Formulae and Definitions and Constants
Boyle's Law |
At constant temperature, volume occupied by fixed amount of gas inversely proportional to the applied pressure |
pV = pV |
Charles' Law |
At constant pressure, volume of a fixed amount of gas directly proportional to its absolute temperature |
V/T = V/T |
Avogadro's Law |
At the same temperature and pressure, = volumes of any gas contains the same number of particles |
V ∝ n |
Dalton's Law of partial pressure |
In a mixture of gases which do not interact with one another, the total pressure of the mixture is the sum of the partial pressure of the constituent gases |
P = P + P + P |
Pressure |
Force per unit area |
R |
Gas constant |
Partial pressure |
The pressure exerted by the gas if it alone occupies the container at the same temperature |
P = x ⋅ P(total) |
General gas law / Ideal gas law |
(pV)/T = (pV)/T |
Density, d |
m/V |
Molar mass |
(mRT)/pV |
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(dRT)/p |
Mole fraction (x) |
nA / (nA + nB) |
Vapour pressure |
Pressure exerted by a vapour in equilibrium with its liquid at a fixed temperature |
Boiling point |
Temperature at which its vapour pressure equals external pressure |
Volatility |
The readiness of a liquid to evaporate |
Crystal lattice |
Regular arrangement of atoms, molecules or ions |
Unit cell |
Small repeating unit that makes up a crystal |
Crystal system |
Method of classifying crystalline substances based on their unit cellst |
Coordination number |
Number of nearest neighbouring atoms that are in direct contact with a given atom |
Allotropes |
Different structural forms of the same element |
Allotropy |
Elements that can exist in more than one crystalline structural form (under same temperature and pressure) |
Solids
Fixed volume and shape |
Particles closely packed, strongly held in fixed positions by strong attractive forces |
Extremely difficult to compress |
Definitions and formulae again
Forward |
Left to right |
Backward |
Right to left |
Chemical equilibrium |
Rates of forward and backward reaction are equal (conc const) |
Dynamic equilibrium |
Both forward and reverse reactions continue indefinitely even though chemical equilibrium is attained |
Law of mass action / equilibrium law |
Kc = [product]x / [reactant]y |
Equilibrium constant of concentratoin |
Kc |
Equilibrium partial pressure of the gases present |
Kp = (product)x / (reactant)y |
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K = 1/K^-1 |
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Kp - Kc(RT)^Δn |
Heterogeneous equilibrium |
Rreactants and products are present in more than one phase |
Le Chatelier's Principle |
If an external stress is applied to a system at equilibrium, the system adjusts in such a way that the stress is partially offset as the system reaches a new equilibrium position |
Isolated system |
No exchange of matter or energy between the system and its surroundings |
Electrolyte |
Chemical compound that will conduct electricity in molten state or aqueous solution |
Strong electrolyte |
Compound which is fully dissociated into ions when in molten or aqueous solution |
Weak electrolyte |
Partially dissociates " " |
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1 - α (almost) = 1 |
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Ka = cα^2 |
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α = √(Ka / c ) |
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[H+] = cα / √(Ka x c ) |
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pKa = -log Ka |
Equivalence point |
The point at which there are equal amounts of H3O+ and OH- in the titration flask= |
End point |
The point at which the indicator changes colour |
Buffer solution |
Solution that keeps its pH almost the same |
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pH = pKa + log [salt]/[acid] |
Henderson-Hasselbalch equation |
pOH = pKb + log [salt]/[base] |
Buffer capacity |
[acid] = [salt] |
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Maxwell-Boltzmann Distribution Curve
Particles at constant temperature, constant random motion |
Speed of particles varies, wide range |
Most particles move at a speed very close to the average |
Peak of each curve = most probable speed |
Area under the curve = total number of gas particles |
Areas under both curves are equal |
Increase in temperature, increase in motion |
Curve shifts right and flattens out |
At higher temperature, less most probable speed, more high speed particles |
Average kinetic energy same |
Lighter molecules move faster than heavier molecules |
Vaporisation
Open container |
Water molecules at surface gain energy, change to water vapour |
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Water vapour molecules escape into air |
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Volume decrease |
Closed container |
Water vapour cannot escape |
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Vapour formed, molecules collide with wall of container (vapour pressure) |
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Some vapour molecules lose energy, condense |
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Vaporisation and condensation occur continuously, dynamic equilibrium |
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Rate of vaporisation = Rate of condensation (saturated vapour pressure) |
Allotropes of carbon
Diamond |
Hard |
Interconnected, 3D array of strong covalent bonds |
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Geometrical rigidity |
Insulator |
Four valence electrons used in bonding |
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No free mobile electrons |
Insoluble |
Strong covalent bond network |
Very high melting point |
Strong covalent bond network |
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Large amount energy |
Graphite (sp3 hybridisation, layered) |
Soft and slippery |
Weak vdW between layers, slide over easily |
Electrical conductor |
Delocalised p electrons free to move |
Insoluble |
Strong covalent bond network |
Very high melting point |
Strong covalent bonds within layers |
Fullerene, C60, 20 hexa, 12 penta, sp2 hybridised |
Soft and slippery |
Covalent bonds in molecules |
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Weak vdW between molecules |
Electrical insulator |
No free electrons |
Insoluble in water |
Bonded very tightly |
Kinetic Concept of Liquid
A liquid has fixed volume, shape follows container |
Greater forces of attraction than gas, less than solid |
Particles move randomly (vibrational, rotational, some translational) |
Particles closely packed (not easily compressed) |
Equilibrium constant and position of equilibrium
Qc < Kc |
Left to right |
Qc = Kc |
no change |
Qc > Kc |
Right to left |
Buffer solution
Conditions |
Enough acid to react with any base added |
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Enough base to react with any acid added |
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Acid and base in buffer do not neutralise each other completely |
Types |
Acidic buffer |
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Basic buffer |
Assumptions to calculate pH of acidic buffers |
[HA] assumbed to be the concentration of acid used (acid very slightly dissociated) |
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[A-] assumed to be concentration of salt used (salt fully dissociates, concentration of A- by weak acid negligible) |
Explanation for titration |
Initially, pH falls significantly |
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pH falls slowly (buffer zone) |
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mixture of unreacted weak base and salt, () formed |
Preparation |
Dissolving () mol of () and 1 mol of () in water and diluting to 1dm^3 |
Lattice structure
Metallic solid |
Body centered cubic / face centered cubic / hexagonal close packed |
Copper: face centered cubic, coordination number: 12 |
Simple molecular solid |
Lattice points occupied by molecules |
Attractive force: vdW, Between iodine: covalent bonds |
Iodine: Face centered cubic |
Ionic solid (NaCl) |
Held by strong electrostatic forces |
Two interpenetrating face-centered cubic arrays |
6:6 coordination number |
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Ideal Gas Concept
Molecules occupy negligible volume compared to the volume of the container |
There are no forces of attraction between the molecules |
Deviation
Reasons |
Gas molecules have finite volume |
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Intermolecular forces of attraction |
Positive deviation |
Cause |
Repulsion forces |
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Finite volume of particles |
Explanation |
Very high pressure, volume of container very small |
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Particles very close together, repulsion forces |
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Particles collide with walls more often |
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Exerted pressure greater |
Negative deviation |
Cause |
Intermolecular forces of attraction |
Explanation |
External pressure increase, particles move closer together |
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Attractive forces occur |
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Particles collide less frequently with container |
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Exerted pressure lower |
Ideal behaviour |
Low pressure (no intermolecular forces) |
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High temperature (high kinetic energy) |
Vapour pressure & Boiling point & Volatility
Vapour Pressure |
Causes |
Collision of particles onto the wall of the container |
Factors |
Temperature |
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Temperature increase, more fraction of molecules move fast enough to escape surface of liquid |
Boiling point |
Factors |
External pressure |
Volatile liquid |
Characteristics |
Higher VP |
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Lower BP |
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Weak intermolecular forces (high tendency escape become vapour) |
* liquid boils when vapour pressure equals external pressure |
bubbles of vapour formed in liquid, escape to atmosphere, VP high enough overcome ext P |
Kinetic Theory of Gases
The gas consists of tiny particles of negligible volume |
Intermolecular forces of attraciton do not exist between gas particles |
The molecules of a gas are in continuous random motion |
The gaseous particles are perfectly elastic |
The average kinetic energy of the gas molecules is directly proportional to the absolute temperature |
Le Chatelier's Principle
Types of solids
Crystalline |
Well-defined shape |
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Particles occur in orderly arrangement |
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Ice, diamond, NaCl |
Amorphous |
Poorly defined shape |
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No long range ordering |
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Glass, rubber, plastic |
Acids and bases
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Acid |
Base |
Arrhenius Theory |
Substances which dissociate in water to produce H+ |
Substances that dissolve in water to produce OH- |
Bronsted-Lowry Theory |
Substances which donate a proton |
Substances which accept a proton |
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Conjugate base |
Conjugate acid |
Lewis Theory |
Electron pair acceptor |
Electron pair donor |
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Strength |
Ability to form H3O+ or OH- (Arrhenius theory) |
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Accept or donate protons (Bronsted-Lowry) |
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Strong acids |
Greater tendency to donate proton |
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Equilibrium more to the right |
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Difficult for conjugate base to accept the proton (weak conjugate base) |
Weak acids |
Position of equilibrium indicates the extent of dissociation of acid, acid strength |
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Acid stronger, Ka bigger |
Indicators
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pK(HIn) |
pH range |
Acid |
Alkali |
Methyl orange |
3.7 |
3.2 - 4.2 |
Red |
Yellow |
Methyl red |
5.1 |
4.2 - 6.3 |
Red |
Yellow |
Bromothymol blue |
7.1 |
6.0 - 7.6 |
Yellow |
Blue |
Phenolphthalein |
9.3 |
8.2 - 10.0 |
Colourless |
Pink |
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Explaination |
pH changes before equivalence point |
pH changes at the equivalence point |
pH chages after the equivalence point |
Choice of indicator |
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