Solutions and Solubility

Concentration Units

The MCAT tests six principal ways to express concentration, and you must be able to convert among them. Molarity (M) = moles solute / liters solution—the workhorse of solution stoichiometry and the unit titrations are reported in. Molality (m) = moles solute / kg solvent—preferred for colligative properties because it is temperature-independent (mass does not change with temperature, but volume does). Mole fraction (χ) = moles solute / total moles all species—used in Raoult's law for vapor-pressure calculations. Mass percent (% w/w) = (mass solute / mass solution) × 100%. Parts per million (ppm) = (mass solute / mass solution) × 10⁶; for dilute aqueous solutions, 1 ppm ≈ 1 mg/L. Normality (N) = equivalents / L solution—tests how many reactive units are present per liter: for acids, it is moles of H⁺; for redox, moles of electrons transferred. The MCAT frequently embeds conversions within passages: given ppm of a pollutant in a lake, convert to molarity; given a mass percent, find the molality needed to calculate freezing-point depression. The most common trap is confusing molarity with molality—they diverge significantly in concentrated solutions. At infinite dilution, M ≈ m because 1 L of water ≈ 1 kg of water.

Dilutions

Dilution is the process of reducing solute concentration by adding more solvent—the number of moles of solute remains constant. The governing equation is M₁V₁ = M₂V₂, where M₁ and V₁ are the initial concentration and volume, and M₂ and V₂ are the final values. This is simply a statement of conservation of moles: n = MV, and n does not change when you add solvent. The MCAT tests dilutions in two classic formats. First, the direct plug-and-chug: "What volume of 12 M HCl is needed to prepare 500 mL of 0.50 M HCl?" Second, the serial dilution: a solution is diluted by a factor (say 10×), then that solution is diluted again by another factor—the final concentration is the initial divided by the product of all dilution factors. This appears in laboratory technique passages (ELISA protocols, bacterial culture dilutions, standard-curve preparation) and often disguises the chemistry in a biology passage. A crucial nuance: M₁V₁ = M₂V₂ only works when both concentrations are in the same units. If a passage gives you a stock solution in mass percent and asks for a diluted molarity, you must convert first. Also, when diluting a strong electrolyte, the concentration of individual ions changes proportionally—diluting 1 M NaCl to 0.1 M reduces both [Na⁺] and [Cl⁻] to 0.1 M.

Solubility Rules

Solubility rules predict whether an ionic compound will dissolve in water—a prerequisite for understanding precipitation reactions, separation schemes, and biological ion availability. The MCAT-tested rules, in priority order: (1) All compounds containing alkali metal ions (Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺) and ammonium ion (NH₄⁺) are soluble. (2) All nitrates (NO₃⁻), acetates (CH₃COO⁻), and perchlorates (ClO₄⁻) are soluble. (3) Most chlorides (Cl⁻), bromides (Br⁻), and iodides (I⁻) are soluble, EXCEPT those of Ag⁺, Pb²⁺, and Hg₂²⁺. (4) Most sulfates (SO₄²⁻) are soluble, EXCEPT those of Ca²⁺, Sr²⁺, Ba²⁺, Pb²⁺, and Hg₂²⁺ (Ag₂SO₄ is moderately soluble). (5) Most hydroxides (OH⁻) are insoluble, EXCEPT alkali metal hydroxides, NH₄OH, and the somewhat-soluble Ba(OH)₂, Sr(OH)₂, and Ca(OH)₂. (6) Most carbonates (CO₃²⁻), phosphates (PO₄³⁻), sulfides (S²⁻), and sulfites (SO₃²⁻) are insoluble, EXCEPT those of alkali metals and NH₄⁺. The MCAT rarely asks pure memorization; instead, it embeds solubility reasoning in passages: predicting which ion precipitates first when two solutions are mixed, identifying unknown salts via qualitative analysis schemes, or explaining why certain minerals dissolve in groundwater. The driving force for precipitation is the formation of a solid that removes ions from solution—Le Chatelier's principle applied to the solubility equilibrium.

Saturated and Unsaturated Solutions

A solution is unsaturated when it can dissolve more solute at a given temperature; saturated when it holds the maximum dissolved solute at equilibrium with undissolved solid; and supersaturated when it contains more dissolved solute than equilibrium permits—a metastable state that crystallizes readily upon disturbance (scratching the glass, adding a seed crystal, or a temperature drop). The solubility of most solid solutes in water increases with temperature (Le Chatelier: heat + solute(s) ⇌ solute(aq), so adding heat drives dissolution endothermically). Gases are the opposite: gas solubility decreases with increasing temperature—think of warm soda going flat—and increases with increasing pressure (Henry's law: C = kP, where C is dissolved gas concentration, k is the Henry's law constant, and P is the partial pressure of the gas above the solution). The MCAT tests Henry's law in two biological contexts: oxygen solubility in blood (why hyperbaric chambers work) and decompression sickness ("the bends")—when a diver ascends too quickly, dissolved N₂ comes out of solution and forms bubbles in tissues. The solubility product (Ksp) quantifies the saturation point for sparingly soluble salts: for AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq), Ksp = [Ag⁺][Cl⁻]. A solution is saturated when the ion product Q equals Ksp; if Q > Ksp, precipitation occurs; if Q < Ksp, more solid can dissolve.

Colligative Properties

Colligative properties depend ONLY on the number of dissolved solute particles, not on their identity—this is the central organizing principle for the entire topic. There are four colligative properties, and each is modified by the van 't Hoff factor i, which accounts for electrolyte dissociation: i = the number of particles one formula unit produces in solution (i = 2 for NaCl, i = 3 for CaCl₂, i ≈ 1 for nonelectrolytes like glucose). (1) Vapor-pressure lowering: Raoult's law states P_solution = χ_solvent × P°_solvent—adding a nonvolatile solute lowers the vapor pressure because solute particles occupy surface sites, reducing the number of solvent molecules that can escape. (2) Boiling-point elevation: ΔT_b = i × K_b × m, where K_b is the ebullioscopic constant (0.512 °C/m for water). Adding solute raises the boiling point because the lowered vapor pressure means a higher temperature is required to reach atmospheric pressure. (3) Freezing-point depression: ΔT_f = i × K_f × m, where K_f is the cryoscopic constant (1.86 °C/m for water). Adding solute depresses the freezing point by disrupting the crystal lattice formation—this is why salt melts ice on roads and why antifreeze (ethylene glycol) protects car engines. (4) Osmotic pressure: Π = iMRT, where Π is osmotic pressure, M is molarity, R is 0.08206 L·atm/mol·K, and T is Kelvin temperature. Osmotic pressure is the pressure that must be applied to prevent net water flow across a semipermeable membrane—water flows from the low-solute (hypotonic) side to the high-solute (hypertonic) side.

Osmotic Pressure

Osmotic pressure deserves its own section because it is the single most biologically tested colligative property on the MCAT. The equation Π = iMRT tells you the pressure required to stop osmosis, but the exam expects you to reason qualitatively about tonicity: a hypotonic solution has lower osmolarity than the cell interior—water enters, cells swell and may lyse; an isotonic solution has equal osmolarity—no net water movement, cells maintain normal volume; a hypertonic solution has higher osmolarity—water leaves, cells shrink (crenate). In medicine, isotonic saline is 0.9% NaCl (≈ 0.154 M, osmolarity ≈ 308 mOsm/L due to i = 2). The MCAT will ask: what happens to a red blood cell placed in 0.5% NaCl? It is hypotonic (0.5% < 0.9%) so water enters and the cell lyses. What about 5% glucose? Glucose is a nonelectrolyte (i = 1), so its osmolarity is its molarity—and at typical clinical concentrations, 5% dextrose is approximately isotonic (≈ 278 mOsm/L). A classic trap: a passage says "1 M NaCl" and asks for osmolarity—remember to multiply by i = 2 to get 2 Osm/L. Another trap: comparing two solutions of different electrolytes. 1 M NaCl has a higher osmolarity (2 Osm/L) than 1 M glucose (1 Osm/L), so water flows from the glucose side to the NaCl side. The MCAT also tests reverse osmosis—applying pressure greater than Π to the high-solute side forces water through the membrane against its natural gradient, used in water purification and kidney dialysis.

Electrolytes

Electrolytes are solutes that dissociate into ions when dissolved, enabling the solution to conduct electricity. Strong electrolytes dissociate completely: soluble ionic compounds (NaCl, KBr, CaCl₂), strong acids (HCl, HNO₃, H₂SO₄ in first dissociation), and strong bases (NaOH, KOH). Their van 't Hoff factor i equals the number of ions per formula unit at any reasonable concentration. Weak electrolytes dissociate partially: weak acids (acetic acid, HF), weak bases (NH₃), and slightly soluble salts. Their effective i lies between 1 and the theoretical maximum, approaching the maximum only at infinite dilution. Nonelectrolytes do not dissociate at all: glucose, urea, ethanol, and most organic molecules—i = 1 for these. The MCAT tests the distinction between strong and weak electrolytes in three contexts. First, colligative-property calculations: a 1 m solution of NaCl depresses the freezing point by 3.72°C (i × K_f × m = 2 × 1.86 × 1), while 1 m glucose depresses it by only 1.86°C. Second, conductivity experiments: a light bulb in series with a solution glows brightly for strong electrolytes, dimly for weak electrolytes, and not at all for nonelectrolytes. Third, osmotic reasoning: neglecting i leads to errors—if the question says "0.15 M NaCl" and asks for osmolarity, the answer is ~0.30 Osm/L, not 0.15. A subtle distinction the MCAT exploits: MgCl₂ theoretically has i = 3, but in concentrated solutions ion pairing reduces the effective i below 3. You use the theoretical i unless given experimental data (ΔT_f measured) to calculate the actual i.

How it works

The logic of solutions and solubility reduces to counting particles and comparing concentrations. First, identify the solute and whether it dissociates—this determines the van 't Hoff factor i, which multiplies every colligative effect. Second, express concentration in the unit appropriate for the question: molarity for stoichiometry and osmotic pressure, molality for boiling-point elevation and freezing-point depression, and mole fraction for vapor-pressure calculations. Third, for any colligative question, apply the relevant equation: ΔT_b = iK_bm, ΔT_f = iK_fm, Π = iMRT, or P = χP°. Fourth, for solubility questions, apply the solubility rules or compare Q to Ksp—precipitation occurs when Q exceeds Ksp, and a common ion suppresses solubility via Le Chatelier's principle. Every solutions problem on the MCAT is ultimately a particle-counting problem: how many solute particles are present per unit of solvent, and what physical consequence does that number produce?

How it works

The logic of solutions and solubility reduces to counting particles and comparing concentrations. First, identify the solute and whether it dissociates—this determines the van 't Hoff factor i, which multiplies every colligative effect. Second, express concentration in the unit appropriate for the question: molarity for stoichiometry and osmotic pressure, molality for boiling-point elevation and freezing-point depression, and mole fraction for vapor-pressure calculations. Third, for any colligative question, apply the relevant equation: ΔT_b = iK_bm, ΔT_f = iK_fm, Π = iMRT, or P = χP°. Fourth, for solubility questions, apply the solubility rules or compare Q to Ksp—precipitation occurs when Q exceeds Ksp, and a common ion suppresses solubility via Le Chatelier's principle. Every solutions problem on the MCAT is ultimately a particle-counting problem: how many solute particles are present per unit of solvent, and what physical consequence does that number produce?

Comparisons

• C/P (Solution stoichiometry): M₁V₁ = M₂V₂ for dilutions; converting among molarity, molality, mass percent, and ppm; using molarity in titration calculations.
• C/P (Colligative properties): Calculating ΔT_f, ΔT_b, Π, and ΔP given concentration and van 't Hoff factor; predicting which solution has the lowest freezing point or highest boiling point.
• C/P (Equilibrium): Ksp and the common-ion effect; predicting precipitation when Q > Ksp; Le Chatelier shifts in saturated solutions.
• B/B (Osmosis and tonicity): Red blood cells in hypotonic/hypertonic/isotonic solutions; IV fluid osmolarity (0.9% saline, 5% dextrose, Lactated Ringer's); water movement across cell membranes.
• B/B (Renal physiology): Countercurrent multiplier in the loop of Henle depends on osmotic gradients; ADH regulates water reabsorption by altering collecting duct permeability to water.
• B/B (Gas exchange): Henry's law governs O₂ and CO₂ solubility in blood; decreased solubility of gases at higher temperature; decompression sickness and hyperbaric oxygen therapy.
• B/B (Electrophysiology): Ion gradients across neuronal membranes—Na⁺/K⁺ ATPase maintains concentration differences; electrolyte dissociation is essential for action potentials.

Common confusions

• Forgetting the van 't Hoff factor i: a 1 m NaCl solution has 2× the colligative effect of 1 m glucose. The MCAT will give you identical molalities for an electrolyte and nonelectrolyte and ask which has the lower freezing point—the electrolyte always wins.
• Using molarity instead of molality for ΔT_f and ΔT_b: molality is moles/kg solvent, independent of temperature. Molarity changes with temperature because volume expands. The MCAT will give you density and mass of solution and expect you to find molality.
• Confusing osmolarity with tonicity: osmolarity is a colligative property (depends on total particle concentration), while tonicity describes the effect of a solution on cell volume. A solution can be isosmotic but hypotonic (e.g., urea is permeable and does not exert sustained osmotic pressure).
• Misapplying M₁V₁ = M₂V₂ to serial dilutions: the final concentration after N sequential dilutions is C₀/(D₁ × D₂ × ... × D_N), not C₀/(D₁ + D₂ + ...).
• Ignoring the common-ion effect: adding NaCl to a saturated AgCl solution decreases AgCl solubility because the added Cl⁻ shifts the equilibrium toward solid AgCl.
• Assuming all salts follow their theoretical i at all concentrations: ion pairing in concentrated solutions reduces effective i. Use theoretical i unless experimental colligative data is given—then use the data to calculate actual i.
• Applying Henry's law backward: gas solubility increases with pressure (C = kP) but decreases with temperature. Warm soda goes flat because k decreases at higher T; deep-sea divers get the bends because ascending reduces P and N₂ comes out of solution.
• Forgetting that mass percent uses mass of solution (solute + solvent), not just solvent. A 10% NaCl solution has 10 g NaCl per 100 g of solution (90 g water + 10 g NaCl).

Quick review

• Molarity (M) = mol/L; molality (m) = mol/kg solvent; mole fraction (χ) = mol/total mol; mass % = (mass solute/mass solution)×100.
• M₁V₁ = M₂V₂ for dilutions—moles of solute are conserved; serial dilution multiplies factors, not adds.
• Solubility rules: all Na⁺, K⁺, NH₄⁺, NO₃⁻, CH₃COO⁻ salts are soluble. Most Cl⁻, Br⁻, I⁻ soluble except Ag⁺, Pb²⁺, Hg₂²⁺. Most SO₄²⁻ soluble except Ca²⁺, Sr²⁺, Ba²⁺, Pb²⁺.
• Saturated: Q = Ksp. If Q > Ksp, precipitation. Common-ion effect reduces solubility via Le Chatelier.
• Henry's law: C = kP (gas solubility ∝ pressure). Gas solubility decreases with increasing temperature.
• van 't Hoff i = particles/formula unit: NaCl i=2, CaCl₂ i=3, glucose i=1. Weak electrolytes have i between 1 and max.
• ΔT_f = iK_fm (K_f for water = 1.86 °C/m); ΔT_b = iK_bm (K_b for water = 0.512 °C/m).
• Π = iMRT: osmotic pressure. Water flows from hypotonic (low solute) to hypertonic (high solute).
• Isotonic saline = 0.9% NaCl (≈ 308 mOsm/L); 5% dextrose ≈ isotonic (~278 mOsm/L).
• Raoult's law: P_solution = χ_solvent × P°_solvent. Adding nonvolatile solute lowers vapor pressure.
• For colligative ranking questions: higher i × m means lower freezing point, higher boiling point, higher osmotic pressure.
• Effective osmolarity = i × M. 1 M NaCl → 2 Osm/L; 1 M CaCl₂ → 3 Osm/L; 1 M glucose → 1 Osm/L.