GR 12 Physics and Chemistry Definitions

Newton's Laws and Applications of Newton's Laws

• Types of Forces:

  • Weight ($w$ or $F_g$): The gravitational force the Earth exerts on any object on or near its surface.
  • Normal Force ($N$ or $F_N$): The force or the component of a force which a surface exerts on an object with which it is in contact, and which is perpendicular to the surface.
  • Frictional Force ($f$ or $F_f$): The force that opposes the motion of an object and which acts parallel to the surface.
    • Static Frictional Force ($f_s$): The force that opposes the tendency of motion of a stationary object relative to a surface.
    • Kinetic Frictional Force ($f_k$): The force that opposes the motion of a moving object relative to a surface.
  • Applied Force: A push or a pull applied to an object.
  • Tension ($T$ or $F_T$): Force transmitted through strings or cables.

• Newton's First Law of Motion: A body will remain in its state of rest or motion at constant velocity unless a non-zero resultant/net force acts on it.

• Newton's Second Law of Motion: When a resultant/net force acts on an object, the object will accelerate in the direction of the force at an acceleration directly proportional to the force and inversely proportional to the mass of the object.

• Newton's Third Law of Motion: When one body exerts a force on a second body, the second body exerts a force of equal magnitude in the opposite direction on the first body.

• Newton's Law of Universal Gravitation: Each body in the universe attracts every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

Momentum and Impulse

• Momentum ($p$): The product of an object's mass and its velocity.

• Newton's Second Law of Motion in Terms of Momentum: The resultant/net force acting on an object is equal to the rate of change of momentum of the object in the direction of the resultant/net force.

• Impulse: The product of the resultant/net force acting on an object and the time the resultant/net force acts on the object.

• Impulse-Momentum Theorem:

$F_{net}\\nabla t = m\Delta v$

• Closed / Isolated System: A system on which the resultant/net external force is zero. A closed or isolated system excludes external forces that originate outside the colliding bodies (e.g., friction). Only internal forces (e.g., contact forces between colliding objects) are considered.

• Principle of Conservation of Linear Momentum: The total linear momentum of a closed system remains constant (is conserved).

Projectile Motion in One Dimension (1D)

• Projectile: An object upon which the only force acting is the force of gravity.

Work, Energy, and Power

• Work ($W$): The work done on an object by a constant force $F$ is given by:

$W = F\Delta x \cos(\theta)$

*   $F$ is the magnitude of the force.
*   $\Delta x$ is the magnitude of the displacement.
*   $\theta$ is the angle between the force and the displacement.

• Work-Energy Theorem: The net/total work done on an object is equal to the change in the object's kinetic energy OR the work done on an object by a resultant/net force is equal to the change in the object's kinetic energy. In symbols:

$W_{net} = \Delta K = K_f - K_i$

• Conservative Force: A force for which the work done in moving an object between two points is independent of the path taken.

  • Examples include: gravitational force, elastic force in a spring, and electrostatic forces (Coulomb forces).

• Non-Conservative Force: A force for which the work done in moving an object between two points depends on the path taken.

  • Examples include: frictional force, air resistance, tension in a cord, etc.

• Principle of Conservation of Mechanical Energy: The total mechanical energy (sum of gravitational potential energy and kinetic energy) in an isolated system remains constant. A system is isolated when the resultant/net external force acting on the system is zero.

• Power ($P$): The rate at which work is done or energy is expended.

Doppler Effect

• Doppler Effect: The change in frequency (or pitch) of the sound detected by a listener because the sound source and the listener have different velocities relative to the medium of sound propagation.

Electrostatics, Electric Fields, and Electric Circuits

• Coulomb's Law: The magnitude of the electrostatic force exerted by one point charge ($Q_1$) on another point charge ($Q_2$) is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance ($r$) between them.

• Electric Field: A region of space in which an electric charge experiences a force.

• Direction of an Electric Field: The direction of the electric field at a point is the direction that a positive test charge would move if placed at that point.

• Electric Field at a Point: The electrostatic force experienced per unit positive charge placed at that point.

• Ohm's Law: The potential difference across a conductor is directly proportional to the current in the conductor at constant temperature.

• Root Mean Square (rms) for Alternating Current / Voltage: The rms value of AC is the DC potential difference/current which dissipates the same amount of energy as AC.

Optical Phenomena and Properties of Materials

• Photoelectric Effect: The process whereby electrons are ejected from a metal surface when light of suitable frequency is incident on that surface.

• Threshold Frequency ($f_0$): The minimum frequency of light needed to emit electrons from a certain metal surface.

• Work Function ($W_0$): The minimum energy that an electron in the metal needs to be emitted from the metal surface.

• Atomic Absorption Spectrum: Formed when certain frequencies of electromagnetic radiation that passes through a medium (e.g., a cold gas) are absorbed.

• Atomic Emission Spectrum: Formed when certain frequencies of electromagnetic radiation are emitted due to an atom's electrons making a transition from a high-energy state to a lower energy state.

Organic Chemistry Structure, Functional Groups, and Isomerism

• Organic Molecules: Molecules containing carbon atoms.

• Hydrocarbon: Organic compounds that consist of hydrogen and carbon only.

• Homologous Series: A series of organic compounds that can be described by the same general formula OR in which one member differs from the next with a $\text{CH}_2$ group.

• Saturated Compounds: Compounds in which there are no multiple bonds between $\text{C}$ atoms in their hydrocarbon chains.

• Unsaturated Compounds: Compounds with one or more multiple bonds between $\text{C}$ atoms in their hydrocarbon chains.

• Functional Group: A bond or an atom or a group of atoms that determine(s) the physical and chemical properties of a group of organic compounds.

• Structural Representations:

  • Molecular Formula: A chemical formula that indicates the type of atoms and the correct number of each in a molecule.
  • Structural Formula: A structural formula of a compound shows which atoms are attached to which within the molecule. Atoms are represented by their chemical symbols and lines are used to represent ALL the bonds that hold the atoms together.
  • Condensed Structural Formula: This notation shows the way in which atoms are bonded together in the molecule, but DOES NOT SHOW ALL bond lines.

• Structural Isomers: Organic molecules with the same molecular formula, but different structural formulae.

  • Chain Isomers: Same molecular formula, but different types of chains.
  • Positional Isomers: Same molecular formula, but different positions of the side chain, substituents, or functional groups on the parent chain.
  • Functional Isomers: Same molecular formula, but different functional groups.

• Homologous Series and Functional Group Structures:

  • Alkanes: Only $\text{C}-\text{H}$ and $\text{C}-\text{C}$ single bonds.
  • Alkenes: Carbon-carbon double bond ($\text{C}=\text{C}$).
  • Alkynes: Carbon-carbon triple bond ($\text{C}\equiv\text{C}$).
  • Haloalkanes: Halogen atom ($\text{X} = \text{F, Cl, Br, I}$) bonded to a saturated $\text{C}$ atom ($\text{C}-\text{X}$).
  • Alcohols: Hydroxyl group bonded to a saturated $\text{C}$ atom ($\text{C}-\text{O}-\text{H}$).
  • Aldehydes: Formyl group ($\text{O}=\text{C}-\text{H}$).
  • Ketones: Carbonyl group bonded to two $\text{C}$ atoms ($\text{C}-\text{C}(=\text{O})-\text{C}$).
  • Carboxylic Acids: Carboxyl group ($\text{O}=\text{C}-\text{O}-\text{H}$).
  • Esters: Ester group ($\text{O}=\text{C}-\text{O}-\text{C}$).

Physical Properties of Organic Compounds and Intermolecular Forces

• Molar Volume of Gases: $1\,\text{mole}$ of any gas occupies $22.4\,\text{dm}^3$ at $0\,^\circ\text{C}$ ($273\,\text{K}$) and $1\,\text{atmosphere}$ ($101.3\,\text{kPa}$).

• Intermolecular Forces (Van der Waals Forces):

  • Dipole-Dipole Forces: Forces between two polar molecules.
  • Induced Dipole Forces or London Forces: Forces between non-polar molecules.
  • Hydrogen Bonding: Forces between molecules in which hydrogen is covalently bonded to nitrogen, oxygen, or fluorine – a special case of dipole-dipole forces.

• Physical Property Relationships:

  • Boiling Point: The temperature at which the vapour pressure of a substance equals atmospheric pressure. The stronger the intermolecular forces, the higher the boiling point.
  • Melting Point: The temperature at which the solid and liquid phases of a substance are at equilibrium. The stronger the intermolecular forces, the higher the melting point.
  • Vapour Pressure: The pressure exerted by a vapour at equilibrium with its liquid in a closed system. The stronger the intermolecular forces, the lower the vapour pressure.

Organic Reactions and Polymerisation

• Addition Reactions:

  • Hydrohalogenation: The addition of a hydrogen halide to an alkene.
  • Halogenation: The reaction of a halogen ($\text{Br}_2$, $\text{Cl}_2$) with a compound.
  • Hydration: The addition of water to a compound.
  • Hydrogenation: The addition of hydrogen to an alkene.

• Elimination Reactions:

  • Dehydrohalogenation of Haloalkanes: The elimination of hydrogen and a halogen from a haloalkane.
  • Dehydration of Alcohols: Elimination of water from an alcohol.
  • Cracking of Alkanes: The chemical process in which longer chain hydrocarbon molecules are broken down to shorter more useful molecules.

• Substitution and Other Reactions:

  • Hydrolysis: The reaction of a compound with water.

• Macromolecules and Polymers:

  • Macromolecule: A molecule that consists of a large number of atoms.
  • Polymer: A large molecule composed of smaller monomer units covalently bonded to each other in a repeating pattern.
  • Monomer: Small organic molecules that can be covalently bonded to each other in a repeating pattern.
  • Polymerisation: A chemical reaction in which monomer molecules join to form a polymer.
  • Addition Polymerisation: A reaction in which small molecules join to form very large molecules by adding on double bonds.
  • Addition Polymer: A polymer formed when monomers (usually containing a double bond) combine through an addition reaction.
  • Condensation Polymerisation: Molecules of two monomers with different functional groups undergo condensation reactions with the loss of small molecules, usually water.
  • Condensation Polymer: A polymer formed by two monomers with different functional groups that are linked together in a condensation reaction in which a small molecule, usually water, is lost.

Chemical Reaction Rates and Energy Changes

• Heat of Reaction ($\Delta H$): The energy absorbed or released in a chemical reaction.

• Exothermic Reactions: Reactions that release energy ($\Delta H < 0$).

• Endothermic Reactions: Reactions that absorb energy ($\Delta H > 0$).

• Activation Energy: The minimum energy needed for a reaction to take place.

• Activated Complex: The unstable transition state from reactants to products.

• Reaction Rate: The change in concentration of reactants or products per unit time.

• Factors Affecting Reaction Rate: Nature of reacting substances, surface area, concentration (pressure for gases), temperature, and the presence of a catalyst.

• Catalyst (Positive Catalyst): A substance that increases the rate of a chemical reaction without itself undergoing a permanent change. A catalyst increases the rate of a reaction by providing an alternative path of lower activation energy, thereby decreasing the net/total activation energy.

Chemical Equilibrium

• System Types:

  • Open System: Continuously interacts with its environment.
  • Closed System: Isolated from its surroundings.

• Reversible Reaction: A reaction is reversible when products can be converted back to reactants.

• Chemical Equilibrium: A dynamic equilibrium when the rate of the forward reaction equals the rate of the reverse reaction.

• Factors Influencing Position of Equilibrium: Pressure (gases only), concentration, temperature.

• Le Chatelier's Principle: When the equilibrium in a closed system is disturbed, the system will re-instate a new equilibrium by favouring the reaction that will oppose the disturbance.

Acids, Bases, and Aqueous Equilibria

• Arrhenius Theory:

  • Acid: A substance that produces hydrogen ions ($\text{H}^+$) / hydronium ions ($\text{H}_3\text{O}^+$) when it dissolves in water.
  • Base: A substance that produces hydroxide ions ($\text{OH}^-$) when it dissolves in water.

• Lowry-Brønsted Theory:

  • Acid: A proton ($\text{H}^+$ ion) donor.
  • Base: A proton ($\text{H}^+$ ion) acceptor.

• Strength of Acids and Bases:

  • Strong Acids: Ionise completely in water to form a high concentration of $\text{H}_3\text{O}^+$ ions.
  • Weak Acids: Ionise incompletely in water to form a low concentration of $\text{H}_3\text{O}^+$ ions.
  • Strong Bases: Dissociate completely in water to form a high concentration of $\text{OH}^-$ ions.
  • Weak Bases: Dissociate/ionise incompletely in water to form a low concentration of $\text{OH}^-$ ions.

• Concentration of Acids and Bases:

  • Concentrated Acids/Bases: Contain a large amount (number of moles) of acid/base in proportion to the volume of water.
  • Dilute Acids/Bases: Contain a small amount (number of moles) of acid/base in proportion to the volume of water.

• Conjugate Acid-Base Pairs: When the acid, $\text{HA}$, loses a proton, its conjugate base, $\text{A}^-$, is formed. When the base, $\text{A}^-$, accepts a proton, its conjugate acid, $\text{HA}$, is formed.

• Ampholyte / Amphiprotic Substance: A substance that can act as either an acid or as a base.

• Auto-Ionisation of Water: The reaction of water with itself to form $\text{H}_3\text{O}^+$ ions and $\text{OH}^-$ ions:

$2\text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^-$

• Equilibrium Constant for Water ($K_w$): The equilibrium constant for the ionisation of water or the ionic product of water or the ionisation constant of water:

$K_w = [\text{H}_3\text{O}^+][\text{OH}^-] = 1 \times 10^{-14}$

*   This numerical value applies at $298\,\text{K}$.

• Hydrolysis: The reaction of a salt with water.

• Titration Concepts:

  • Equivalence Point of a Titration: The point at which the acid/base has completely reacted with the base/acid.
  • Endpoint of a Titration: The point where the indicator changes colour.

Electrochemical Reactions

• Galvanic Cell: A cell in which chemical energy is converted into electrical energy. A galvanic (voltaic) cell has self-sustaining electrode reactions.

• Electrolytic Cell: A cell in which electrical energy is converted into chemical energy.

• Oxidation and Reduction in Terms of Electron ($e^-$) Transfer:

  • Oxidation: A loss of electrons.
  • Reduction: A gain of electrons.

• Oxidation and Reduction in Terms of Oxidation Numbers:

  • Oxidation: An increase in oxidation number.
  • Reduction: A decrease in oxidation number.

• Agents and Electrodes:

  • Oxidising Agent: A substance that is reduced / gains electrons.
  • Reducing Agent: A substance that is oxidised / loses electrons.
  • Anode: The electrode where oxidation takes place.
  • Cathode: The electrode where reduction takes place.

• Electrolyte: A solution/liquid/dissolved substance that conducts electricity through the movement of ions.

• Electrolysis: The chemical process in which electrical energy is converted to chemical energy OR the use of electrical energy to produce a chemical change.

Chemical Industry and Environment

• The Fertiliser Industry: Focuses on nitrogen ($\text{N}$), phosphorus ($\text{P}$), and potassium ($\text{K}$).

• Eutrophication: The process by which an ecosystem (e.g., a river or dam) becomes enriched with inorganic plant nutrients, especially phosphorus and nitrogen, resulting in excessive plant growth. As plant growth becomes excessive, the amount of dead and decaying plant material increases rapidly.

Physics Quantities, Symbols, and SI Units

• Mass:

  • Preferred Symbol: $m$
  • Unit Name: kilogram
  • Unit Symbol: $\text{kg}$

• Position:

  • Preferred Symbol: $x, y$
  • Unit Name: metre
  • Unit Symbol: $\text{m}$

• Displacement:

  • Preferred Symbol: $\Delta x, \Delta y$
  • Alternative Symbol: $s$
  • Unit Name: metre
  • Unit Symbol: $\text{m}$

• Velocity:

  • Preferred Symbol: $v_x, v_y$
  • Alternative Symbol: $u, v$
  • Unit Name: metre per second
  • Unit Symbol: $\text{m}\cdot\text{s}^{-1}$

• Initial Velocity:

  • Preferred Symbol: $v_i$
  • Alternative Symbol: $u$
  • Unit Name: metre per second
  • Unit Symbol: $\text{m}\cdot\text{s}^{-1}$

• Final Velocity:

  • Preferred Symbol: $v_f$
  • Alternative Symbol: $v$
  • Unit Name: metre per second
  • Unit Symbol: $\text{m}\cdot\text{s}^{-1}$

• Acceleration:

  • Preferred Symbol: $a$
  • Unit Name: metre per second per second
  • Unit Symbol: $\text{m}\cdot\text{s}^{-2}$

• Acceleration Due to Gravity:

  • Preferred Symbol: $g$
  • Unit Name: metre per second per second
  • Unit Symbol: $\text{m}\cdot\text{s}^{-2}$

• Time (instant):

  • Preferred Symbol: $t$
  • Unit Name: second
  • Unit Symbol: $\text{s}$

• Time Interval:

  • Preferred Symbol: $\Delta t$
  • Unit Name: second
  • Unit Symbol: $\text{s}$

• Energy:

  • Preferred Symbol: $E$
  • Unit Name: joule
  • Unit Symbol: $\text{J}$

• Kinetic Energy:

  • Preferred Symbol: $K$
  • Alternative Symbol: $E_k$
  • Unit Name: joule
  • Unit Symbol: $\text{J}$

• Potential Energy:

  • Preferred Symbol: $U$
  • Alternative Symbol: $E_p$
  • Unit Name: joule
  • Unit Symbol: $\text{J}$

• Work:

  • Preferred Symbol: $W$
  • Unit Name: joule
  • Unit Symbol: $\text{J}$

• Work Function:

  • Preferred Symbol: $W_0$
  • Unit Name: joule
  • Unit Symbol: $\text{J}$

• Power:

  • Preferred Symbol: $P$
  • Unit Name: watt
  • Unit Symbol: $\text{W}$

• Momentum:

  • Preferred Symbol: $p$
  • Unit Name: kilogram metre per second
  • Unit Symbol: $\text{kg}\cdot\text{m}\cdot\text{s}^{-1}$

• Force:

  • Preferred Symbol: $F$
  • Unit Name: newton
  • Unit Symbol: $\text{N}$

• Weight:

  • Preferred Symbol: $w$
  • Alternative Symbol: $F_g$
  • Unit Name: newton
  • Unit Symbol: $\text{N}$

• Normal Force:

  • Preferred Symbol: $N$
  • Alternative Symbol: $F_N$
  • Unit Name: newton
  • Unit Symbol: $\text{N}$

• Tension:

  • Preferred Symbol: $T$
  • Alternative Symbol: $F_T$
  • Unit Name: newton
  • Unit Symbol: $\text{N}$

• Friction Force:

  • Preferred Symbol: $f$
  • Alternative Symbol: $F_f$
  • Unit Name: newton
  • Unit Symbol: $\text{N}$

• Coefficient of Friction:

  • Preferred Symbol: $\mu, \mu_s, \mu_k$
  • Unit Name: none

• Torque:

  • Preferred Symbol: $\tau$
  • Unit Name: newton metre
  • Unit Symbol: $\text{N}\cdot\text{m}$

• Wavelength:

  • Preferred Symbol: $\lambda$
  • Unit Name: metre
  • Unit Symbol: $\text{m}$

• Frequency:

  • Preferred Symbol: $f$
  • Alternative Symbol: $\nu$
  • Unit Name: hertz or per second
  • Unit Symbol: $\text{Hz}$ or $\text{s}^{-1}$

• Period:

  • Preferred Symbol: $T$
  • Unit Name: second
  • Unit Symbol: $\text{s}$

• Speed of Light:

  • Preferred Symbol: $c$
  • Unit Name: metre per second
  • Unit Symbol: $\text{m}\cdot\text{s}^{-1}$

• Refractive Index:

  • Preferred Symbol: $n$
  • Unit Name: none

• Focal Length:

  • Preferred Symbol: $f$
  • Unit Name: metre
  • Unit Symbol: $\text{m}$

• Object Distance:

  • Preferred Symbol: $s$
  • Alternative Symbol: $u$
  • Unit Name: metre
  • Unit Symbol: $\text{m}$

• Image Distance:

  • Preferred Symbol: $s'$
  • Alternative Symbol: $v$
  • Unit Name: metre
  • Unit Symbol: $\text{m}$

• Magnification:

  • Preferred Symbol: $m$
  • Unit Name: none

• Charge:

  • Preferred Symbol: $Q, q$
  • Unit Name: coulomb
  • Unit Symbol: $\text{C}$

• Electric Field:

  • Preferred Symbol: $E$
  • Unit Name: newton per coulomb or volt per metre
  • Unit Symbol: $\text{N}\cdot\text{C}^{-1}$ or $\text{V}\cdot\text{m}^{-1}$

• Electric Potential at Point P:

  • Preferred Symbol: $V_P$
  • Unit Name: volt
  • Unit Symbol: $\text{V}$

• Potential Difference:

  • Preferred Symbol: $V, \Delta V$
  • Unit Name: volt
  • Unit Symbol: $\text{V}$

• emf:

  • Preferred Symbol: $E$
  • Alternative Symbol: $\varepsilon$
  • Unit Name: volt
  • Unit Symbol: $\text{V}$

• Current:

  • Preferred Symbol: $I, i$
  • Unit Name: ampere
  • Unit Symbol: $\text{A}$

• Resistance:

  • Preferred Symbol: $R$
  • Unit Name: ohm
  • Unit Symbol: $\Omega$

• Internal Resistance:

  • Preferred Symbol: $r$
  • Unit Name: ohm
  • Unit Symbol: $\Omega$

• Magnetic Field:

  • Preferred Symbol: $B$
  • Unit Name: tesla
  • Unit Symbol: $\text{T}$

• Magnetic Flux:

  • Preferred Symbol: $\Phi$
  • Unit Name: tesla metre squared or weber
  • Unit Symbol: $\text{T}\cdot\text{m}^2$ or $\text{Wb}$