Periodic Table Trends: Atomic Radii, Ionization

• The trends of atomic radii, ionization energies, and electronegativity of elements depend on their position in the periodic table.
• Key concepts include chemical equations, chemical reactions, stoichiometry, calculations based on chemical equations, and the limiting reactant concept.

Understanding the Periodic Table

• The periodic table arranges elements in a tabular format by increasing atomic number corresponding to the number of protons
• Periodicity refers to the recurring patterns of similar properties at regular intervals based on increasing atomic number.
• Textbooks categorize main group and transition elements into A and B subgroups, respectively.
• The s-block and p-block elements were previously numbered as groups I to VII and zero (0), respectively.
• The periodic table also includes the d-block and f-block elements.
• Chemists like Newland, Lother, and Mendelev in the 19th century contributed to the development of the modern periodic table.

Blocks and Trends

• The periodic table can be divided into blocks such as s-block, p-block, d-block, and f-block.
• Elements are arranged by their atomic number in the periodic table.
• Elements in the same group (vertical column) share similar properties.
• A period consists of elements within the same row.
• Elements show changing trends across a period
• Elements in the same vertical column (group) have the same number of electrons in their valence shell.
  • For example, Lithium, has an electron configuration of [He] 2s1
  • Sodium, has an electron configuration of [Ne] 3s1
  • Potassium, has an electron configuration of [Ar] 4s1
  • Rubidium has an electron configuration of [Kr] 5s1
• Elements in the same period (horizontal row) have progressively different chemical and physical properties.
  • For example, Lithium has an electron configuration of [He]2s1
  • Beryllium has an electron configuration of [He]2s2.
  • Boron has an electron configuration of [He]2s22p1.
  • Carbon has an electron configuration of [He]2s22p2

Ground State Electron Configuration

• Ground state electron configurations for the outermost electrons are shown for each element
  • ns1 is the generic configuration for group 1A
  • ns2 is the generic configuration for group 2A
  • ns2np1 is the generic configuration for group 3A
  • ns2np2 is the generic configuration for group 4A
  • ns2np3 is the generic configuration for group 5A
  • ns2np4 is the generic configuration for group 6A
  • ns2np5 is the generic configuration for group 7A
  • ns2np6 is the generic configuration for group 8A
• Periodicity refers to the recurring trends in the properties of elements, caused by regular variations in their atomic structure
• Periodic properties rely on the electronic configuration of the elements
  • Atomic radius, ionic radius, ionization energy, electron affinity, and electronegativity

Atomic Radius

• Atomic radius relates to half the distance between the nuclei of two of the same atoms in a diatomic molecule.
• Atomic radius decreases across a period because the positive charge from protons increases.
• Added electrons experience a greater positive charge, pulling them in the same direction
• Atomic radius trends are influenced by valence electron energy level, nuclear charge, and the shielding effect of inner electrons.
• The potential distance from the nucleus increases with higher energy levels.
• 1 < 2 < 3 < 4 < 5 < 6 < 7
• A higher nuclear charge pulls electrons closer to the nucleus.
• Nuclear charge is equal to the atomic number and determines atom size.
• Shielding or screening from inner electrons reduces outermost electron attraction, increasing size.

Ionization Energy

• Ionization energy (IE) refers to the energy in KJ/mole which is needed to strip the most loosely bound electron from an isolated gaseous atom and convert it into a positive gaseous ion.
• Supplying a small quantity of energy to an atom promotes electrons to a higher energy level.
• If the volume of energy supplied is large then the electron will be completely removed.
• First ionization energy is the minimum energy in kJ/mol to pull out an electron or first electron from a gaseous atom in its ground state and turn it into a gaseous ion.
• first ionization energy is given by: X(g) -> X+(g) + e-
• second ionization energy is given by: X+(g) -> X2+(g) + e-
• third ionization energy is given by: X2+(g) -> X3+(g) + e-
• Subsequent ionization energies increase: I1 < I2 < I3
• Ionization energy is always endothermic, requiring energy addition to remove an electron.
• Rising atom size reduces the energy needed to strip an electron.
• Ionization energy values relate inversely to atomic radius.
• Bigger atoms will have a smaller ionization energy, and larger atomic radii.
• Nuclear charge influences ionization energy, with larger charges leading to greater ionization energy.
• A greater shielding effect lowers ionization energy.
• Ionization energy lessens as there is more area between the nucleus and the outer electrons of an atom.
• Removal of an electron from a full or half-full sublevel demands added energy.
• Full and half-full orbitals exhibit increased stability.
• Filled ns and np orbitals and half-filled np3 orbitals
• They also possess greater ionization energy than anticipated.
• Group trends are dependent on first IE, second IE, third IE, fourth IE, etc
• First IE drops down a group
• Atomic radius of the atoms increases along with Shielding effect.
• Atoms that are positioned in the same period posses electrons that are in the same energy level.
• They share the exact same shielding.
• Nuclear charge rises across the period
• IE normally grows from left to right
• Though there are exclusions at filled and 1/2 full orbitals.
• Second and third row elements in the periodic table demonstrate gradually rising ionization energies with electron removal from valence orbitals (2s, 2p, 3s, 3p), followed by a sharp increase when removing electrons from filled core levels.
• First ionization energies rise across the periodic table's periods because valence electrons do not shield each other, steadily raising the effective nuclear charge.
• Atomic sizes dwindle as valence electrons are more intensely pulled in by the nucleus, which then drives up ionization energies.
• The first ionization energies highlight three specific trends.
  • Second, third, fourth, fifth, and sixth row components of the s and p blocks comply with the same model or display the same trends.
  • Across every single row, ionization energies head upward left to right.
• First ionization energies slide downward within a group because filled inner shells successfully screen valence electrons, limiting the effective nuclear charge.
• As they acquire electrons, atoms turn out to be larger.
• Valence electrons that are farther away from the nucleus exhibit a less tightly bound state making them much easier to dislodge while also causing ionization energies to drop.
• Greater nucleus radius is relative to a smaller ionization energy.
• Elements with the lowest ionization energies are positioned in the lower-left corner of the periodic table because of these factors.
• Ionization is hardest in the upper-right corner of the periodic table.
• Ionization energies move diagonally from lower left to upper right.
• Deviations from this pattern are attributable to distinctly stable electronic configurations, known as pseudo-inert gas configurations, within either the parent atom or the resulting ion.

Electronegativity

• Electronegativity gauges how much an atom within a molecule attracts electrons.
• Linus Pauling (1901-1994) first proposed the idea, and later received a Nobel Prize for the work.
• Electronegativity measures the ability of atom that is capable of attracting toward itself the electrons in a covalent bond
• Metals display a low tendency for electron attraction and more often, release electrons.
• Nonmetals hold a high affinity for attracting electrons and have a lower chance at releasing them.
• Smaller atoms draw electrons more strongly compared to bigger ones and consequently, have a higher electronegativity.
• Atoms are likely to have relatively filled electron shells and have superior electro-negativities compared to those only sparsely occupying them.
• If atoms exhibit parallel electro-negativities, the bond that exists within them will be primarily covalent.
• A large difference pertaining to electronegativity can cause a bond with an extremely high degree of polar traits, resulting in the bond being prominently ionic.
• Atoms are further away from the nucleus and also heavily protected from that same nuclear charge moving down a group within the periodic table which causes atom measurement to increase.
• As a result, there is weaker nucleus attraction for said electrons and to that end, electronegativity fades as you go down the group.
• Atoms share parallel energy levels with smaller measurements all across the period.
• Raising the nucleus attraction for valence electrons boosts electronegativity increases across a period.
• Fluorine registers the very highest, and most, electronegative element.

Errors, Accuracy and Precision

• Numerical answers from all measurements contain some level of error
• Errors stem from instruments and can be attributed to the inability of an analyst to accurately read an instrument.
• Measurement inaccuracy corresponds to the difference between values that are observed against values that are true.
• Absolute error is the term for the same type of measurement inaccuracy.
  • Absolute error = measured value less the true value
• Error can be conveyed by:
  • Relative error which = absolute error / true value
• Percentage relative error which = |absolute error| / true value * 100
• Accuracy reflects how much a calculation mirrors the real or true value.
• Precision shows the extent to which recurring or recurring results match and agree with one another.
• If the true measurement is a value such as 2.000g
  • A student measures values such as the values: 1.964 g, 1.978 g, 1.960 g the average measurement is 1.967 g with a range of 0.018 a student measures values such as the values: 1.968 g, 1.969 g, 1.973 g the average measurement is 1.970 g with a range of 0.005
  • A student measures values such as the values: 2.001 g, 2.002 g, 2.003 g the average measurement is 2.002 g with a range of 0.002
  • Student C was the most accurate and precise
• When observing and evaluating
  • Data points in area A are considered to be of low accuracy, with low precision
  • Data points in area Bare considered to be of low accuracy with high precision
  • Data points in area C are considered to be of high accuracy with high precision

Stoichiometry

• Stoichiometry addresses reactants that are consumed and refers to substances produced (products) during chemical reactions
• Relative atomic masses explain that atoms are incredibly small and cannot be weighed as single unit.
• Instead, the mass of a single atom can instead be measured scientifically and in accordance with the other.
• As being the ultimate standard, in order to then measure in atomic mass units, Carbon 12 consists of exactly 12 atomic mass units.
• Isotopes create such average atomic mass situations with isotopes (i.e two+ atoms sharing one single atomic number yet carrying differing mass numbers.)
• An example is Carbon having an atomic mass is 12.01 instead of 12.00
• To address this then, it can be calculated in relation to overall atomic mass due to related abundance.
  • As exhibited with 12C having a relative abundance standing at 98.89% with 13C’s corresponding rate of 1.11%
  • Then the same atomic mass stands at (98.89 / 100 x 12.00) + (1.11 / 100 x 13.00) = 12.01
• Avogadro's number and the presence of Moles
  • Mole denotes the sum total of particular substance consisting of atoms and molecules that exist in as much 12 g of carbon 12 isotope
• Counting atoms, in light of containing multiple atoms, it’s in “mole” units and can be helpful for sorting, and counting, different types of atoms. In summary, it’s as much the total of carbon atoms while taking 12 g in pure 12C
  • For example, 12 g of 12C bears out 6.023 x 10 to the 23rd power atoms.
  • This then reveals Avogadro's Number: 6.023 x 10 to the 23rd power.
• 1 mole of 12C = 6.023 x 10 to the 23rd power atoms.
• 1 mole of H₂O molecules = 6.023 x 10 to the 23rd power H₂O molecules 1 mole of NO3- ions = 6.023 x 10 to the 23rd power NO3- ions
• 1 mole of H atoms = 6.023 x 10 to the 23 atoms.
• 1 mole of O atoms = 6.023 x 10 to the 23 atoms.
• 1 mole of H₂ molecules = 6.023 x 10^23 molecules
• Molar mass represents the mass in grams taken from one mole of compound substance can be determined by totaling atomic masses coming from atoms inside said portion/compound.
  • A mole of Mg atom is typically calculated as taking up 24.31 g, and it’s average molar mass sums to 24.31 g / mol
  • Methane (CH4) shows what’s calculated as CH4= (12.01 x 1) + (1.008 X 4)= 16.04 g /mol
• There is arelationship between mass, number of moles and Molar mass : no of moles is taken as mass / Molar mass
• Percentage composition means elements total a portion as a percentage and in a compound are decided depending on moles of compound type, and later, ratios alongside percentages

Chemical Equations and Stoichiometry

• Chemical equations offer shorthand for how chemical reactions are portrayed.
  • The equation involves symbols and formula to tell more of compound and element details/specifics, such as, CH4 plus 2O2 which then results in CO2 ++ 2H2O revealing CH4 and O2 coming on the left side, which signifies reactants,
• Atoms tend to be rearranged with certain bonds being broken while new ones are created
• In chemical reactions, atoms remain conserved. This alludes the claim that said atoms carry equivalent ratings regarding overall creation and disintegration and this must have the same quantity of each sort of atom that can be gained through the product and reactant sides
• This can be adhered to through a process coined as “balancing a chemical equation” and needs to be applied as part of the chemical equation”
• Identities present in the reactant and products are needed though must not be confused during balancing, or balancing of chemical equations
  • Chemical formulas for all products and reactants in the equation can not be altered or updated.
  • Ex: Instead of H₂O (❌) one must select either H₂O₂ (❌)or make available the H4O2(❌). Rather than O2 it tends to be O3. To adhere to this , it’s vital that while balancing chemical equations, the subscripts are avoided which then makes it a more appropriate change that involves also making an alteration with the addition of either removal of the particular atoms involved.
  • Most chemical equations can be sorted/balanced out through a test-and-check plan. To achieve higher accuracy and faster correct responses, begin to analyze what molecules tend to have the most complication or to also take a higher rate to measure out Balancing chemical equations, you start with; KCIO3 → KCI ++ O2 (unassigned/not balanced) 2KCIO3 → 2KCl + 3O2 (balanced)
  • All chemical equations need to be fully sorted and balanced first to achieve correct and full stoichiometric points. As exhibited with: C3H8 (g) + 5O2 (g) → 3CO2 (g) + 4H2O (g) 1 mole of C3H8 goes through 5 moles worth of O2 and then makes 3 moles for the CO2 and 4 moles in H₂O

Limiting Reagent

• Limiting reagents relate to all chemical reactions with total consumption and the rate of creating product relates to that amount
• Toast, as an example, involves 2 bread slices plus 1 egg. From there, you can expect to make said food from all slices while only obtaining 20 given slices and 12 additional eggs. This alludes that it requires 2Bd+1egg to →1 Bdegg
  • As a conclusion, bread proves to become, and is, the limiting reagent.
  • First it means you'll need to have correct balancing, then set yourself up in full mole ratio so later you can set your mole percentage over to make use in volume, to get to do vice-versa, and understand this step should only become a recommendation in which needs to be balanced out If it is recognized you have the capacity over where you are to have 35 kg pertaining specifically to N2 including 15 kg worth of H2 then one must realize there happens to an overall point in time for the limiting reactant. N2(g) + H2(g) → NH3(g) In what comes next, it’s all too well and commonly known that 1 mole, and at best, also commonly shared, as the well maintained balance takes on; N2(g) + 3H2(g) → 2NH3(g) After converting into moles, there is a well established balance with 28g out of N₂ alongside 6g worth of H2 At this rate now, and based on that outcome, we expect 35kg is what exactly to expect while factoring in; 6/28 * 35 = 7.5 kg worth of H₂ The fact is, because of how 35kg relating back only to the original N2 volume can cause 7.5 kg value in H2, only confirms what overages there prove to become and that all N₂ comes as is finished first Yield is often referred to as overall product of a certain chemical reaction. What is "percentage yield?" To get an answer of that kind of problem, it’s better made common knowledge it relates to percentage of real ratio and theoric