Unit 3 Beta

Properties of Substances and Mixtures: the one-page sheet

3.1 Intermolecular and Interparticle Forces

Particles attract each other by London dispersion forces (all particles, stronger with more electrons), dipole-dipole forces (polar molecules), hydrogen bonds (H on N, O or F to a lone pair on N, O or F) and ion-dipole forces. These forces, not covalent bonds, are overcome when a substance melts or boils, so stronger forces mean higher melting and boiling points.

Intermolecular forces act between particles; covalent bonds act inside them. Boiling and melting never break covalent bonds.
Dispersion forces act in all substances and grow with the number of electrons and contact area, not with mass as such.
Hydrogen bonds need H on N, O or F in one molecule and a lone pair on N, O or F in another.
To compare boiling points, name every force in both substances, then decide which attraction is larger.

momentary dipoles attract their neighbors: London dispersion forces act in every substance dispersion forces grow with polarizability, so boiling points rise down a group neighbors line up and add dipole-dipole forces it attracts a lone pair on N, O or F of another molecule: a hydrogen bond more energy is needed to separate them, so melting and boiling points rise

intermolecular force: An attraction between separate particles (molecules, atoms or ions), as opposed to a bond inside one particle. Intermolecular forces are much weaker than covalent bonds.
polarizability: How easily a particle's electron cloud is distorted. More electrons, held farther from the nucleus, make a particle more polarizable.
London dispersion force: The attraction between momentary dipoles in neighboring particles. It acts between all particles and grows with polarizability and contact area.
dipole-dipole force: The attraction between the δ+ end of one polar molecule and the δ− end of another.
dipole-induced dipole: The attraction between a polar molecule and the dipole it creates in a nearby nonpolar particle.
hydrogen bond: A strong dipole-dipole attraction between an H atom bonded to N, O or F and a lone pair on an N, O or F atom of another molecule.
ion-dipole force: The attraction between an ion and the oppositely charged end of a polar molecule, such as Na⁺ and the oxygen end of water.
boiling point: The temperature at which a liquid boils. The normal boiling point is at sea-level air pressure; stronger attractions between particles raise it.
melting point: The temperature at which a solid turns to liquid. Stronger attractions between particles raise it.

3.2 Properties of Solids

Solids are ionic, metallic, molecular or covalent network. Molecular solids are molecules held by intermolecular forces: soft, low-melting and nonconducting. Covalent network solids are one continuous web of covalent bonds: very hard, very high-melting and (except graphite) nonconducting.

Ask what the particles are and what holds them: ions (ionic bonds), cations and electrons (metallic), molecules (IMFs) or atoms (covalent network).
Molecular solids melt low and never conduct; covalent network solids melt very high and are very hard.
Crystalline solids have repeating order and sharp melting points; amorphous solids soften over a range.

melting overcomes weak attractions, so they melt low and are soft molecular solids do not conduct in any state melting must break covalent bonds, so network solids melt very high and are very hard most network solids do not conduct

molecular solid: A solid made of separate molecules held to each other by intermolecular forces. Molecular solids are soft, melt at low temperatures and do not conduct electricity.
covalent network solid: A solid in which every atom is covalently bonded to its neighbors in one continuous web, such as diamond or quartz. Very hard, with very high melting points.
crystalline solid: A solid whose particles are arranged in an ordered pattern that repeats in every direction. An amorphous solid, such as glass, has no such long-range order.

3.3 Solids, Liquids, and Gases

Solids, liquids and gases differ in how close their particles are and how they move. Phase changes overcome or form attractions but keep molecules whole. In a sealed container evaporation and condensation reach a dynamic equilibrium; the vapor's pressure, the vapor pressure, rises with temperature and with weaker attractions, and a liquid boils when it equals the outside pressure.

Solid: touching, fixed, vibrating. Liquid: touching, sliding. Gas: far apart, flying freely.
Phase changes overcome or form attractions between particles; molecules stay whole.
1 atm = 760 torr = 760 mm Hg = 101.325 kPa.
Every liquid has a vapor pressure at every temperature. It rises with temperature and is higher when intermolecular forces are weaker.

some at the surface escape their neighbors' attractions, at any temperature escape and return reach equal rates: a dynamic equilibrium the vapor exerts a steady pressure, the vapor pressure vapor pressure is higher lower air pressure means a lower boiling point

state of matter: Solid, liquid or gas: the arrangement and motion of a substance's particles. Solid particles vibrate in place, liquid particles slide past each other, gas particles fly freely far apart.
pressure: The force per unit area from gas particles hitting a surface. 1 atm = 760 torr = 760 mm Hg = 101.325 kPa.
phase change: A change of state (melting, freezing, vaporization, condensation, sublimation, deposition) that rearranges particles but does not change what they are.
dynamic equilibrium: A state in which two opposite processes run at equal rates, so nothing changes overall, such as evaporation and condensation in a sealed container.
vapor pressure: The pressure of a substance's vapor in equilibrium with its liquid (or solid) in a closed container. It rises with temperature and is higher for liquids with weaker intermolecular forces.

3.4 Ideal Gas Law

The ideal gas law, PV = nRT, links pressure, volume, kelvin temperature and moles of a gas; R must match the units. The combined gas law follows one sample through a change. The law also gives molar mass and density, and in a mixture each gas has a partial pressure equal to its mole fraction times the total.

PV = nRT. T in kelvin; with atm and L, R = 0.08206 L·atm/(mol·K).
For one sample under new conditions: P₁V₁/T₁ = P₂V₂/T₂.
At STP (0 °C, 1 atm) one mole of gas fills 22.4 L. Molar mass from gas data: M = mRT/PV = dRT/P.
P(total) = P(A) + P(B) + …; P(A) = X(A) × P(total).

more particles (n) or faster particles (higher T) raise the pressure pressure and volume are inversely proportional at fixed n and T knowing three variables gives the fourth, with T in kelvin and R matched to the units partial pressures add, and each equals its mole fraction times the total

ideal gas law: PV = nRT: the equation linking the pressure, volume, kelvin temperature and moles of a gas that behaves ideally.
gas constant: R in PV = nRT: 0.08206 L·atm/(mol·K) with atm and liters, or 8.314 J/(mol·K) in SI units.
combined gas law: P₁V₁/T₁ = P₂V₂/T₂, for one sample of gas changing conditions; temperatures in kelvin.
STP: Standard temperature and pressure: 0 °C (273.15 K) and 1 atm. One mole of an ideal gas occupies 22.4 L at STP.
partial pressure: The pressure one gas in a mixture would exert alone in the same container. The partial pressures add up to the total pressure (Dalton's law).
mole fraction: The moles of one component divided by the total moles of a mixture. In a gas mixture, P(A) = X(A) × P(total).

3.5 Kinetic Molecular Theory

The kinetic molecular theory models a gas as tiny particles in constant random motion, with no attractions and elastic collisions, whose average kinetic energy is proportional to kelvin temperature. It explains pressure and the gas laws, and why lighter gases move faster at the same temperature. Speeds follow a Maxwell-Boltzmann distribution that shifts right and flattens as temperature rises.

Model: tiny particles, negligible volume, no attractions, elastic collisions, average KE ∝ kelvin T.
Same temperature means same average kinetic energy; lighter particles move faster, by the square root of the mass ratio.
Pressure comes from collisions with the walls: more particles, less volume or higher temperature all raise it.
Maxwell-Boltzmann curves: higher T or lighter gas moves the peak right and makes it lower and wider; the area is constant.

they keep moving and hitting the walls, which is the pressure heating speeds particles up, so they hit the walls more often and harder lighter particles move faster speeds form a Maxwell-Boltzmann distribution that shifts and flattens as temperature rises

kinetic energy: The energy of motion, KE = ½mv². The average kinetic energy of gas particles is proportional to the kelvin temperature.
kinetic molecular theory: The kinetic molecular theory: a model of an ideal gas as tiny particles in constant random motion that do not attract each other and collide elastically, with average kinetic energy proportional to kelvin temperature.
thermal energy: The energy a sample holds because its particles move. Heating a sample adds thermal energy.
Maxwell-Boltzmann distribution: A graph of the fraction of gas particles at each speed (or energy). A higher temperature or a lighter gas moves its peak to higher speeds and flattens it.

3.6 Deviation from Ideal Gas Law

Real gases depart from PV = nRT because their particles attract each other, which lowers the pressure, and take up space, which raises the volume at very high pressure. Deviations are largest at high pressure and low temperature and for particles with strong intermolecular forces; gases are most ideal at high temperature and low pressure.

Ideal gas: PV/nRT = 1. Below 1, attractions dominate; above 1, particle volume dominates.
Attractions lower the pressure: worst for polar or polarizable molecules, at low T and high P.
Particle volume raises the volume: worst at very high P and for large molecules.
Most ideal: high temperature, low pressure, small particles with weak attractions.

a particle near the wall is pulled back, so the measured pressure is lower than ideal deviations grow at high pressure and low temperature at very high pressure the real volume is larger than ideal real gases behave most ideally there, especially small, weakly attracting ones like He

real gas: A gas whose particles have volume and attract each other, so it departs from PV = nRT. Deviations are largest at high pressure and low temperature and for particles with strong attractions.

3.7 Solutions and Mixtures

A solution is a homogeneous mixture of a solute in a solvent. Molarity is moles of solute per liter of solution, made precisely with an analytical balance and a volumetric flask filled to the mark. Diluting keeps the moles of solute, so M₁V₁ = M₂V₂ with V₂ the total volume. Ionic solutes give ions, so their solutions conduct.

M = mol solute / L solution. Convert mL to L first.
Prepare: analytical balance, volumetric flask, dissolve, dilute to the mark, invert.
Dilution: M₁V₁ = M₂V₂; V₂ is the total final volume.
Electrolytes give ions in water and conduct; count each ion: 0.10 M CaCl₂ is 0.20 M Cl⁻.

we state its concentration as molarity, moles of solute per liter of solution solutions are made up to the mark of a volumetric flask, not by adding a volume of water moles stay the same on dilution, so M₁V₁ = M₂V₂ with V₂ the total volume their solutions conduct electricity: they are electrolytes

solution: A homogeneous mixture: a solute (the dissolved substance) spread evenly through a solvent. In an aqueous solution, the solvent is water.
molarity: Concentration in moles of solute per liter of solution (mol/L, written M).
dilution: Making a solution weaker by adding solvent. The moles of solute stay the same, so M₁V₁ = M₂V₂, where V₂ is the final total volume.
volumetric flask: A flask made to hold one exact volume, marked by a line on its neck; used with an analytical balance to prepare solutions of known molarity.
electrolyte: A solute whose aqueous solution conducts electricity because it contains moving ions. Strong electrolytes give many ions, weak ones few, nonelectrolytes none.

3.8 Representations of Solutions

When an ionic compound dissolves, ion-dipole attractions pull it apart into separate ions, and each is hydrated: water's oxygen faces cations and its hydrogens face anions. A correct particle diagram shows separate ions in the formula ratio, whole polyatomic ions, an even spread and zero total charge; molecular solutes stay as whole molecules.

Dissolved ionic compounds are separate, hydrated ions; molecular solutes stay as whole molecules.
Water orientation: O (δ−) toward cations, H (δ+) toward anions.
Keep the formula ratio (CaCl₂: 1 Ca²⁺ to 2 Cl⁻) and keep polyatomic ions whole.
Spread solute particles evenly: a solution is homogeneous.

they attract the ions at the surface of an ionic crystal the solid dissociates into separate ions water points O toward cations and H toward anions, forming a hydration shell a correct diagram keeps the formula ratio and a total charge of zero

dissociation: The separation of an ionic compound into its ions as it dissolves, such as NaCl(s) → Na⁺(aq) + Cl⁻(aq).
hydration: The surrounding of a dissolved particle by water molecules. Around a cation, water's oxygen points in; around an anion, a hydrogen points in.

3.9 Separation of Solutions and Mixtures

Mixtures are separated by physical properties that trace back to particle forces. Filtration removes undissolved solids by size. Chromatography separates components by their attraction to a stationary phase versus a mobile phase, measured by Rf. Distillation separates liquids by vapor pressure: weaker intermolecular forces vaporize first.

Filtration: undissolved solid from liquid, by size.
Chromatography: stronger attraction to the stationary phase means slower movement. Rf = spot distance ÷ solvent distance.
Paper is polar: polar components lag; a more polar solvent carries them farther.
Distillation: weaker intermolecular forces, higher vapor pressure, vaporizes first.

physical methods can separate them without changing them the one held more by the stationary phase moves more slowly and has a smaller Rf it boils off first and is collected first filtration removes solids but cannot separate a solution

chromatography: Separating a mixture by how strongly each component is attracted to a stationary phase (paper, a plate or a column) compared with a moving mobile phase. Rf = spot distance ÷ solvent-front distance.
distillation: Separating a mixture by boiling off the most volatile component and condensing its vapor. The component with weaker intermolecular forces vaporizes first.
filtration: Separating an undissolved solid from a liquid by passing the mixture through a filter; the liquid that passes through is the filtrate.

3.10 Solubility

A substance dissolves when the attractions it forms with the solvent are comparable to the solute–solute and solvent–solvent attractions it replaces, so like dissolves like. Long nonpolar chains lower solubility in water. Gases dissolve more at higher partial pressure and less at higher temperature.

Dissolving trades attractions: overcome solute–solute and solvent–solvent, form solute–solvent.
Like dissolves like: polar and ionic in polar, nonpolar in nonpolar.
Oil and water separate because water attracts itself far more strongly, not because they repel.
Gas solubility in water rises with partial pressure and falls with temperature.

it must form solute–solvent attractions of comparable strength to proceed many of them dissolve well in water they do not dissolve well in water but do in nonpolar solvents gases dissolve less as temperature rises, and more as their partial pressure rises

solubility: The amount of a substance that dissolves in a given amount of solvent at a given temperature. Substances dissolve well when solute-solvent attractions are comparable to the solute-solute and solvent-solvent attractions they replace ("like dissolves like").

3.11 Spectroscopy and the Electromagnetic Spectrum

Electromagnetic radiation ranges from radio waves to X-rays; shorter wavelengths carry more energy per photon. A molecule absorbs a photon only when its energy matches a gap between levels: microwaves change rotation, infrared changes vibration, and visible and ultraviolet light move electrons to higher levels. Spectroscopy uses these absorptions to identify substances.

Shorter wavelength, higher frequency, more energy per photon.
Microwave: rotation. Infrared: vibration. Visible and UV: electronic transitions. X-ray: core electrons removed.
A photon is absorbed only if its energy matches the gap between two levels.
A colored substance absorbs some visible light; we see the light it does not absorb.

radio < microwave < infrared < visible < ultraviolet < X-ray in energy a photon is absorbed only if its energy matches a gap microwaves rotate molecules, infrared vibrates bonds, visible and UV light promote electrons absorption spectra identify substances

electromagnetic spectrum: The full range of electromagnetic radiation, from long-wavelength radio waves through microwaves, infrared, visible and ultraviolet light to short-wavelength X-rays.
wavelength: The distance between neighboring crests of a wave (λ). Frequency (ν) is the number of crests passing a point per second; shorter wavelength means higher frequency and more energy per photon.
molecular vibration: Energy held in a molecule's bond vibrations or rotation. Infrared light changes vibrational energy; microwaves change rotational energy.
electronic transition: The move of an electron between energy levels, such as from the ground state to an excited state, caused by absorbing a visible or ultraviolet photon of matching energy.

3.12 Properties of Photons

Light travels at c = λν, so wavelength and frequency are inversely related. Each photon carries E = hν = hc/λ joules, and a mole of photons carries 6.022 × 10²³ times that. Energy levels are quantized, so atoms and molecules absorb or emit only photons whose energy equals a gap between levels.

c = λν with c = 2.998 × 10⁸ m/s; λ in meters (1 nm = 10⁻⁹ m).
E = hν = hc/λ with h = 6.626 × 10⁻³⁴ J·s. This is one photon, in joules.
Per mole: multiply by 6.022 × 10²³, then divide by 1000 for kJ/mol.
A photon is absorbed or emitted only when its energy equals a gap between levels.

c = λν, so wavelength and frequency are inversely proportional shorter wavelength, higher frequency, more energy per photon: E = hc/λ only photons whose energy matches a gap are absorbed or emitted each emits its own set of wavelengths, a line spectrum

photon energy: The energy of one photon, E = hν = hc/λ, where h = 6.626 × 10⁻³⁴ J·s is Planck's constant. Energy levels are quantized, so only photons of matching energy are absorbed or emitted.
speed of light: c = 2.998 × 10⁸ m/s, the speed of all electromagnetic radiation in a vacuum; c = λν links wavelength and frequency.

3.13 Beer-Lambert Law

A spectrophotometer measures how much light of one wavelength a solution absorbs. The Beer-Lambert law, A = εbc, makes absorbance proportional to concentration and path length. Measurements are made at λmax, and a calibration curve of standards gives an unknown's concentration; anything that adds absorbance, such as fingerprints or a missed blank, makes it read too high.

A = εbc: A unitless, ε in L/(mol·cm), b in cm, c in mol/L.
Measure at λmax, the wavelength of maximum absorbance.
Calibration curve: A against c is a straight line through the origin with slope εb.
Errors that add absorbance (fingerprints, no blank) make the concentration too high.

more particles in the path absorb more light absorbance is proportional to both: A = εbc measurements there are most sensitive to concentration an unknown's absorbance on that line gives its concentration

absorbance: A unitless measure of how much light of one wavelength a sample absorbs; 0 means none. Transmittance is the fraction of light that passes through.
Beer-Lambert law: A = εbc: absorbance equals the molar absorptivity ε (L/(mol·cm)) times the path length b (cm) times the concentration c (mol/L).
spectrophotometer: An instrument that passes light of a chosen wavelength through a sample in a cuvette and measures its absorbance. Measurements are made at λmax, and a calibration curve of standards gives an unknown's concentration.