that each component’s vapor pressure in a mixture is proportional to its mole fraction. The vapor pressure of a volatile solvent or solute is determined by multiplying its pure vapor pressure by its mole fraction. The overall pressure results from the sum of these partial contributions in the liquid phase.

Deriving Vapor Pressure Equations from Fundamental Laws Each component’s partial pressure is expressed as the product of its pure vapor pressure and its mole fraction, forming the equations pₐ = pₐ⁰xₐ and pᵦ = pᵦ⁰xᵦ. Their sum gives the total vapor pressure of the solution. Dalton’s law then relates the vapor-phase composition to these pressures, confirming the consistency between liquid and vapor mole fractions.

Volatility Variations Shape Vapor Pressure Contributions Components with higher volatility possess greater pure vapor pressures, thus contributing more significantly when present in higher mole fractions. The differential vapor pressures reflect the inherent nature of each substance under identical temperature conditions. This variation in volatility outlines the dynamic behavior of mixed volatile systems.

Non-Volatile Solutes Reduce Overall Vapor Pressure Adding a non-volatile solute, whose intrinsic vapor pressure is zero, diminishes the solvent’s ability to contribute to the overall vapor pressure. The solute occupies surface positions that the volatile solvent would otherwise occupy, limiting the number of solvent molecules transitioning into the vapor phase. As a result, the mixture exhibits a vapor pressure lower than that of the pure volatile component.

Quantitative Relationship in Vapor Pressure Lowering The decrease in vapor pressure is quantified by subtracting the solution’s vapor pressure from that of the pure solvent, expressed as pₐ⁰(1 - xₐ) or equivalently pₐ⁰xᵦ. This relationship directly ties the pressure lowering to the mole fraction of the non-volatile solute. It emphasizes that while the solvent’s nature influences the absolute pressure, the change is driven solely by the solute concentration.

Solute-Driven Vapor Pressure Reduction Vapor pressure reduction is determined by the formula delta p = p°(moles of solute)/(moles of solvent + moles of solute), where p° reflects the solvent’s inherent property. The decrease in vapor pressure depends solely on the number of non-volatile solute particles, making it a colligative property with respect to the solute. This highlights that while the solvent’s intrinsic vapor pressure matters, the lowering effect itself is governed by particle count rather than particle identity.

Dual Colligative Nature of Relative Vapor Pressure Lowering Normalizing the vapor pressure drop by p° yields delta p/p°, which equals the mole fraction of the solute and therefore depends strictly on the ratio of solute to solvent molecules. This relative measure disregards the chemical nature of both components, establishing it as a colligative property for both solute and solvent. The approach emphasizes that the effect arises purely from particle numbers, offering a more comprehensive insight into solution behavior.

High Pressure Locks CO2 in Sealed Beverages Sealed carbonated drinks utilize high pressure to dissolve CO2 in the liquid, ensuring a zesty taste and lively fizz. When the container opens and atmospheric pressure takes over, the dissolved gas escapes, leaving behind a flat, flavorless liquid. This behavior vividly demonstrates that pressure is key to maintaining gas solubility in liquids.

Henry’s Law Quantifies Pressure–Solubility Balance Henry’s law establishes a direct proportionality between a gas’s partial pressure and its solubility, expressed as P = kH × (mole fraction of gas). An increase in pressure forces more gas into solution, while the proportionality constant kH remains unaffected by pressure changes. Under constant atmospheric conditions, a higher kH indicates a lower dissolved gas concentration, ensuring the product of kH and solubility remains constant.

Temperature and Molecular Interactions Modulate Solubility The Henry’s constant, kH, is sensitive to temperature, the nature of the gas, and the solvent, though it does not depend on pressure. As temperature increases, kH rises and gas solubility correspondingly declines, altering the balance in the system. Additionally, gases with stronger intermolecular forces (indicated by a higher van der Waals constant) are more easily liquefied, resulting in a lower kH and enhanced solubility.

Ideal Solutions: Equal Interactions and Zero Mixing Energetics In an ideal solution, the intermolecular attractions between like and unlike molecules are equivalent, ensuring conformity to Raoult’s law. The energy required to break the original bonds exactly matches the energy released during the formation of new bonds, resulting in a net enthalpy change of zero. The total volume remains unaffected as the individual volumes simply add up without contraction or expansion. Although highly dilute solutions may approximate this behavior, perfect ideality is never fully realized in real systems.

Mixing Randomness: Entropy as the Engine of Spontaneity Mixing two distinct substances introduces significant randomness, as particles become intermingled in unpredictable arrangements. This increase in disorder leads to a positive change in entropy, making the mixing process spontaneously favorable. The inherent drive toward a more probabilistic state compensates for the absence of energy and volume changes in an ideal mixture. Enhanced entropy is the underlying force that propels the spontaneous transition from order to disorder during mixing.

Understanding Ideal Solutions and Deviations Raoult's law describes an ideal solution where a component’s vapor pressure is proportional to its mole fraction, as seen in examples like benzene-toluene and n-hexane/n-heptane mixtures. Ideal solutions follow predictable behavior when intermolecular interactions are unchanged by mixing. Deviations occur when the interactions in the solution differ from those in the pure components. Recognizing these differences sets the stage for exploring both positive and negative deviations.

Positive Deviation from Ideal Behavior When the interactions between unlike molecules become weaker compared to the pure components, molecules escape more readily, resulting in a vapor pressure higher than predicted by Raoult's law. This phenomenon is known as positive deviation, where the measured pressure exceeds the ideal value. The mixing process in such cases absorbs energy, giving rise to a positive enthalpy change and an increased volume. Despite the energy dynamics, the randomness of mixing ensures a positive change in entropy, which is reflected in graphical plots showing elevated total pressure.

Negative Deviation Due to Stronger Interactions Stronger attractions between different molecules cause them to stay closer together, lowering the vapor pressure below that predicted for an ideal solution. This effect, known as negative deviation, emerges because the enhanced interactions reduce the tendency of molecules to escape into the vapor phase. The process releases energy, resulting in a negative enthalpy change and a contracted final volume compared to the initial state. Graphical analysis confirms this behavior by showing a total pressure that falls under the ideal solution curve while entropy continues to rise due to increased randomness.

Graphical Insights into Vapor Pressure Reduction A linear pressure-temperature relationship, based on PV = nRT, reveals that a pure solvent attains a higher vapor pressure at any given temperature than a solution containing a nonvolatile solute. The presence of nonvolatile solutes restricts the area available for vapor formation, leading to decreased vapor pressure in the solution. This graphical comparison illustrates how the pure solvent’s vapor pressure exceeds that of the solution under identical conditions.

Boiling Point Elevation by Solute-Induced Pressure Modification Boiling point is reached when a liquid’s vapor pressure equals atmospheric pressure, and the pure solvent achieves this condition at a lower temperature than the corresponding solution. The solution, hindered by nonvolatile solute particles, requires additional heating to match atmospheric pressure, resulting in an elevated boiling point. This boiling point elevation is directly proportional to the solute’s molality, expressed by the relation ΔT₍b₎ = k₍b₎ · m, where k₍b₎ is the solvent-specific ebullioscopic constant.

In snowy regions, salt is applied to melt snow by lowering the freezing point of water. Salt, as a non-volatile solute, decreases the solvent’s freezing temperature so that the solution freezes at a lower point than pure water. The decrease in freezing point is directly proportional to the salt's molality, following the relation ΔTf = kf × molality. For water, the cryoscopic constant kf is 1.86, which quantifies this effect for numerical applications.

Driving Forces of Osmosis and Pressure A semi-permeable membrane divides a container into a pure solvent side and a solution side, allowing only the solvent to pass through while blocking solute particles. The solvent moves from the region of higher concentration to lower concentration, building up a pressure on the solution side. This pressure, described by the equation π = cRT, can be seen either as the force exerted by the moving solvent or as the external pressure needed to halt the flow.

Reverse Osmosis and Isotonic Equilibrium When pressure on the solution side exceeds the osmotic pressure, the solvent reverses its flow back into the pure solvent compartment, a process known as reverse osmosis. This mechanism is applied in water purification systems to separate pure water from solutes. Furthermore, solutions with equal osmotic pressures remain in equilibrium, forming isotonic conditions.