Chem Notes

Unit 1: Quantitative Chemistry, Measurement and Data Processing

Unit Conversions: dm3 (decimeter^3) = L (liters) cm3 (centimeter^3) = mL (milliliters)
0 ° C (degrees celsius) = 273.15 K (Kelvin) convert Celsius into Kelvin by adding 273.15 to the current value

The difference between Accuracy and Precision:
Accuracy → difference between average of measured values and true value
Precision → the reproducibility of the measurements, how close they are to eachother

Types of Error:
Systematic Error → fundamental flaws in equipment, observer.
Leads to values all higher or lower than actual value.
High precision, low accuracy.

Random Error → uncertainty in measurement devices.
Leads to random variation in values.
Always occurs and can generally not be improved.

Precise measurements have low random error.
Accurate measurements have low systematic error and generally low random error.

Uncertainties:
Graduated/Analog Device → ±1/2 of the smallest increment on the device.

Digital Device → ±1 on the last digit the device records (it estimates for you.)

Exact Values → No uncertainty.

For all uncertainties the recorded value MUST be to the same decimal place as the uncertainty.
Change your final answer's significant digits if necessary.

Uncertainties should be rounded to ONE digit.

Propagation of Uncertainties:
Addition and Subtraction → Add uncertainties.
Multiplication and Division → Calculate Relative Uncertainty by dividing the Absolute Uncertainty by the recorded value. Add them together and multiply by your final processed raw data value.

For temperature, RU must be calculated in kelvins.

The uncertainty for repeated measurements is averaged along with the values.
If it is the same for all measurements, it stays the same.

Percent Error:
% error = [pic]

If the percent error is larger than the total uncertainty that you calculated, systematic error must be involved as random error cannot explain it.

If % uncertainty > % error, random errors > systematic errors, so precision must be improved.

If % error > % uncertainty, systematic errors > random errors, so accuracy must be improved.

Properties of Matter:
Physical → can be observed without changing chemical makeup of substance
Chemical → describe chemical changes that substance can undergo

Intensive Properties → independent of sample size
Extensive Properties → depend on sample size

Percent Composition:
% by mass of an element = [pic]

Empirical/Molecular Formulas:
Molecular → Not reduced to lowest terms as it represents a composition of one molecule.
For Molecular compounds.
Empirical → Derived from an experiment and express formula with lowest whole number ratios.
For Ionic compounds.

To Determine Empirical:
Step 1: Determine the mass of each element in a given mass of the unknown compound

Step 2: Convert to relative moles using molar masses

Step 3: Use the numbers derived as subscripts

Step 4: Convert to whole numbers if required. Divide all subscript numbers by smallest of the subscript number. Multiply by larger factors if required.

To Determine Empirical with Percent by Mass:
Convert % masses of each element as a relative mass in a 100g sample. ex. 40% of calcium in the sample is 40g.

Indirect Analysis:
Ex. An unknown hydrocarbon fuel undergoes a complete combustion. It produces only carbon dioxide and water.

→ The CO2 and H2O can be separated and individually weighed. Since all the carbon in the fuel wound up in the carbon dioxide and all the hydrogen wound up in the water, the masses of these elements can be obtained from the masses of these compounds.

→ Since the mass of the fuel that is burned is known percent by mass can be calculated.
Percentage for the oxygen has not been accounted for, it is equal to 100% - (%C - %H).

Molecular Masses:
You must determine whether the formula is Empirical or Molecular, and then the Molecular formula can be converted to properly.

If the experimental molecular mass equals the Empirical formula's molecular mass, then the Molecular formula is also the Empirical formula.

If the experimental molecular mass does not equal the Empirical formula's molecular mass, then the Molecular formula is the Empirical formula's molecular mass multiplied by some factor.

Divide the experimental by empirical to find the factor and thus the molecular formula.

Unit 2: Atomic Structure

|Subatomic Particle |Relative Mass |Location |Varied? |
|Proton |1 |Nucleus |No – will change atom |
|Electron |1 |Nucleus |Yes - ions |
|Neutron |5 x 10-4 |Around the nucleus/ |Yes – isotopes (same atom, diff # of|
| | |electron orbitals/ |neutrons) |
| | |no exact location | |

History of the Atom:
Thomson → determined the mass/charge ratio of electrons
Millikan → determined charge of e-
Rutherford → discovered a positively charged nucleus
Chadwick → discovered the neutron

Mass Spectrometry:

Step 1: Vaporization
Step 2: Ionization (to form ions)
Step 3: Acceleration (accelerate ions to create magnetic field)
Step 4: Deflection (deflected by another magnetic field. Heavier the particle the more inertia it has and the less deflection will occur.)
Step 5: Detection (separates according to mass, recording relative abundance of the various isotopes of the atom.)

Isotopes:
Will affect physical properties as most properties are determined by composition of particles in the nucleus (mass).

Radioisotopes:
Isotopes that emit radiation. Many isotopes have unstable nuclei which break down and that causes radiation to be emitted. It is very harmful.

Alpha Radiation → alpha decay, Helium-4 is emitted aka alpha particles
Beta Radiation → beta decay, e- is emitted aka beta particles
Gamma Radiation → beta decay, gamma rays are emitted aka high energy photons

Read more about Radioisotopes uses in the IB study guide or internet.

EMR:
→ Scientific term for light.
→ Light can be a particle or a wave. (wave particle duality of EMR)
The most appropriate theory is used.

|Phenomenon |Can be explained in terms of waves? |Can be explained in terms of particles? |
|Reflection |Yes |Yes |
|Refraction |Yes |Yes |
|Interference |Yes |No |
|Diffraction |Yes |No |
|Polarization |Yes |No |
|Photoelectric effect |No |Yes |

Terminology:

Amplitude:
→ Intensity of EMR wave. The height of the crest of each wave.
Perceive this as brightness when dealing with visible light.

Cycle:
→ One complete oscillation.

Frequency:
→ Number of cycles the waves undergoes per second.
→ Units are 1/s or Hz (hertz.)
→ The symbol is f or v (nu)
→ as a wave moves away from its source the max and min points are evenly spaced

Wavelength:
→ distance between any point on a wave and the corresponding point on the next crest (or trough)
→ distance the wave travels in one cycle
→ Units are meters or nanometers
→ Symbol is λ (lambda)

Speed of a Wave: λf = c
[pic]

c = constant for speed of light = 3.00 x 108 m/s

As the wavelength increases, the frequency decreases and vice versa.
This results in an inversely proportional relationship.

Particle Nature of Light:
→ Max Planck is attributed to this discovery.
→ The energy of an atom is quantized, meaning it only exists in certain fixed quantities rather than being continuous.
→ The loss of a “packet” of energy is called a quantum = fixed quantity of e-.
→ An atom changes energy state by emitting or absorbs one or more quanta (aka photons)

[pic] h = Planck's constant = 6.626 x 10-34 J*s f = frequency

Bohr's Equation:
→ Allows us to calculate the energy of an electron.
[pic]
E = energy of electron b = combined constant (2.18 x 10-18 J) n = quantum number aka energy level from 1 to infinity

Energy Levels: n = quantum number n = 1 means the electron is in the first orbit, this is the ground state n ≥ 2 for Hydrogen it is said to be in an excited state

Electrons are restricted to energy levels and are not found in between.
They move when atoms emit photons whose energy specifically equals the difference between energy levels.

Photon:
→ Particle with zero mass consisting of a quantum of EMR.
→ Unit of energy equal to hf (h = Planck's constant, f = frequency)

→ As the energy levels increase, the difference in energy becomes smaller until a point occurs when we cannot distinguish between the energy of one level versus another.
→ This point is referred to as the convergence point.
→ The lines in the spectra converge as the energy levels themselves converge.

Lyman: UV range of the EMR spectrum.
Occurs when electrons drop from n values above 1 to n = 1.

Balmer: UV-visual range of the EMR spectrum.
Occurs when electrons drop from n values above 2 to n = 2.

Paschen: IR range of the EMR spectrum.
Occurs when electrons drop from n values above 3 to n = 3.

Rydberg Equation:
[pic]

λ = wavelength of spectral line
RH = Rydberg constant (1.09678 x 107 m-1) n1 and n2 = variables whose values must be whole numbers

n2 must > n1

Spectrums:

Matter Waves:
[pic]
h = Planck's constant (J*s) m = mass of particle (kg) v = velocity of particle (m/s)

Diffraction:
→ The interference that occurs when 2 waves cross each other.
When they are “in phase” (aka peaks coincide with each other), the amplitudes add together to create a sum. This is called constructive interference.
When they are “out of phase” (aka peak coincides with trough of another), the amplitudes cancel each other out. This is called destructive interference.

These 2 types of interferences are called diffraction.

Quantum Numbers:
Allow us to indicate where an electron “is”.

Principal Quantum Number (n)
The values of n are the natural numbers (1 to infinity.)
It represents the energy level the electron occupies.

Angular Momentum Quantum Number aka Secondary Quantum Number (l)
The values of l are from 0 to (n – 1).
It represents the shape of the orbital and the energy of the electron, dividing the energy levels into sublevels.

When l = …
0 = s sublevel
1 = p sublevel
2 = d sublevel
3 = f sublevel

Magnetic Quantum Number (ml)
The values of ml are from -l to +l (aka the secondary quantum number, not to be confused with 1)
It represents the individual orbitals of the sub-level.

It is important to remember that:
a) Each orbital is indicated by a separate circle
b) All the orbitals in a sub-level have equal energy
c) As energy level increases, the spacing between the levels gets smaller which leads to overlapping between energy levels with different n values.
For example, the 4s orbital has a lower energy value than the 3d orbital.

When filling up electrons you must start from -l.

Electron Spin Number (ms)
The values of ms are -1/2 or +1/2.
It represents the spin of the electron in the orbital (counter clockwise or clockwise.)

Pauli Exclusion Principle
No two electrons in an atom can have the same four quantum numbers.
This means that no more than 2 electrons can fit into an orbital (spin number).

Electrons that spin in the same direction are said to have parallel spins.

Aufbau Principle:
Sublevels are filled in order of increasing energy.

Hund's Rule:
Orbitals with the same sub-level are filled with single electrons with parallel spins first before being paired up.

Magnetic Fields:
Diamagnetism → Atoms that contain only paired electrons have no attraction for an external magnet.
Paramagnetism → Atoms with more electrons that spin in one direction than the other have an attraction for an external magnet, as the magnetic fields do not cancel out.

Writing out Electrons:
Electron Configuration → Writing out the energy level, sub level and then the amount of electrons in the total amount of orbitals as the exponent.
Abbreviated Electron Configuration → The core electron configuration is represented by the closest noble gas to the period, and then the outer electrons are written as normal.
Valence Shell Configuration →
The representative elements (aka the non-transitional elements) valence shells only consists of s and p orbitals as their d orbitals do not participate in bonding. So only s and p orbitals are included in this configuration.
However, for the transitional elements, their d orbitals do participate in bonding, so they are included in the configuration.

Exceptions to the Rule:
Chromium → The predicted configuration would be:
3d4 4s2.
In this case, Chromium has a tendency to fill it up to halfway as it is more stable.
So it uses the 4s electron.
It then becomes 3d5 4s1.

Copper → The predicted configuration would be:
3d9 4s2.
Again, like Chromium, Copper fills the last 3d orbital as it is more stable. (empty, halfway or full is most stable state)
So it uses the 4s electron.
It then becomes 3d10 4s1.

Unit 3: Periodicity

Brief History:
Dmitri Mendeleev is the original creator of the periodic table. Some points to note...
- arranged in order of increasing atomic number
- “the chemical and physical properties of the elements vary in a periodic way with their atomic numbers”
- the rows are called periods
- the columns are called groups (all elements in a group share the same physical and chemical properties)

Terminology:
Group A Elements → representative elements, longer columns
Group B Elements → transition elements
Lanthanide/Actinide Series → inner transition elements at the bottom

Melting and Boiling Points:
Non-metals → An increase in m.p/b.p as you move from top to down.
This is because the bonding between non-metals is based on LDF.
As you move from top to down, the increase in the number of electrons results in an increase in LDF, and therefore an increase in melting point and boiling point.

Metals → A decrease in m.p/b.p as you move from top to down.
This is because the bonding between metals is dependent on the size of the atom. A smaller atom will cause a stronger pull on the electrons, causing the bond to be stronger.
As you move from top to down, the increase in the number of electrons results in a larger electron shell and shields the attraction of the nucleus to the outside electrons. This causes a decrease in melting point and boiling point as it reduces the strength of the bonds.

Reactivity:

Metals → An increase in reactivity as you move from top to down in GROUP 1A and GROUP 2A.
A metal bonds by losing electrons to achieve a stable octet.
As you move from top to down, an increase in the shielding of the nucleus reduces attraction to outside electrons. This makes it easier to lose electrons. Therefore, the metal is more easily able to lose its electrons, resulting in an increase in reactivity.

Non-metals → A decrease in reactivity as you move from top to down.
A non-metal bonds by gaining electrons to achieve a stable octet.
The effect of shielding causes the nucleus of the non-metals to not attract as easily to the outside electrons, making it harder for the non-metal to gain an electron. Therefore, the non-metal is less easily able to gain electrons, resulting in a decrease in reactivity.

Left to Right → An increase in reactivity for non-metals.
Again, non-metals bond by gaining electrons.
As you move from left to right there is an increase in protons which results in a stronger attraction for outside electrons. The increase in electrons is not related to the attraction as these trends only focus on the attraction of the nucleus towards the bonding electrons in a bond. Therefore, it is easier for the non-metal to gain electrons and an increase in reactivity is seen.

Halides (Halogen Ions):
Remember that a Halide will react and lose an electron to any Halogen atom above it.
But it will not lose an electron to a Halogen atom below it.

Metal Oxides:
These are ionic compounds.
They conduct electricity when molten as they break apart into ions when dissolved.
High m.p and b.p.

They are called basic anhydrides, meaning that when they react with water they become a compound that further reacts with water to become a base, but do not become bases immediately.
Thus they are obviously tend to be basic.

Aluminium Oxide → Amphoteric.
This means it can be acidic or basic depending on what it reacts with.
It is unique as it has covalent and ionic character but is considered ionic.

Silicon Dioxide → Network covalent structure.
Insoluble in water.
Extremely high m.p and b.p, and does not conduct electricity.

Non-Metal Oxides:
These are covalent compounds.
They do not conduct in liquid state.
Low m.p and b.p as they do not break apart into ions, molecules simply move farther apart.
Low masses = Low LDF

They are called acidic anhydrides, meaning that when they react with water they become a compound that further reacts with water to become an acid, but do not become acids immediately.

Period 3 Chlorides:

NaCl → Only neutral chloride in period 3.
It creates NaOH and Hcl, both which dissociate/ionize 100% to form a neutral ionic salt solution.

MgCl2 → Slightly acidic.
Complex magnesium ions form. This is called a hydrated ion.
[Mg(H2O)6]^2+

Most metallic ions will form hydrated ions.
These types of ions tend to form acidic solutions, and the greater the pull from the metal ions, the more hydrogens are ripped off of water to form hydronium ions. This determines the degree of acidity.

Hydrated Ions:
→ When metals become ions, it loses electrons.
In this case, for period 3 metals, they lose all the electrons in the energy level 3.
For example,

Magnesium's electron configuration is: 1s2, 2s2, 2p6, 3s2.
It loses the 3s2 electrons, leaving the energy level 3 empty.

Six is the maximum number of water molecules that is possible to fit around a magnesium ions and most other metal ions. The 2+ charge is spread through the entire complex.

Back to Period 3 Chlorides:

AlCl3 → Very acidic (ph 2-3).
Like Magnesium, it forms a hydrated ion.
The charge of aluminum is much higher so it easily pulls of the hydrogens off the water to form hydronium ions. Since there is also chloride, these become hydrochloric acid.

SiCl4 → Fumes in moist air.
With water it reacts to become SiO2 and Hcl.

PCl3 → LDF and dipole-dipole forces.
Reacts violently to form phosphoric acid (H3PO3) and Hcl.

PCl5 → Behaves like an ionic compound when solid.
Two stage reaction.

First Stage forms POCl3 and Hcl.

Second Stage occurs when water is boiling.
It reacts further to form H3PO4 and Hcl.

Cl → Diatomic molecular gas that only contains LDF.
Forms HOCl and Hcl.

Trends for Oxides and Chlorides:
1. As you move from left to right across period 3, oxides start off as ionic solids but becomes molecular gases.

2. All the chloride compounds react with water to produce Hcl and some other product depending on the starting compound.

3. Aluminum is weird due to EN difference. Below 180c, the compound is an ionic lattice with a lot of covalent character. As the temp increases to 180-190c it converts into a molecular form called a dimer and loses all its ionic character.

Categories of Electrons:
Inner Electrons → Electrons in any previously completely filled energy level.
Outer Electrons → Electrons in the highest energy level.
Valence Electrons → Electrons that take part in bonding to form compounds.
Group A elements do not use d orbital electrons.
Transitional Elements do use d orbital electrons, but be wary of elements who are not technically considered transitional elements (full d-block elements).

D-block Properties:

Atomic Radius
Left to Right → Remains relatively constant as 4s orbitals have higher energy than 3d orbitals.
Thus, electrons are being added to the 3d orbitals and not the outside so there is not much change.

Up to Down → Small increase until it hits period 5 and 6, where the f-block is then added. Same effect as d-block. This causes negligible changes from then on.

Ionization Energy
Left to Right → Electrons being added to the core actually cause a significant increase in shielding, so it is a bit easier to pull off electrons.

Up to Down → General increase until it hits Period 5 to 6, where it is negligible. This is because atomic radius barely changes so Ionization Energy remains practically the same.

Electronegativity
Left to Right → Electrons being added to the core actually cause a significant increase in shielding, so the electronegativity goes down a bit.

Up to Down → General increase until it hits Period 5 to 6, where it is negligible. This is because atomic radius barely changes so electronegativity remains practically the same.

Transition Metals and Colored Compounds:
1 small thing to note is that all transition metals have an oxidation state of 2+.
Usually the highest oxidation state is equal to the elements group number, but the higher it is the rarer it is.

→ Many transition metals are colored as they have partially filled d sublevels that can absorb visible light to excite the electron to a slightly higher d sublevel.

In this case the d orbitals split from being 5 equal energy orbitals to 2 distinct levels. That way electrons can jump from one level to the next.

This only occurs in a transition metal ion however and those can be found in complex ions or hydrated ions. Other representative metal ions are colorless.

Types of Bonds:
Intramolecular → hold atoms together within a molecule
- Ionic bonding
- Covalent bonding
- Metallic bonding

Intermolecular → hold molecules in a covalent compound together
- Hydrogen bonding
- Ion-dipole interaction
- Dipole-dipole interaction
- Van der Waal's Forces (LDF)

Ionic Bonding in Detail:
- Forms between metals and non-metals when the EN difference between the atoms is 1.7 or greater.
- Metal becomes a cation, Non-metal becomes an anion.
- Must be in a gaseous state for this to occur.

Crystal Lattice → The structure that the ions form when the electron transfer is complete and they have electrostatic attractions for each other. Ions become tightly packed, releasing energy and the crystal lattice is at a much more stable state due to its lower energy.

The energy released is equal to the energy required to break the lattice apart, also known as lattice energy.

Unit cell indicates the smallest unit in the lattice that, if repeated in all directions, will give rise to the crystal.

Coordination number for an atom in a crystal is the number of nearest neighbors surrounding it.

Types of Cubic Unit Cells:

Simple Cubic → The centers of eight identical particles define the corners of a cube, which then touch along the edges but not diagonally or through the middle.
Coordination number is 6. (ex. Sodium Chloride)

Body-Centered Cubic → Particles lie at the corners and at the center. These particles do not touch at the edge but all touch the particle in the center.
Coordination number is 8.

Face-Centered Cubic → Particles lie at the corners and at the center of each face of the unit cell, but not in the center.
These particles at the corners touch the face-centered particles but not each other.
Coordination number is 12.

Covalent Bonding in Detail:
- Forms between atoms that have a difference in EN value of less than 1.7
- Usually happens with 2 non-metals but may happen with a metal and a non-metal if EN values are close to being equal.
- Electrons are shared and electron density is greatest halfway between atoms as they are attracted to both nuclei

Dipoles → When electron density is greater to one end of the bond, the ends take n a partial positive/negative charge called a bond dipole.

Symmetrical molecules cancel out these dipoles and are non-polar.
Non-symmetrical molecules do not cancel these dipoles and are polar.

If the EN values are close to equal, the dipole is much weaker. In this case, the dipole are classified as an Instantaneous Dipole or Dipole Moment as fluctuating electron movement within the electron cloud forms dipoles and degrade dipoles very quickly.

A dipole that is induced by another dipole moment in the molecule is called an Induced Dipole.

Coordinate Covalent Bond (aka Dative Bond) → One atom donates both of the electrons that are shared in the bond.

Often seen in polyatomic ions or when the central atom on a molecule does not have enough electrons to form a stable octet.

Lewis Dots
1. Count up all the valence electrons in the atom and account for charges.
2. Determine which atom has the most bonding electrons.
3. Place the peripheral atoms around the central atom.
4. Start by forming single bonds between the central and the peripheral atoms.
Then, re-calculate the # of electrons you have left.
5. Use the leftover electrons to form octets around the peripheral atoms.
6. Then, if there are leftover electrons to form an octet around the central atom.
7. If there are no left, you will need to form one or more double bonds, or even a triple bond.

Inter-molecular bonding in Detail
Hydrogen Bonding → only occurs when Hydrogen are bonded to very small electronegative atoms that has a lone pair of electrons (F, O, N)
Can occur with larger P, S and Cl atoms but H-bonds are much weaker due to the size.

Basically a much stronger permanent dipole bond, and these are the strongest intermolecular bonds.

Ion-dipole Interactions → occurs when a molecule contains a dipole and this dipole interacts with an ion. The attraction between the ion and the dipole is called an ion-dipole interaction.

The formation of the bond releases energy but the breaking of the ion-ion bond requires energy.

IF the energy released when the ion-dipole bond forms is less than the energy required in breaking the ion free, the process is endothermic.

IF the energy released is more than the energy required, then the solution heats up and it is exothermic.

Dipole-Dipole Interaction → occurs when dipole moments come into close proximity of each other.
The strength of the dipole moment is dependent on the ability of the electron cloud to be deformed – thus, larger atoms form stronger dipole-dipole interactions than small atoms.

London Dispersion Forces → occurs due to electrons being anywhere at any given instant in time, causing instantaneous dipoles to form, which will induce further instantaneous dipoles to form in neighboring molecules.

Present in all substances and only occurs in lower energy states, otherwise neighboring molecules are too far away.

The more electrons in the cloud the greater the chance of an instantaneous dipole forming, and the greater the melting point or boiling point (same as above.)

Bond Properties in Covalent Bonds:
Bond Order → the number of pairs of electrons shared between two atoms.
Bond Energy → the energy released when a bond is formed, equal to the amount of energy required to break the bond. Indicator of bond strength.

AS bond order increases, bond length decreases.
AS bond order increases, bond energy increases.

Positioning of Molecules:
VSEPR Theory → each group of valence electrons around a central atom is located as far away from each other as possible in order to minimize repulsion

Negative Charge Center → electron pairs around the central atoms.
Remember that double and triple bonds count as one pair.

Repulsion Order → LP-LP > LP-BP > BP-BP
Higher bond order repels lower bond order more strongly (double bond > single bond)

|# of charge centers |BP |LP |Shape name |Bond angles |
|1 |1 |0 |Linear |180 |
|2 |2 |0 |Linear |180 |
|3 |3 |0 |Trig. Planar |120 |
|3 |2 |1 |Trig. Planar Bent |120 |
|4 |4 |0 |Tetrahedral |109.5 |
|4 |3 |1 |Trig. Pyramidal |107 |
|4 |2 |2 |Tetrahedral Bent |104.5 |
|5 |5 |0 |Trigonal Bipyramidal |90, 120 |
|5 |4 |1 |Seesaw |