Solubility
Solubility is the analytical composition of a saturated solution, expressed in terms of the proportion of a designated solute in a designated solvent when the solvent is present in excess.[1] This property quantifies the maximum amount of solute that can dissolve in a given quantity of solvent at equilibrium under specified conditions, such as temperature and pressure, forming a homogeneous mixture known as a solution.[1] Solubility is typically expressed in units including grams of solute per 100 grams or milliliters of solvent, molarity (moles per liter), molality (moles per kilogram of solvent), or mole fraction, depending on the context and precision required.[2] A key guiding principle for predicting solubility is "like dissolves like," meaning substances with similar intermolecular forces—such as polar solutes in polar solvents or nonpolar solutes in nonpolar solvents—tend to form solutions more readily due to favorable interactions between solute and solvent particles.[3] For ionic compounds, solubility often follows specific rules based on the ions involved, such as nitrates being generally soluble in water.[4] Several factors influence solubility, including temperature, pressure, and the chemical nature of the solute and solvent. For most solid solutes in liquid solvents, solubility increases with rising temperature as the kinetic energy enhances the disruption of solute lattice structures.[5] In contrast, the solubility of gases in liquids generally decreases with increasing temperature, as higher thermal energy favors the escape of gas molecules from the solution.[6] Pressure significantly affects gas solubility, with higher pressures increasing the amount of gas that dissolves according to Henry's law, which states that the solubility of a gas is directly proportional to the partial pressure of the gas above the solution.[7] These factors are critical in applications ranging from pharmaceutical formulations, where controlled solubility ensures drug delivery, to environmental processes like ocean carbon cycling influenced by gas solubility in water.[8]Fundamentals of Solubility
Definition and Basic Principles
Solubility refers to the maximum amount of a solute that can dissolve in a given quantity of solvent under specified conditions of temperature, pressure, and composition, resulting in the formation of a saturated solution where the solution is in dynamic equilibrium with any undissolved solute. This property is fundamental to understanding solution formation and is expressed quantitatively as the analytical composition of the saturated solution, often in terms of concentration, mass per volume, or mole fraction.[1] The process of dissolution represents a physical equilibrium, in which the rate of solute particles entering the solution equals the rate at which they crystallize out, maintaining a constant solute concentration once saturation is reached./Equilibria/Solubilty/Solubility_and_Factors_Affecting_Solubility) The concept of solubility has evolved through historical observations and formal definitions. Early insights into gas solubility were provided by English chemist William Henry in the early 19th century, who through systematic experiments demonstrated the proportional relationship between gas pressure and its solubility in liquids, laying groundwork for later quantitative studies.[9] Over time, these empirical foundations led to modern standardization by the International Union of Pure and Applied Chemistry (IUPAC), which defines solubility precisely to account for diverse solute-solvent systems and conditions, ensuring consistency in scientific communication and application.[1] To describe the extent of solubility, qualitative terms are commonly used based on approximate thresholds in grams of solute per 100 mL of solvent at standard conditions: substances are considered soluble if exceeding 1 g/100 mL, sparingly soluble if between 0.1 and 1 g/100 mL, and insoluble if less than 0.1 g/100 mL.[10] [11] For instance, sodium chloride (NaCl) exemplifies high solubility in water, dissolving at about 36 g/100 mL at 25°C, enabling its widespread use in aqueous solutions.[12] In contrast, silver chloride (AgCl) is insoluble, with a solubility of only approximately 0.00019 g/100 mL at 25°C, which underlies its precipitation in qualitative analysis.[13] These qualifiers help predict behavior in chemical processes without requiring exact measurements.Molecular View of Dissolution
The dissolution of a solute in a solvent occurs at the molecular level through the process of solvation, where solute particles are surrounded and stabilized by solvent molecules, forming new intermolecular interactions that replace the original solute-solute attractions.[14] For ionic solutes in polar solvents like water, this involves strong ion-dipole forces, in which the partial charges on the solvent molecules align with the full charges on the ions, effectively pulling them apart from the solid lattice.[15] In cases of non-ionic solutes, weaker van der Waals forces or dipole-dipole interactions may contribute to solvation, facilitating the integration of the solute into the solvent structure.[14] A key aspect of dissolution is the energy balance between breaking solute-solute bonds and forming solute-solvent bonds; for ionic solids, this pits the lattice energy—the energy required to separate ions in the crystal—against the hydration energy released when ions interact with water molecules.[16] If the hydration energy sufficiently offsets the lattice energy, the process becomes energetically favorable, though the overall spontaneity depends on the Gibbs free energy change, given by \Delta G = \Delta H - T \Delta S where \Delta H represents the enthalpy change (primarily from net energy shifts in bond breaking and forming), \Delta S is the entropy change (reflecting increased disorder from dispersing solute particles), and T is the absolute temperature.[17] Negative \Delta G indicates a spontaneous dissolution, with entropy often playing a crucial role in overcoming any endothermic enthalpy contributions.[17] In the solvation shell, or solvent cage, solvent molecules form a structured layer around the solute, dynamically orienting to maximize favorable interactions; for example, water molecules arrange with their oxygen atoms facing Na^+ ions and hydrogen atoms toward Cl^- ions, creating a hydration sphere that stabilizes the ions in solution.[18] This cage formation enhances solubility by isolating solute particles and preventing recombination, while the solvent's polarity is essential, as it enables the "like dissolves like" principle where solutes with similar intermolecular forces to the solvent are more readily solvated.[19]Quantification of Solubility
Measures per Solvent or Solution
Solubility is often quantified relative to the amount of solvent used, providing a measure independent of the total solution volume. One common expression is grams of solute per 100 grams of solvent (g/100 g), which directly indicates the mass ratio and is particularly useful for comparing solubilities across different solvents without considering density variations. Another key unit is molality (m), defined as the number of moles of solute per kilogram of solvent, which normalizes concentrations based on solvent mass and remains constant despite changes in solution volume. For instance, the solubility of potassium nitrate (KNO₃) in water at 25°C is approximately 38 g per 100 g of water, highlighting its high solubility in this metric.[20] In contrast, measures expressed per quantity of solution account for the total mixture and are suited for volumetric analyses or reactions in fixed volumes. Grams of solute per 100 milliliters of solution (g/100 mL) is a practical unit for laboratory preparations, as it aligns with common measurement tools like pipettes and reflects the density of the solution implicitly.[19] Molarity (M), or moles of solute per liter of solution, facilitates stoichiometric calculations in chemical reactions, while mole fraction (X), the ratio of moles of solute to total moles in the solution, offers a dimensionless scale ideal for thermodynamic discussions. The same KNO₃ solubility at 25°C corresponds to approximately 35 g/100 mL of solution, though exact values depend on whether expressed per solvent mass or solution volume. This approximation holds better for dilute systems where solution density ≈1 g/mL.[20] Each unit has specific advantages depending on the context; for example, molality is preferred for colligative properties like boiling point elevation because it is unaffected by temperature-induced volume changes, unlike molarity, which varies with solution density.[3] Mole fraction, meanwhile, simplifies Raoult's law applications by being independent of the solvent's mass or volume. For ionic compounds, saturation equilibrium is conceptually bounded by the solubility product constant (Ksp), an equilibrium constant that equals the product of ion concentrations (in moles per liter) raised to their stoichiometric powers in a saturated solution.[21] This value serves as a limit indicating the maximum solubility under ideal conditions, with lower Ksp values signifying poorer solubility, though it applies primarily to sparingly soluble salts and assumes no common ion effects or complex formations.[21]Handling Liquid and Gaseous Solutes
Liquid solutes are handled differently in solubility quantification due to their fluid nature, which allows for complete miscibility or partial mixing without the need to disrupt a rigid structure. Miscibility refers to the ability of two or more liquids to form a homogeneous solution in all proportions, as seen in the ethanol-water system where polar interactions enable full dissolution.[22] In contrast, limited solubility occurs when liquids do not mix completely, such as oil and water, where nonpolar hydrocarbons separate into distinct layers due to unfavorable interactions.[22] Common units for expressing the solubility of liquid solutes include volume percent (v/v), defined as the volume of solute per 100 volumes of solution, and mole fraction, which represents the ratio of moles of solute to total moles in the mixture.[19][23] Gaseous solutes are quantified primarily through their equilibrium distribution between the gas phase and the liquid solvent, often expressed in volume/volume (V/V) terms or as a function of partial pressure. Henry's law provides the fundamental relationship, stating that at constant temperature, the solubility S of a gas in a liquid is directly proportional to the partial pressure P of the gas above the liquid: S = k_H \cdot P where k_H is the Henry's law constant, which varies with temperature and the gas-solvent pair.[24] This constant can be expressed in units such as atm/mol or mol/(L·atm), allowing conversion between concentration and pressure.[25] A practical example is the dissolution of carbon dioxide (CO₂) in carbonated beverages, where high pressure during bottling increases k_H \cdot P, dissolving CO₂ to create fizz upon opening as pressure drops and the gas escapes.[26] Unlike solid solutes, which require energy to overcome lattice energy for dissolution, liquid and gaseous solutes lack a crystalline lattice, so their solubility emphasizes equilibrium partitioning driven by intermolecular forces and phase distribution.[27][28] This partitioning reflects a dynamic balance where the solute distributes between phases based on solubility parameters, without the enthalpic barrier of lattice disruption characteristic of solids.[29]Unit Conversions and Equivalents
Converting between different units of solubility is essential for comparing data across scientific literature, engineering applications, and regulatory standards, as solubility is often reported in context-specific formats such as mass per mass, moles per volume, or mole fractions.[30] Common conversions involve transforming molality (moles of solute per kilogram of solvent) to molarity (moles of solute per liter of solution) or mass-based units like grams of solute per 100 grams of solvent to mole fraction. These transformations require knowledge of molar masses, solution densities, and sometimes approximations for dilute solutions.[31] The conversion from molality to molarity accounts for the volume of the solution, which depends on the solvent's density and the solute's contribution to the total mass. For dilute aqueous solutions, an approximation is M ≈ m (since 1 kg water ≈ 1 L). For more accurate results, especially in concentrated solutions, the full calculation uses the actual solution density (\rho): M = \frac{m \cdot \rho}{1 + m \cdot \frac{M_{\text{solute}}}{1000}} where M is molarity in mol/L, m is molality in mol/kg, \rho is solution density in g/mL, and M_{\text{solute}} is the molar mass of the solute in g/mol. This incorporates the total mass and volume of the solution.[31] Similarly, converting from grams of solute per 100 grams of solvent (g/100 g) to mole fraction (X) involves calculating the moles of each component. The mole fraction of the solute is given by: X = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}} where n_{\text{solute}} and n_{\text{solvent}} are the moles of solute and solvent, respectively, determined from their masses and molar masses. For example, if 36 g of solute is dissolved in 100 g of solvent, divide each mass by the appropriate molar mass to find the moles, then apply the formula.[30] A practical example is the solubility of sodium chloride (NaCl) in water at 25°C, reported as 36 g NaCl per 100 g water.[12] First, convert to molality: moles of NaCl = 36 g / 58.44 g/mol ≈ 0.616 mol; molality m = 0.616 mol / 0.100 kg = 6.16 m. To find molarity, note the total mass of solution = 136 g and density of the saturated solution ≈ 1.202 g/mL, so volume ≈ 136 g / 1.202 g/mL ≈ 0.113 L; thus, M ≈ 0.616 mol / 0.113 L ≈ 5.4 M.[12] This conversion highlights the need for solution density, which is often assumed as 1 g/mL for dilute cases but leads to errors in concentrated solutions like this one.[32] In different systems, particularly for trace solubilities, parts per million (ppm) is widely used, defined as milligrams of solute per kilogram of solution (or equivalently, \mug/g for mass basis). This unit is common in environmental contexts, such as assessing pollutant solubility in water bodies, where concentrations below 1 mg/L (≈ 1 ppm assuming density ≈ 1 g/mL) indicate trace levels.[33] For instance, the solubility of sparingly soluble salts like lead(II) sulfate in natural waters is often expressed in ppm to evaluate environmental risks.[34] Errors in unit conversions can arise from variations in temperature and solution density, which affect both the reported solubility and the conversion factors. Solubility itself often changes with temperature (e.g., increasing for most solids in water), and density decreases as temperature rises, potentially introducing up to 5-10% error in molarity calculations if not adjusted.[35] For precise work, use temperature-specific density values and re-evaluate solubility data at the exact conditions.[36]Factors Influencing Solubility
Temperature Dependence
The solubility of solid solutes in liquid solvents generally varies with temperature, depending on whether the dissolution process is endothermic or exothermic. In endothermic dissolution, where the process absorbs heat, solubility increases as temperature rises, shifting the equilibrium toward greater dissolution to absorb the added thermal energy. For instance, the solubility of potassium nitrate (KNO₃) in water exemplifies this trend, increasing from about 13 g per 100 mL at 0°C to 247 g per 100 mL at 100°C.[37] Conversely, exothermic dissolution releases heat, leading to decreased solubility with increasing temperature as the system shifts to counteract the added heat by favoring the undissolved state. Calcium hydroxide (Ca(OH)₂) in water demonstrates this behavior, with solubility dropping from 0.173 g per 100 mL at 20°C to 0.066 g per 100 mL at 100°C. This temperature dependence can be understood through Le Chatelier's principle, which predicts that the equilibrium position will adjust to minimize changes in conditions. For dissolution, the process is treated as a reversible equilibrium: solute(s) ⇌ solute(aq) + heat (for exothermic) or solute(s) + heat ⇌ solute(aq) (for endothermic). Increasing temperature thus drives endothermic equilibria forward, enhancing solubility, while opposing exothermic ones, reducing it./Equilibria/Solubilty/Temperature_Effects_on_Solubility) Quantitatively, the relationship between temperature and solubility is described by the van't Hoff equation, derived from the temperature dependence of the equilibrium constant K (here, related to the solubility product or saturation concentration). The equation is: \frac{d(\ln K)}{dT} = \frac{\Delta H}{RT^2} where \Delta H is the enthalpy change of dissolution, R is the gas constant, and T is the absolute temperature. Integrating this form allows prediction of how solubility varies with temperature, assuming \Delta H is constant; a positive \Delta H (endothermic) yields increasing K with T, while negative \Delta H (exothermic) yields decreasing K./26%3A_Chemical_Equilibrium/26.07%3A_The_van_%27t_Hoff_Equation) Exceptions to these patterns occur, particularly with hydrated salts undergoing phase transitions. For example, sodium sulfate decahydrate (Na₂SO₄·10H₂O) exhibits retrograde solubility above approximately 32°C, where its solubility peaks and then slightly decreases due to dehydration and transition to the anhydrous form, altering the effective dissolution thermodynamics.Pressure Effects
The solubility of gases in liquids is significantly influenced by pressure, as described by Henry's law, which states that at constant temperature, the solubility S of a gas in a liquid is directly proportional to the partial pressure P of the gas above the liquid:S = k \cdot P
where k is the Henry's law constant, typically expressed in units such as mol/L/atm or mol/L/bar.[38] This relationship arises from the increased frequency of gas molecule collisions with the liquid surface under higher pressure, leading to greater dissolution until equilibrium is reached./Physical_Properties_of_Matter/Solutions_and_Mixtures/Ideal_Solutions/Dissolving_Gases_In_Liquids_Henrys_Law) For instance, the solubility of oxygen in human blood, which follows Henry's law, approximately doubles when the total pressure increases from 1 atm to 2 atm, assuming the partial pressure of oxygen also doubles in compressed air; this enhances oxygen delivery but is limited by blood's low baseline solubility of about 0.003 mL O₂/100 mL blood/mm Hg at 37°C.[39] Henry's law constants for common gases vary widely; for oxygen in water at 25°C, k is approximately 0.0013 mol/L/atm, while for carbon dioxide it is higher at 0.034 mol/L/atm, reflecting differences in gas-liquid interactions.[40] In contrast, the solubility of liquids in liquids and solids in liquids exhibits minimal dependence on pressure under normal conditions, due to the low compressibility of these phases, which results in negligible changes in molar volume during dissolution./13:_Solutions/13.04:_Effects_of_Temperature_and_Pressure_on_Solubility) However, under extreme pressures, such as those encountered in deep-sea environments (up to several hundred atm) or industrial high-pressure processes, solubility of solids can increase slightly if the partial molar volume of the solute in solution is less than in the solid phase, as predicted by thermodynamic relations.[41] A practical application of pressure effects on gas solubility is in scuba diving, where increased ambient pressure at depth raises the solubility of nitrogen in blood and tissues according to Henry's law; upon rapid ascent and pressure reduction, dissolved nitrogen forms bubbles, potentially causing decompression sickness if not managed through staged decompression stops.[42]