Atomic Structure Quantitative Chemistry and Redox for the ESAT

Isotopes and Atomic Notation

Atoms of the same element always possess the same number of protons in their nuclei, giving them a constant atomic number. However, the number of neutrons can vary. Isotopes are defined as atoms of an element with the same number of protons but different numbers of neutrons, resulting in different mass numbers. The term comes from the Greek roots isos, meaning same, and topos, meaning place, because they occupy the same position in the Periodic Table.

A specific isotope is identified using standard notation showing the mass number and atomic number.

For example, hydrogen has three isotopes: $^1_1H$, $^2_1H$, and $^3_1H$. While each has 1 proton, they have 0, 1, and 2 neutrons respectively.

Mass Spectrometry and Abundance

A mass spectrometer is used to identify isotopes and their relative abundances. In this device, atoms are ionised, accelerated, and separated by their mass to charge ratio ($m/z$) as they drift toward a detector. The resulting mass spectrum plots the relative number of ions against their $m/z$ values.

In a neon mass spectrum, three peaks appear at 20, 21, and 22, indicating three isotopes.

For boron, the spectrum shows peaks at 10 and 11 in a 1:4 ratio.

This means 20% of atoms are boron 10 and 80% are boron 11. For diatomic molecules like bromine ($Br_{2}$), the spectrum is more complex, showing peaks for individual $Br^{+}$ ions (79 and 81) and molecular $Br_{2}^{+}$ ions (158, 160, and 162) due to the different combinations of isotopes.

Relative Atomic Mass $A_{r}$

The relative atomic mass ($A_{r}$) of an element is the weighted mean of the mass numbers of its isotopes, taking their abundances into account. It is relative to $1/12$ the mass of a carbon 12 atom.

To calculate $A_{r}$ from percentage data: $A_{r}(X) = \frac{(a \times q) + (b \times r) + \dots}{100}$, where $a$ and $b$ are percentages and $q$ and $r$ are mass numbers.

For chlorine, which is 75% $^{35}Cl$ and 25% $^{37}Cl$: $A_{r}(Cl) = (\frac{75}{100} \times 35) + (\frac{25}{100} \times 37) = 26.25 + 9.25 = 35.5$.

The Periodic Table and Reactivity

The Periodic Table arranges elements by increasing atomic number. Horizontal rows are called Periods, and vertical columns are called Groups. The Period number indicates the outermost filled electron shell, while the Group number reflects the number of electrons in the outer shell, determining chemical properties.

Key groups include Group 1 (alkali metals), Group 2 (alkaline earth metals), Group 17 (halogens), and Group 18 (noble gases). In metal groups, reactivity increases down the group. For example, potassium reacts more vigorously with water than sodium or lithium, as seen in their characteristic lilac, yellow orange, and crimson flames respectively. In non metal groups, reactivity decreases down the group.

Chemical Formulae and Equations

Chemical reactions rearrange atoms to form new substances without destroying nuclei. The total mass of reactants equals the total mass of products.

State symbols identify the physical form: solid (s), liquid (l), gas (g), and aqueous (aq). Balanced equations must have the same number of each atom type on both sides.

Ionic equations exclude spectator ions that do not participate in the reaction. For example, the neutralisation of any acid and alkali is simplified to: $H^{+}(aq) + OH^{-}(aq) \rightarrow H_{2}O(l)$.

Reversible Reactions and Equilibrium

Many reactions are reversible, denoted by the $\rightleftharpoons$ symbol. In a closed system, these can reach dynamic equilibrium, where the forward and reverse reactions occur at the same rate.

Le Chatelier's principle states that if conditions change, the equilibrium shifts to oppose the change: 1. Increasing concentration of a reactant shifts the equilibrium right. 2. Increasing temperature shifts the equilibrium in the endothermic direction. 3. Increasing pressure shifts the equilibrium to the side with fewer gas molecules.

Quantitative Chemistry and Moles

The mole is the unit for the amount of substance, containing $6.022 \times 10^{23}$ particles (Avogadro's constant). The relationship is: $n = \frac{m}{M}$, where $n$ is the number of moles, $m$ is mass in grams, and $M$ is the molar mass ($A_{r}$ or $M_{r}$).

At room temperature and pressure (rtp), one mole of any gas occupies $24.0 dm^{3}$. For solutions, concentration is measured in $mol dm^{-3}$ or $g dm^{-3}$: $n = V \times c$, where $V$ is volume in $dm^{3}$.

Percentage yield measures efficiency: $\text{percentage yield} = \frac{\text{actual yield}}{\text{predicted yield}} \times 100$.

Oxidation, Reduction, and Redox

Oxidation is the gain of oxygen or the loss of electrons. Reduction is the loss of oxygen or the gain of electrons (OIL RIG: Oxidation Is Loss, Reduction Is Gain).

Oxidation states are used to track electron transfer. Rules include: 1. Elements have an oxidation state of 0. 2. Monatomic ions match their charge. 3. Oxygen is usually -2. 4. Hydrogen is usually +1. An increase in oxidation state signifies oxidation, while a decrease signifies reduction.