Science: Common Definitions, Equations And Laws

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Pure Substance

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a substance with constant composition

Compounds - can be further broken into elements through chemical process
Elements - cannot be broken down further elements

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Mixture

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a mixture of substances with variable composition.

Homogenous - the same throughout
Heterogenous - containing regions with different properties

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The Mole

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is defined as the amount of substance that contains the same number as 12g of pure carbon C-12

This number is known as Avogadro's number

It is defined in terms of quantity and mass so it represents both a fixed no. of entities and a fixed mass

1 mole has a mass ratio of 1g:1amu so 1 mole of substance has a mass that is numerically the same whether expressed in grams or amu

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Avogadro's Number

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6.022 x 10^23

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Atomic Mass

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is defined as the mass of 1 atom of an element.

It is expressed in amu (atomic mass units)

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Molecular Mass

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also called formula mass, is the mass of 1 molecule or formula unit of a substance.

It is the sum of the masses of its components and is expressed in amu (atomic mass units)

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Molar Mass`

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is defined as the mass of 1 mole of a substance

It is expressed in g/mol (grams that 1 mole weighs)

g/mol is now also known as the Dalton (Da)

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Atomic Mass Unit

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1 atom C-12 = 12 amu

1 amu = 1/12 mass of C-12 atom

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Mass-Mole Number Formula

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n = m/M

where
n is number of moles
m is mass in grams
M is molar mass in g/mol

see solution stoichiometry

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Uses for Mass-Mole-Number formula

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-number of moles
-mass in grams
-molar mass in g/mol
-number of entities (1mol = 6.022 x 10^23)
-mass/molar percent of elements in a compound (N.B. numerically identical)

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Law of Mass Conservation

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the total mass of substances does not change during a chemical reaction

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Stoichiometric Equivalency

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means that a definite amount of one substance reacts with, produces or is formed from a definite amount of another.

In a balanced chemical equation, any 2 substances are stoichiometrically equivalent

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Limiting Reactant

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is the substance that limits the reaction. It is the reactant that yeilds the lowest amount of product

Any chemical reaction witha specified amount of reactant or product will have a limiting reactant

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Yields

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Theoretical - the amount of product produced when a perfect, complete reaction is assumed

Actual - the observed, realistic yield

Percent - Actual/Theoretical x 100

In a multi-step synthesis the overall yield is the percent yield at each step multiplied together

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Isostopes

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are atoms of an element with differeing numbers of neutrons

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Planck's formula

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E = nhv

where
E is energy of radiation
v is frequency
n is a positive integer
h is Planck's proportionality constant = 6.626 x 10^ -34

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Heisenberg Uncertainty Principle

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It is impossible to know the exact position and momentum of a particle simutaneously

∆x x m∆u ≥ h/4π

where
∆x is uncertaintly in position
m is mass
∆u is uncertaintly in speed
h is Planck's constant

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The Exclusion principle

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no two electrons in the same atom can have the same 4 quantum numbers. i.e. each orbital can hold a max of 2 electrons

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Ground-state electron configuration

State the rules for filling orbitals

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the configuration of electrons that produces the lowest energy arrangement

1. lowest energy orbitals fill first
2. 2 electrons in each orbital, each with opposite spins
3. Hund's rule

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Hund's rule

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if there are 2 or more orbitals of equal energy empty, then 1 electron occupies each with parallel spins until all half full

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List 2 forms of notation for ground-state electron configuration

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1. electron configuration

nl^#

where
n is principal energy QN
l is letter designation of sub-level (s, p, d, f)
# is number of electrons in the orbital

2. orbital diagrams
a box for each orbital in an energy level, grouped by sublevel amd with a vertical or horizontal arrow indicating an electron and its spin

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Photons

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are particles of light who's energy is fixed by its frequency not its amplitude

1 photon = 1 quantum

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Quantum Numbers

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a unique combination of numbers that describe an atomic orbital

Principal Quantum Number (n)
-is a positive integer and indicates the size of the orbital, and therefore the distance from the nucleus

Angular Momentum Quantum Number (l)
-is an integer from 1 to n-1 that indicates the shape of the orbital (s, p, d, f)

Magnetic Quantum Number (ml)
-is an integer from -1 to 1 and prescribes the orientation of the orbital

2l + 1 or n^2

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State Function

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are functions that are dependent only on the current state, regardless of the path taken to reach it

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Energy

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All energy is either

Potential - related to position
Kinetic - related to motion

When energy is transferred it appears as heat (q) and/or work (w)

∆E = q + w

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Units of Energy

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Joule - is the energy exerted by the force of one newton acting to move an object through a distance of one metre

1J = 1kg.m^2/s^2

Calorie - is the quantity of energy neede to raise the temperature of 1g water by 1 degree C

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Pressure-Volume work

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P∆V

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Enthalpy

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the change in enthalpy equals the heat gained or lost at constant pressure

∆H = ∆E + P∆V = q (constant pressure)

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Heat of Reaction

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the enthalpy change of a reaction.

exothermic - +∆H
endothermic - -∆H

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Standard Heat of reaction

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The heat of reaction when all substances involved are measured in their standard states

i.e. gas - 1 atm
aq solids - 1M concentration
pure substances - usually the most stable form at 1 atm and termp of interest (usually 25 degrees C)

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Heat of Combustion ∆H(comb)

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1 mole of substance reacts with oxygen (O2) in combustion

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Heat of Formation ∆H(form)

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1 mole of substance is produced from its elements

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Standard Heat of Formation

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the enthalpy change for a formation equation when all substances are in their standard states

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Formation Equation

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the equation for a reaction where 1 mole of compound forms from its elements

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Heat of Fusion ∆H(fus)

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1 mole of substance melts

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Heat of Vaporisation ∆H(vap)

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1 mole of substance vaporises

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Heat Capacity

Specific Heat Capacity (c)

Molar Heat Capacity (C)

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the quantity of heat required to change temperature of a substance by 1K

the quantity of heat required to change the temperature of 1g of substance by 1K

the quantity of heat required to change the temperature of 1mol of substance by 1K

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Hess's Law of Heat Summation

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the enthalpy change of an overall process is the sum of the enthalpy changes of its individual steps

This summation will work regardless of whether the overall change actually occurs through steps or others. The hypothetical steps are chosen for their known ∆H values

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Ionisation Energy

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is the energy in kJ required for the complete removal of 1 mole of electrons from 1 mole of gaseous atoms or ions

1st IE-energy required to remove the outermost electron
2nd IE-removal of second electron etc

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Electron Affinity

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is the enegy chage in kJ accompanying the addition of 1 mole of electrons to 1 mole of gaseous atoms or ions

1st EA-refers to the formation of 1 mole of monovalent (1-) gaseous anions
2nd EA-bivalent (2-) etc

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Spontaneous Change

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A spontaneous change is a process that occurs by itself under specified conditions, without an ongoing input of energy from its surroundings

NB: spontaneous does not mean instantaneous

If a change is spontaneous in one direction, it will be non-spontaneous in the other

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Entropy

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the change in entropy is a measure of the change in molecular disorder caused by the reaction

S = k.lnw

where
w is the number of microstates
k is R/Avo's no.

Entropy is an extensive preopert, meaning it depends on the amount of substance, and unlike enthalp it cab meaured directly due to the baseline provioded by the 3rd law of thermodynamics

A process pontaneously approaches equilibrium so that

∆S(univ.) ˃ 0

When the process reaches equilibrium

∆S = 0

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Gibb's Free Energy

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a measure of the spontaneity of a process and of the useful energy available from it

G = H - TS

∆G ˂ 0 - spontaneous process
∆G = 0 - a process at equil.
∆G ˃ 0 - non-spontaneous process

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Thermodynamic Laws

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1. the total energy of the universe is constant
2. a spontaneous change is accompanied by an increrase in the total entropy of a system and its surroundings

∆S(univ.) = ∆S(sys) + ∆S(surr)

3. a perfect crystal has an entropy of 0 at a temperature of absolute 0

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Precipitation Reaction

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2 soluble ionic compounds react to form an insoluble product called a precipitate

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Acid-Base Reaction

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An acid and a base react to form water and an ionic compound called a salt

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Metathesis Reaction

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occurs when the ions in the starting solutions exchange partners

This is also called double-displacemenet

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Oxidation-Reduction Reaction

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describes the net movement of electrons from one reactant to another

By this definition, the formation of ionic and covalent compoundfs are both examples of redox

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Thermochemical Equations

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are balanced equations that include the heat of reaction

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Oxidation Number

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is the charge that an atom would have if its electrons were not shared but transferred completely

NB: Oxidation numbers have a sign before the number, while ionic charge has one after

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Factors that influence reaction rate

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1. concentration
2. physical state
3. temperature

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Reaction Rate

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is the change in concentration per unti of time

Rate = ∆conc/∆T

If measuring reactants, rate will be neg as conc decreasing
If measuring products rate will be positive as conc increasing

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Rate Law

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is the rate as a function of reactant concentration, product concentration and temperature

Rate = k[A]^m[B]^n

where
k is the rate constant
m and n are reaction orders

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Rate Constant (k)

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is specific for a given reaction at a given temperature.

It does not change as the reaction proceeds

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Integrated Rate Law

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takes into account the concentration changes over time

Integrating the rates over time gives

1st order
ln[A] (t=0) - ln[A] (t=t) = kt

2nd order
1/[A]˅t = kt - 1/[A]˅0

Zero order
[A]˅t = -kt + [A]˅0

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Reaction Order

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with respect to a certain reactant, is defined as the power to which its concentration term in the rate equation is raised

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Half Life of a reaction (t˅1/2)

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is the time required for the reactant concentration to reach half its initial rate

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Arrhenius Equation

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takes into account how the rate is affected by a change in temperature

k = Ae^(-E˅a/RT)

where
E˅a is the activation energy
A is the frequency factor

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Activation Energy

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is the energy threshold that colliding molecules must exceed in order to react

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Reaction Mechanisms

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are a aequence of single reaction steps that sum to an overall reaction

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Reaction Intermediates

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are the substances that are created and used up in the overall reaction mechanism and therfore do not appear in the net equation

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Elementary Steps

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are the individual steps that make up a reaction mechanism.

Each describes a single molecular event and is characterised by molecularity (the number of particles involved)

Unimolecular - 1 particle
Bimolecular - 2 particles etc

We can determine the rate law from the equation of an elementary step (unlike theoverall reaction). This is because the rate must be directly proportional to the product of the reactant concentrations as it is only one step. In this case, the equation coefficianets become the reaction orders

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Rate Determining Step

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is the elementary step that is slower than the others, thereby limiting the overall rate

The rate law for this step represents the rate law for the overall equation

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Catalysis

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is the speeding up of a chemical reaction

Homogenous - exists in solution with a reaction mixture and is therefore in the same phase
Heterogenous - acts on a reaction that occurs in a different phase

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Equilibrium

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refoers to the extent of a reaction

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Equilibrium Constant

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At equilibrium, the ratio of rate constants equals the ratio of concentration terms

k(fwd)/k(rev) = [A]˅a/[B]˅b = K

where
K is the equilibrium constant

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Reaction Quotient

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Q = [A]/[B] forward reaction
Q = [B]/[A] reverse reaction

i.e. forward and reverse reaction quotients are reciprocals

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Boyle's Law

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PV = constant

V = Constant/P

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Charles's Law

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at constant pressure, the volume occupied by a fixed amount of gas is directly proportional to its absolute temperarure

V = Constant x T

V/T = Constant

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Avogadro's Law

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at a fixed temperature and pressure, equal volumes of any ideal gas contain equal numbers of particles

V/n = Constant

V = Constant x n

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Ideal Gas Law

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Combination of 3 gas laws relating volume, pressure, temperature and number of particles

PV = nRT

This can be manipulated by subsituting m/M for n and rearranging to give to m/V which equals density.

A similar process gives an equation for Molar Mass

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STP

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Standard temperature and pressure

0 degrees C
1 atm

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Standard Molar Volume of a gas

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the volume of 1 mole of an ideal gas at STP

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Partial Pressure

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Each gas in a mixture behaves as if it were the only gas present

This is assuming no chemical interactions

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Dalton's Law of Partial Pressures

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In a mixture of unreacting gases, the total pressure is the sum of the partial pressures of the individual gases (i.e. the pressures they would exert if alone)

P(total) = P(1) + P(2) + P(3) + etc

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Effusion and Diffusion

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Effusion describes the passage of a gas through a tiny orifice into an evacuated space

Diffusion describes the mixing of gases, or the movement of one gas through another