Substance can be solid at low temperature, liquid at intermediate temperature, and gas at high temperature {phase, chemistry}|. States or phases have different relations between material volume, temperature, and potential energy.
free energy
Current phase has lowest free energy for temperature. Potential energy depends on distance between molecules. Entropy depends on molecule number and temperature.
phases: solid
Solid phase has lowest volume and smallest potential energy, because average distance between molecules is smallest. Solids have low chemical potential. Low temperature makes material solid, because decrease in potential energy is higher than decrease in entropy. Solid phase has most order, because it has patterned crystal structure and temperature is lowest. Solid phase has least randomness and lowest entropy. Solids can have several crystal forms and so different solid phases.
phases: gas
Gas phase has highest volume and greatest potential energy, because average distance between molecules is greatest. Gases have high chemical potential. High temperature makes material gas, because increase in entropy is higher than increase in potential energy. Gas phase has least order, because all molecules are independent, with no physical structure, and temperature is highest. Gas phase has greatest randomness and highest entropy.
phases: liquid
Compared to solid, liquid phase has more volume and more potential energy, as distance between molecules becomes more. Intermediate temperature makes material liquid, because entropy change is similar to potential energy change. Liquid phase has less order than solid phase, because crystal structure breaks down into fluid structure, and temperature is more.
factors
Temperature, pressure, phase number, and substance amounts, concentrations, and pressures affect chemical systems.
factors: independence
Some factors relate to others, and some are independent. Available phases are independent, because substances can go to all phases.
factors: temperature
Temperature can freely vary, must be the same throughout system, and does not depend on other factors.
factors: pressure
Pressure can freely vary, must be the same throughout system, and does not depend on other factors.
factors: substances
Number of independent components is number of substances minus one. Because total percentage must be 100%, because sum of mole fractions must equal one, one substance's percentage is dependent.
factors: number
With no equilibria in system, number of independent factors is (c - 1) * p + 2, where c is component number, and p is phase number.
factors: equilibrium
Substance amounts in two phases in contact at phase boundary typically are in equilibrium. Chemical potentials of both phases must be equal. Number of equilibria is c * (p - 1), where c is component number, and p is phase number.
factors: degrees of freedom
Factor number and equilibria number determine how many factors {degrees of freedom, equilibrium} can freely change in chemical systems. Degrees of freedom equal free-variable number v minus equilibria number e {phase rule, components}: v - e. Degrees of freedom total: c - p + 2 = 1 + 1 + (c - 1) * p - c * (p - 1), where c is component number, and p is phase number.
factors: equilibrium and ions
If chemical systems have ions, electrical neutrality requires adding one more equilibrium to chemical system.
factors: equilibrium and initial state
Knowing chemical-system initial state fixes one more factor and adds one more equilibrium.
factors: equilibrium and field
If force field is present in chemical system, it adds one more phase to chemical system.
factors: equilibrium and phases
Two immiscible substances can make two heterogeneous phases, even if both are liquids, because they have boundary. Both components are in equilibrium. Heterogeneous phase is mixture and has several components, several phases, and several equilibria.
Two miscible substances can combine to make only one homogeneous phase, with no boundary, because they mix and so are not in equilibrium. Homogeneous phase counts as one component and one phase.
phase change
Physical systems tend to go to lowest potential energy and greatest entropy. Electrical forces push or pull atoms and change potential energy to kinetic energy. Friction opposes electrical forces, so kinetic energy tends to become heat. Physical systems tend toward most randomness and lowest physical order and so greatest entropy. Number of molecules freed from order relates to average random kinetic energy and so temperature.
phase change: free energy
Total available energy is free energy and is energy from order breakdown plus potential energy. Physical systems tend to go to lowest free energy. Lowest free energy is optimum between lowering potential energy and raising entropy.
phase change: temperature
System has same average random translational kinetic energy throughout. Temperature stays constant during phase change from gas to liquid, or liquid to solid, because all heat energy removed is potential energy, which kept molecules apart, not kinetic energy. Temperature stays constant during phase change from solid to liquid or from liquid to gas, because added kinetic energy from heat becomes potential energy that makes molecules farther apart.
Substances can bind onto solid surfaces {adsorption}|.
Equal gas volumes at same temperature and pressure contain same number of molecules {Avogadro's hypothesis} {Avogadro hypothesis}. At standard temperature and pressure, number is one mole {Avogadro's number}, which is 6*10^23 molecules.
Particles in suspension move randomly in all directions with many velocities {Brownian motion}|. Brownian motion depends on time.
cause
Fluid-molecule collisions cause fluid random motions and microscopic-particle oscillations. Particles travel short average distance, through mean free path, before next collision. Collision frequency varies inversely with mean free path.
examples
Telephone errors have bursts, with random intervals between errors. Brownian-motion zerosets, or random Cantor sets with fractal dimension between zero and one, can model them.
examples: random walk
Processes {random walk} can take same-length steps in all directions. Average distance from origin is square root of step number. Return to origin is probable. Random walk can be along a line or have more dimensions.
comparison
Brownian motion is neither fractal nor self-similar.
Materials have ability to conduct electricity {conductivity}|.
conductor
Conductor molecules can have half-filled electron energy level, so electrons can jump to same energy level in neighboring molecules. Metallic crystals are conductors.
semiconductor
Semiconductor molecules can have energy level filled with electrons and slightly higher empty energy level, so electrons can jump into neighboring molecules at normal temperatures. Covalently bonded crystals are semiconductors.
insulator
Insulator molecules can have energy level filled with electrons and much higher empty energy level, so electrons cannot jump into neighboring molecules at normal temperatures. Ionic crystals and hydrogen-bonded crystals like ice, hydrogen fluoride, and proteins are insulators. Insulators are typically transparent.
In inorganic ionic crystals, a number {coordination number} of other atoms surround each atom. Eight opposite-charge atoms surround each atom, if atoms have equal size. Six opposite-charge atoms surround each atom, if atoms have unequal size. Four opposite-charge atoms surround each atom, if atoms have very unequal size.
Substance solid, liquid, and gas phases can all be present at triple point at high temperature {critical temperature}| and high pressure {critical pressure}.
At critical temperature and pressure, substance solid, liquid, and gas phases are all present {triple point} {criticality, phase}|. At high pressure and temperature, gas and liquid can be one phase, dense gas or gaseous liquid.
If substance releases into another substance, released substance tends to flow {diffusion}| throughout other substance, until released substance evenly distributes.
cause
Random molecule elastic collisions cause diffusion. Diffusion decreases system order. Gases tend to expand as molecules collide. Expansion rate depends on molecule velocity and size and on barriers to motion.
spectrum
In media, introduced foreign substance diffuses outward over time depending on number {spectral dimension} of medium-particle nearest neighbors. For ink in water, ink volume V increases as time t to 3/2 power: V = t^1.5.
For most solids, heat capacity per mole is constant {Dulong and Petit law} {law of Dulong and Petit}.
Molecular collisions cause gas to flow through container holes {effusion}|.
Two phases can have no net flow between them {equilibrium between phases}. At boiling-point or melting-point temperature, both phases, liquid/gas or solid/liquid, respectively, have same free energy and are in equilibrium. If temperature decreases, substance becomes denser, because entropy change is small but potential-energy change is large. If temperature increases, substance becomes less dense, because entropy change is large but potential-energy change is small.
Different pure fluids can come from fluid mixture by controlling pressure, vaporizing mixture at increasing temperatures, and cooling and condensing each vapor {fractionation}|.
Work that gas can do equals heat energy in gas {gas law} {ideal gas law, work}: P*V = n*R*T, where P is pressure, V is volume, n is moles, R is gas constant, and T is absolute temperature. Pressure times gas volume is work that gas can do. Product of gas moles and absolute temperature and gas constant is gas heat energy.
volume
Volume {molar volume} of one mole of ideal gas at standard temperature of 25 C and standard pressure of one atmosphere is 22.4 liters.
ideal gas
Ideal gas law assumes that molecules have elastic collisions, have no volume, and have no forces among them. At low pressure, real gas has less pressure than ideal gas, because molecules attract each other. At high pressure, real gas has higher pressure than ideal gas, because molecules repulse each other.
modifications
Ideal-gas-law modifications {van der Waals equation} {virial equation} account for molecule sizes and interactions.
Gas diffusion rate is inversely proportional to gas-density square root {Graham's law} {Graham law}.
Expanding gas can cool if temperature is below maximum temperature {Joule-Thompson inversion temperature}.
Vapor at critical point has white glow {opalescence, glow}|.
Degrees of freedom d are free-variable number n minus equilibria number e {phase rule, degrees of freedom}: d = n - e.
Melting solids along a moving band {zone melting}| can make impurities remain in melted part and pure part solidify behind moving band.
Gases and liquids {fluid}| are similar in flow properties. Van der Waals forces between molecules can cause cohesion, adhesion, adsorption, and surface tension. More polarized materials have increased molecule van-der-Waals forces, so cohesion and surface tension are greater, and adhesion is smaller.
Matter {gas phase} can have low density, flow, be compressible, have no local or global order, and expand to fill volume.
energy
Gases have high kinetic energy. Molecules have speed 500 meters per second. Electric forces between molecules have little effect.
distances
Molecules are 20 nanometers apart. Gases have distances between molecules that are five to ten times more than distances in solids and liquids. Gases are like spaces of vacancies with some positions filled.
size
Gas-molecule diameter is 0.5 nanometers.
relations
If gas volume increases while temperature stays the same, pressure decreases, and entropy and potential energy increase. If gas temperature increases while pressure stays the same, volume increases, and entropy and potential energy increase.
Temperature and pressure depend on kinetic energy, and volume and entropy depend on potential energy. If total energy is constant, P/V = S/T, where P is pressure change, V is volume change, S is entropy change, and T is temperature change. Potential energy increases when entropy increases, and entropy increases when potential energy increases.
Matter {liquid phase} can be dense, flow, have local order several atoms wide, have long-range disorder between local-order regions, have no expansion to fill volume, have less than 3% compression, have translational kinetic energy, and have molecule interactions.
types
Liquids can be molten salts, metallic liquids, hydrogen-bonded liquids, or van der Waals bonded liquids.
cohesion
Cohesive forces can be ionic, dipoles, ions and dipoles, dipoles and induced dipoles, or London forces between neutral atoms. Internal forces can be repulsive if compression is high.
melting
Melting is similar to reaching elastic limit in solid under stress.
At high temperature, materials can exist as ionized gas {plasma phase}|, as substance vaporizes and loses electrons.
High-density proton plasmas {Wigner solid} can act like liquids.
Matter {solid phase}| can be firm, be incompressible, have local and global order, have no flow, and have no expansion to fill volume.
crystal
Most solids are crystals. Crystals can be cubes, prisms, rhomboids, parallelepipeds, hexagons, or diamonds.
types
Elements {molecular elemental solid} can have molecules bound by weak van der Waals forces. Metal elements {metallic elemental solid} have atoms bound with metallic bonds. Non-metal elements {non-metallic network elemental solid} have each atom covalently bound to four or less atoms, in covalent-bond crystal lattices. Salts {ionic solid} can have ionic bonds between ions. Salts {polar solid} can have dipole-dipole bonds between polar molecules.
oscillations
Solid molecules vibrate and rotate but do not translate to new positions. Solids can transmit pressure in force direction but cannot cause pressure.
Solids can have no regular structure {amorphous solid}|, such as glass.
Almost all solids have regular molecule, ion, or atom arrays {crystal}|.
types
Crystals {cubic crystal} can have eight atoms around small atom, three perpendicular four-fold same-length axes, and five crystal classes.
Crystals {rhomboid crystal} can have twelve atoms around similar size atom with every third layer directly above another.
Crystals {rhombohedral crystal} can have one three-fold axis, with one axis perpendicular to the other two but with different length, and two axes with same length at 120-degree angle to perpendicular axis, and make five crystal classes.
Crystals {hexagonal crystal} {hexagon crystal} can have twelve atoms around similar size atom with alternate layers directly above each other.
Crystals {tetrahedral crystal} {tetrahedron crystal} can have four large ions around each small ion.
Crystals {octahedral crystal} {octahedron crystal} can have six large ions around each small ion.
Crystals {triangular crystal} can have three large ions around each small ion.
Crystals {planar crystal} can have two large ions around each small ion.
symmetry
Only one, two, three, four, or six rotational symmetries can fill all space with no gaps or overlaps, so only seven crystal types are common.
packing
The more similar in size atoms or ions are, the more atoms or ions can surround one atom or ion. Number of atoms or ions surrounding one atom also depends on ion charge or covalent-bond number.
lattice
Crystals have lattice structure. Including crystal type and lattice type, 32 crystal classes exist. 14 unit cell and 32 crystal class translations and transformations make 234 possible crystal shapes.
crystal growth
Crystals grow at dislocations, because binding molecules can contact two surface atoms. Impurities, long bond lengths during fast growth, and screw dislocations can cause dislocations and irregularities.
Small crystal faces grow fastest by deposition. Large crystal faces can adsorb other materials.
Crystal surfaces are never flat but are lumpy. Perfect crystals cannot grow.
Diagrams {Miller index} can show crystal planes, using three perpendicular axes. Crystal vertices are one unit length or less apart. Coordinate reciprocals indicate planes through vertices. Putting origin at one vertex and using coordinates for other vertices indicates edges. If plane is parallel to axis, coordinate reciprocal is zero.
Crystal growth can be along one axis {dendritic growth}, because heat leaves best at tips, so deposition is easiest there.
Unit cells can undergo translation and reflection {glide plane}.
Unit cells can undergo translation and turn around axis {screw axis} 0, 180, 120, 90, 72, or 60 degrees.
Crystals {clathrate} can be so open that they can hold small molecules inside, without bonding. Examples are very-cold-water forms and very-cold methane and hydrogen gas mixtures.
Metal crystals {metal crystal} can have hexagonal close packing, face-centered cubic close packing, or body-centered cubic close packing.
Substances {polymorphic solid} can have more than one crystal form.
Crystals {liquid crystal}| {dynamic scattering liquid crystal} (LCD) can have regularity in only one or two dimensions, allowing unit cells to slide past each other in third dimension. Liquid crystals are anisotropic, flow in sheets or steps, and are asymmetric molecules. Numbers can display electronically using reflected or transmitted light, as electric field makes crystal tinted, and no electric field makes crystal transparent.
Liquid crystals {nematic crystal} can have linear crystals with regularity in only one dimension, are like threads with no planes, orient, and are not periodic.
Liquid crystals {smectic crystal} can have planar crystals with regularity in two dimensions, orient, and are not periodic.
Missing atoms, extra atoms, or different atom types {crystal defect} alter regular crystal structure.
Crystal defects {dislocation, crystal} can displace unit cells from usual positions. Inserted atoms wedged into lattice can cause dislocations {edge dislocation}. Dislocations {screw dislocation} can be around axis to make helical unit-cell arrangements. Dislocations in crystals affect brittleness, ductility, and other mechanical crystal properties. Alloys lack dislocations and so do not slide, because odd atoms move to lowest free-energy positions.
Crystal ions can move to interstitial places and so leave vacancies {Frenkel defect}.
Different molecules or atoms {impurity}| can be in crystals.
Extra ions {interstitial ion} can be in ionic crystals.
In ionic crystal, cations and anions can be missing {Schottky defect}.
Ions can be missing from ionic crystals {vacancy}|.
Crystals have repeating atom groups {unit cell}. Crystals have lattice structure.
Only 14 possible arrangements {Bravais lattice} of identical spheres can make unit cells {space lattice}. Three are cubic, two monoclinic, four orthorhombic, two tetragonal, one triclinic, one hexagonal, and one rhombohedral.
Using half-unit circles as atoms, in a 3 x 4 surface area make two-dimensional figures: squares; triangles, hexagons, and rhombuses; centered rectangles; rectangles, and oblique figures.
From most symmetric to least symmetric two-dimensional space lattices (see Figure 1).
Square: Cell is a unit-length-side square, as in the first figure above. The two axes have equal length, both axes are mirror planes, and both axes have 90-degree rotation symmetry. Atoms are at corners. Cell has 90-degree rotation symmetry and two planes with mirror symmetry. Atoms have 4 atoms 1 unit away and 4 atoms SQR(2) away. Density is 12/12 = 1.
Hexagonal: Cell is a unit-length-side triangle with angles 60 degrees, a rhombus with angles 60 and 120 degrees, and a hexagon, as in the second figure above. The two axes have equal length, both axes are mirror planes, and both axes have 60-degree rotation symmetry. Atoms are at corners. Rhombus has 180-degree rotation symmetry and two planes with mirror symmetry. Triangle has 60-degree rotation symmetry and no planes with mirror symmetry. Atoms have 6 atoms 1 unit away. Density is ~13/12 > 1.
Centered rectangular: Cell is a parallelogram with angles not 30, 45, 60, 90, or 120 degrees, short diagonal unit length, and a rectangle with two sides greater than unit length and two side greater than that, as in the third figure above. The two axes have unequal length, one axis is a mirror plane, and both axes have 180-degree rotation symmetry. Atoms are at corners. Cell has 180-degree rotation symmetry and two planes with mirror symmetry. Corner atoms have 4 atoms 1 unit away, 2 atoms farther away, and 2 atoms even farther away, and central atoms have 4 atoms 1 unit away and 4 atoms farther away. Density is ~10/12 < 1.
Rectangular: Cell is a rectangle, as in the fourth figure above. The two axes have unequal length, both axes are mirror planes, and both axes have 180-degree rotation symmetry. Atoms are at corners. Cell has 180-degree rotation symmetry and two planes with mirror symmetry. Atoms have 2 atoms 1 unit away, 2 atoms farther away, and 4 atoms even farther away. Density is 6/12 = 0.5.
Oblique: Cell is a parallelogram with angles not 30, 45, 60, 90, or 120 degrees, as in fifth figure above. The two axes have unequal length, no axes are mirror planes, and both axes have 180-degree rotation symmetry. Atoms are at corners. Cell has 180-degree rotation symmetry and no planes with mirror symmetry. Each atom has 2 atoms 1 unit away, 2 atoms farther away, 2 atoms even farther away, and 2 atoms much farther away. Density is <6/12 < 0.5.
From most symmetric to least symmetric three-dimensional space lattices:
Isometric crystal: Cubic cell base is a square with angles 90 degrees, and height is perpendicular to base. All faces are squares. All axes have equal length. Atoms are at corners, can be in body center, and can be in face centers (three Bravais lattices). Point-group symmetry has three rotations by 90 degrees. For corners only, each atom has 4 atoms around in a plane and 2 atoms (above and below) along the perpendicular, total 6. For face-centered, corner atoms have 8 atoms around in a plane and 2 atoms (above and below) along the perpendicular, and centered atoms have 4 atoms around in a plane and 2 atoms (above and below) along the perpendicular. For body-centered, corner atoms have 4 atoms around in a plane, 2 atoms (above and below) along the perpendicular, and 4 atoms along diagonals, and centered atoms have 8 atoms along diagonals.
Hexagonal crystal: Cell base is a parallelogram with angles 120 and 60 degrees, and height is perpendicular to base. Two faces are parallelograms, and four faces are rectangles. Parallelogram axes have equal length, and height has any length. Atoms are at corners (one Bravais lattice). Point-group symmetry has one rotation by 60 degrees. Each atom has 6 atoms around in a plane and 2 atoms (above and below) along the perpendicular, total 8.
Tetragonal crystal: Cell base is a square, and height is perpendicular to base. Four faces are rectangles, and two faces are squares. Square axes have equal lengths, and height is not equal to square-side length. Atoms are at corners, and can be in body center (two Bravais lattices). Point-group symmetry has one rotation by 90 degrees. For corners only, each atom has 4 atoms around in a plane and 2 atoms (above and below) along the perpendicular, total 6. For body-centered, corner atoms have 4 atoms around in a plane, 2 atoms (above and below) along the perpendicular, and 4 atoms along diagonals, and centered atoms have 8 atoms along diagonals.
Rhombohedral crystal: Trigonal-point-group cell base is a rhombus, and height is not perpendicular to base. All faces are rhombuses. All axes have equal lengths. Atoms are at corners (one Bravais lattice). Point-group symmetry has one rotation by 120 degrees. Each atom has 4 atoms around in a plane and 2 atoms (above and below) along the perpendicular, total 6.
Orthorhombic crystal: Cell base is a rectangle, and height is perpendicular to base. All faces are rectangles. All axes have unequal lengths. Atoms are at corners, can be in body center, can be in base-face centers, and can be in all face centers (four Bravais lattices). Point-group symmetry has three rotations by 180 degrees and two mirror planes. For corners only, each atom has 4 atoms around in a plane and 2 atoms (above and below) along the perpendicular, total 6. For base-face-centered, corner atoms have 8 atoms around in a plane and 2 atoms (above and below) along the perpendicular, and centered atoms have 4 atoms around in a plane and 2 atoms (above and below) along the perpendicular. For all-face-centered, corner atoms have 8 atoms around in a plane and 2 atoms (above and below) along the perpendicular, and centered atoms have 4 atoms around in a plane, 4 atoms along diagonals, and 2 atoms (above and below) along the perpendicular. For body-centered, corner atoms have 4 atoms around in a plane, 2 atoms (above and below) along the perpendicular, and 4 atoms along diagonals, and centered atoms have 8 atoms along diagonals.
Monoclinic crystal: Cell base is a parallelogram, and height is perpendicular to base. Two faces are parallelograms, and four faces are rectangles. The three axes have unequal length. Atoms are at corners and can be in face centers (two Bravais lattices). Point-group symmetry has one rotation by 180 degrees and one mirror plane. For corners only, each atom has 4 atoms around in a plane and 2 atoms (above and below) along the perpendicular, total 6. For face-centered, corner atoms have 8 atoms around in a plane and 2 atoms (above and below) along the perpendicular, and centered atoms have 4 atoms around in a plane and 2 atoms (above and below) along the perpendicular.
Triclinic crystal: Cell base is a parallelogram, and height is not perpendicular to base. All faces are parallelograms. All axes have unequal lengths. Atoms are at corners (one Bravais lattice). There are no point-group symmetries. Each atom has 4 atoms around in a plane and 2 atoms (above and below) along the perpendicular, total 6.
Lattices {primitive lattice} can have atoms at unit-cell corners.
Lattices {body-centered lattice} can have one or two atoms at unit-cell centers. Lattices {body-centered cubic close packing} can have atoms in cube centers, with identical atoms at cube corners.
Lattices {face-centered lattice} can have one atom in unit-cell face. Unit cells with different atoms {face-centered cubic close packing} can have atoms in cube centers and in cubic-unit-cell face centers.
Unit-cells {cubic close packing} can be cubic. Twelve identical atoms surround each atom, and every third layer is directly above another.
Unit cells {hexagonal close packing} can be hexagonal. Twelve identical atoms surround each atom, and alternate layers are directly above each other.
Unit crystals can have same structure after rotation around axis, reflection across axis, inversion through central point, translation along axis, or any combination {symmetry, crystal}. Nature has six symmetry groups: isometric, hexagonal, tetragonal, orthorhombic, monoclinic, and triclinic.
Symmetry groups {hexagonal} can have rotation by 60 degrees. Hexagonal crystals have one six-fold axis, with one axis perpendicular to the other two axes but with different length, and two axes with same length at 60-degree angle to perpendicular axis, and makes seven crystal classes.
Symmetry groups {cubic symmetry group} {isometric symmetry group} can have rotation by 90 degrees, reflection, and inversion.
Symmetry groups {monoclinic symmetry group} can have rotation by 90 degrees. Crystals {monoclinic crystal}| can have one two-fold axis, two perpendicular same-length axes, and one non-perpendicular different-length axis, to make three crystal classes.
Symmetry groups {orthorhombic symmetry group} can have rotation by 180 degrees and reflection. Crystals {orthorhombic crystal} can have three two-fold axes, which are all perpendicular but have different lengths, to make three crystal classes.
Symmetry groups {tetragonal symmetry group} can have rotation by 90 degrees. Crystals {tetragonal crystal} can have one four-fold axis and three perpendicular axes but only two with same length, to make seven crystal classes.
Symmetry groups {triclinic symmetry group} can have rotation by 120 degrees. Crystals {triclinic crystal}| can have three axes, all not perpendicular but all of same length, to make two crystal classes.
Substances can mix with other substances {mixture}|. Mixed-substance chemical potential is less than pure-substance chemical potential, because mixtures have more disorder.
Liquid can be suspension in gas {aerosol}|, like dust and fog.
Liquid can be suspension in liquid {emulsion, mixture}|, like mayonnaise, cheese, and shaken salad dressing.
Liquid can be colloid in another liquid {sol, mixture}|, like india ink.
Gas can be suspension in liquid {foam}|, like whipped cream and foam rubber.
Solid can be colloid in liquid {gel}|, like jelly.
Mixing two substances can make one phase or solution {homogeneous phase}, with no boundaries.
Two substances can mix {heterogeneous phase} but have boundaries between different regions.
Mixtures {colloid}| with particle diameters 1 to 100 nanometers are translucent or opaque, separable by fine membranes, and settle slowly. Solutions can have many small particles, which attract an opposite-charge ion layer, which then attract an ion layer. Layers prevent good precipitation. Hydrophilic colloids are viscous, hard to coagulate, and gel-like. Hydrophobic colloids are sols, make curds, and are easy to coagulate.
Mixtures {suspension}| can have particles with diameter greater than 100 nanometers, be translucent or opaque, be separable by coarse membranes, and settle quickly.
Solvent molecules can surround solute molecules, to make one phase {solution, chemistry}|. Liquid solutions are transparent, because they are one phase with no surfaces for light reflection. To find solution substance concentration, divide substance moles by volume in liters of solution, not just solvent.
Membrane allows solvent molecules to pass but not solute molecules. If membrane separates solution from another solution, solvent passes into solution with higher solute concentration, because more solvent molecules hit membrane on side with less solute and pass through to other side {osmosis}|.
For example, solvent can be water, with many solute molecules inside membrane bag. See Figure 1.
pressure
Osmosis increases solvent amount on membrane side with higher solute concentration, causing extra pressure on that membrane side. The osmotic pressure resists further osmosis, because number of solvent molecules hitting both membrane sides becomes equal.
For example, water passes into bag, making bag bigger and stretching it. Membrane is under pressure. The extra water inside causes higher pressure inside, meaning more water molecules hit membrane inside. See Figure 2.
chemical potential
Mixtures have higher chemical potential than pure liquids, so pure liquid goes from pure-liquid membrane side to mixture membrane side, raises liquid level on mixture side, and lowers chemical potential. Chemical-potential decrease generates osmotic pressure, which tries to bring system into equilibrium.
small solutes
Membrane can allow small solute molecules and ions to pass through, but not large solute molecules. Small molecules diffuse through membrane, tending to make small-solute molecule concentrations equal on both membrane sides.
Osmosis increases solvent amount on membrane side with higher concentration, causing extra pressure {osmotic pressure}| on membrane from that side. The extra pressure resists further osmosis, as number of solvent molecules hitting both sides becomes same.
Solvents can have electronegative atoms {polarity}|.
types
Polar solvents include water, ethyl alcohol, and methyl alcohol. Acetone is slightly polar. Benzene is non-polar.
solution
Like dissolves like. Polar solvents can dissolve in each other. Non-polar solvents can dissolve in each other. Sticky non-polar solids are harder to dissolve in non-polar solvents, because they do not break up. Acetone, methyl alcohol, ethyl ether, and ethyl alcohol are soluble in water. Benzene, carbon tetrachloride, chloroform, hexane, cyclohexane, methylene chloride, toluene, and xylene are insoluble in water.
Solid can dissolve in water to make ion solutes {electrolyte}|.
Two liquids {immiscible liquids}| can be unable to dissolve in each other, like benzene and water.
Two liquids {miscible liquids}| can dissolve in each other, like alcohol and water.
Material true concentration or partial pressure {partial molar quantity} depends on other-substance concentrations or partial pressures, because having different substances contributes more disorder to system. Substances interact, because system has total pressure, temperature, and concentration.
Material true concentration or partial pressure {chemical potential, solution}| {free energy per mole} depends on partial molar quantity, because having different substances contributes more disorder to system. Substances interact, because system has total pressure, temperature, and concentration that distribute among substances. Substance partial molar Gibbs free energy is partial derivative of free energy with substance moles, if temperature, pressure, and other-substance amounts are constant.
Gas solubility in liquid is proportional to partial pressure of gas in contact with liquid {Henry's law} {Henry law}.
Gases in mixtures independently contribute pressure {partial pressure} to total gas pressure {law of partial pressures}.
Solute-vapor partial pressure above solution equals solute mole fraction times pure-solute vapor pressure {Raoult's law} {Raoult law}.
Pure substances have molar quantities, but mixtures have partial molar quantities, which depend on material moles divided by total moles, the mole fraction. Solution properties {colligative property}|, such as partial pressures, boiling point elevation, freezing point depression, osmotic pressure, solubility, volatility, and surface tension, can depend on solute mole fraction. Partial molar quantities are interdependent, because mole fraction total must be one.
Solutions have higher boiling point than pure solvent {boiling point elevation}|, because solute molecules are heavier than solvent molecules and have lower volatility. If liquid includes impurities that are less volatile than liquid, liquid boils only at higher temperature. Salt in water raises boiling temperature. Mixture boiling point is higher, because mixtures are more random, so difference between liquid and gas is less. Immiscible substances lower boiling point, because both vapor pressures add to increase pressure. In boiling-point elevation, temperature change dT equals constant k times molality M: dT = K*M. People know constants for solutes and solvents.
Solutions have lower freezing point than pure solvent {freezing point depression}|, because solute molecules are impurities in solvent crystals and so make crystals harder to form. In freezing-point depression, temperature change dT equals constant k times molality M: dT = K*M. People know constants for solutes and solvents.
Solid solute molecules can crystallize and separate from liquid solvent molecules {precipitation from solution}|.
causes
Decreasing solubility causes precipitation. Solubility decreases by cooling. Solubility decreases by adding organic non-polar solvents, such as acetone and ethanol, to water solution.
polarity
Solubility decreases by neutralizing solution to reduce acidity and polarity. Adding concentrated ammonium sulfate usually causes precipitation from aqueous solution. Molecules precipitate best at isoelectric points, because they have least polarization there.
types
Precipitates {lyophobic}, like sulfur and metal salts, can be small pellet-like precipitates, with molecules that reject water and adsorb ions. Precipitates {lyophilic}, like starch and gelatin, can be large curd-like precipitates, with molecules that adsorb water.
Crystals can precipitate from solution {fractional crystallization}, by evaporating solvent, by cooling solution, or by adding another solvent to solution.
At temperature, a number of solute grams can dissolve in 100 milliliters of solvent {solubility}|. If solubility is greater than one percent, solute can dissolve well in solvent {soluble}.
water solubility
Compounds have solubility in water {aqueous solubility}. Nitrates, acetates, chlorides, bromides, most iodides, most sulfates, sodium salts, potassium salts, and ammonium salts are soluble in water.
Hydroxides except sodium hydroxide and potassium hydroxide; sulfides except sodium sulfide, magnesium sulfide, and aluminum sulfide; arsenates except sodium arsenate and potassium arsenate; carbonates except sodium carbonate and potassium carbonate; and phosphates except sodium phosphate and potassium phosphate are insoluble in water.
precipitation
Solubility is maximum concentration before precipitation from solvent. For precipitation, concentration product {solubility product} must be greater than equilibrium constant.
factors
Solute solubility in solvent depends on solute polarity, size, and surroundableness and solvent polarity, size, and surroundability.
factors: temperature
Higher temperature increases solubility, because increased random motion breaks up and mixes solute and solvent more.
factors: concentration
Low concentration increases solubility, because solvent molecules can better surround solute molecules, with less solute molecules near other solute molecules.
factors: stirring
Stirring increases solubility, because more motion mixes solute and solvent more.
factors: ions
More hydrogen ion increases solubility in polar solvent, by increasing polarity. More ions increase solubility in polar solvent, by increasing polarity.
Ionic solutes with large ions and large charges are harder to dissolve. Ionic solutes with small ions and charges of +1 or -1 are easier to dissolve. Large ions with charge +1 or -1 dissolve better than small ions with charge +2, -2, +3, -3, or greater. Salts with small volume, especially hydrogen ions and acids, increase solubility by allowing more shielding. Higher-charge salts increase solubility more, because they shield better. Salts that form metal-ion complexes increase solubility, by more shielding.
factors: common ion
Low concentration of ion common to two solutes increases solubility, because solvent molecules can better surround solute molecules, with less solute molecules near other solute molecules. Common ion provides more molecules for collision. Solubility decreases if common ion is present in large amounts, because the other ion must then be at low concentration to equal solubility product.
factors: diverse ion
Solubility increases if diverse ion is present, because charges have more shielding and polarity increases.
factors: polarity
Similar-polarity molecules dissolve each other best, because electrical attractions for similar molecules are stronger.
factors: size
Small molecules dissolve better, because solvent molecules can better surround solute molecules.
factors: shape
Spherical molecules dissolve better than elongated ones, because solvent molecules can better surround spherical molecules.
When water molecules surround ions, energy {energy of hydration} {hydration energy}| releases. Small atoms have more hydration than large ones, because water surrounds them better.
Solvent molecules can surround other-substance {solute} molecules.
Solubility can decrease by adding salt with common ion and higher solubility, to make higher concentration and force solute out of solution {common ion effect}.
Ions in solution increase polarity and increase solubility {Debye-Hückel law}.
Substance {solvent, chemistry}| molecules can surround solute molecules.
Solvent is usually water {aqueous solution}.
Solvent can be alcohol {tincture}|.
Solid can dissolve in another solid {alloy}|, as in steel, bronze, and brass. Steel is carbon in iron. Bronze is tin in copper. Brass is zinc in copper.
Liquid can dissolve solid {amalgam}|, as metals can dissolve in mercury.
Solutions have ratio {concentration}| of solute mass or volume to total solution or solvent mass or volume.
Concentration {molal} can measure number of solute moles dissolved in one solution kilogram.
Concentration {molar, concentration} (M) can measure number of solute moles dissolved in one solution liter.
Concentration {mole fraction} can measure number of solute moles dissolved in one solution mole.
Concentration {normal, concentration} (N) can measure number of solute-ion equivalents dissolved in one solution liter.
Concentration {parts per million} (ppm) can measure number of solute milligrams dissolved in one solution liter.
Concentration {percent solution} can measure number of solute grams or milliliters dissolved in 100 solution grams or milliliters.
Solutions {dilute solution}| can have low concentration.
Solutions {concentrated solution} can have high concentration.
Solutions {saturated solution}| can have maximum concentration, at temperature, if dissolved solute is in contact with solid solute.
At a temperature, if no solid is present and solution has no crystallization, solution can have concentration higher than saturated concentration {supersaturated}|.
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Date Modified: 2022.0225