Atomic Structure Isotopes and Quantitative Chemistry

Atomic Structure and Isotopes

Atoms consist of a central nucleus containing protons and neutrons, surrounded by electrons in specific shells or energy levels. Elements are defined by their atomic number, which is the number of protons in the nucleus. However, atoms of the same element can have different mass numbers because they contain different numbers of neutrons. These variations are called isotopes.

The term isotope comes from the Greek 'isos' (same) and 'topos' (place), indicating that isotopes occupy the same position in the Periodic Table. A particular isotope is identified by its mass number ($A$) and atomic number ($Z$) using the notation ${}_{Z}^{A}\mathrm{X}$.

For instance, hydrogen has three isotopes: Protium (${}_{1}^{1}\mathrm{H}$), Deuterium (${}_{1}^{2}\mathrm{H}$), and Tritium (${}_{1}^{3}\mathrm{H}$). They all have 1 proton but possess 0, 1, and 2 neutrons respectively.

Mass Spectrometry and Isotopic Abundance

Mass spectrometry is used to identify the number and abundance of isotopes. In a mass spectrometer, atoms or molecules are ionised, accelerated, and then separated based on their mass-to-charge ratio ($m/z$). The resulting spectrum plots relative abundance against $m/z$.

The mass spectrum of neon shows three peaks, indicating three isotopes with masses 20, 21, and 22. Similarly, the mass spectrum of boron shows two peaks at $m/z$ 10 and 11.

Worked Example: Boron Abundance In a sample of boron, the ratio of peaks for $m/z$ 10:11 is 1:4. This means 20% are ${}^{10}\mathrm{B}$ and 80% are ${}^{11}\mathrm{B}$.

Worked Example: Bromine Molecules Bromine exists as diatomic molecules ($\mathrm{Br}_{2}$). The mass spectrum of $\mathrm{Br}_{2}$ gas shows peaks at $m/z$ 79 and 81 (atomic ions) and peaks at 158, 160, and 162 (molecular ions). Because there are two isotopes of equal abundance (${}^{79}\mathrm{Br}$ and ${}^{81}\mathrm{Br}$), the combinations ${}^{79}\mathrm{Br}-{}^{79}\mathrm{Br}$, ${}^{79}\mathrm{Br}-{}^{81}\mathrm{Br}$, ${}^{81}\mathrm{Br}-{}^{79}\mathrm{Br}$, and ${}^{81}\mathrm{Br}-{}^{81}\mathrm{Br}$ lead to a molecular peak ratio of 1:2:1 for the masses 158:160:162.

Relative Atomic Mass ($A_{\mathrm{r}}$)

The relative atomic mass is the weighted mean of the mass numbers of an element's isotopes, relative to $1/12$ of the mass of an atom of carbon-12.

To calculate $A_{\mathrm{r}}$ from percentage data: $A_{\mathrm{r}}(\mathrm{X}) = \frac{(a \times q) + (b \times r) + \dots}{100}$ Where $a$ and $b$ are percentages and $q$ and $r$ are isotopic masses.

To calculate $A_{\mathrm{r}}$ from mass spectrum heights ($a, b, c$): $A_{\mathrm{r}}(\mathrm{X}) = \frac{(a \times q) + (b \times r) + \dots}{a + b + c + \dots}$

Worked Example: Chlorine A sample of chlorine contains 75% ${}^{35}\mathrm{Cl}$ and 25% ${}^{37}\mathrm{Cl}$. $A_{\mathrm{r}}(\mathrm{Cl}) = (\frac{75}{100} \times 35) + (\frac{25}{100} \times 37) = 26.25 + 9.25 = 35.5$.

The Periodic Table

Elements are arranged by increasing atomic number. Horizontal rows are Periods and vertical columns are Groups. Elements in the same Group share similar chemical properties because they have the same number of electrons in their outermost shell.

Key trends include:

1. Group 1 (Alkali Metals): Reactivity increases down the group. Lithium reacts slowly with water; Potassium reacts vigorously, self-igniting with a lilac flame.
2. Group 17 (Halogens): Reactivity decreases down the group.
3. Group 18 (Noble Gases): Possess complete outer shells and are generally unreactive.

Chemical Reactions and Equations

In chemical reactions, atoms are rearranged; no nuclei are created or destroyed. Total mass is conserved.

Formulae and State Symbols You must know common formulae: Water ($\mathrm{H}_{2}\mathrm{O}$), Methane ($\mathrm{CH}_{4}$), Ammonia ($\mathrm{NH}_{3}$), and the diatomic elements ($H_{2}, N_{2}, O_{2}, F_{2}, Cl_{2}, Br_{2}, I_{2}$). Use state symbols: (s) solid, (l) liquid, (g) gas, and (aq) aqueous solution.

Ionic Equations These show only the species that change state or charge. For example, all acid-alkali neutralisations share the same simplest ionic equation: $\mathrm{H}^{+}(aq) + \mathrm{OH}^{-}(aq) \rightarrow \mathrm{H}_{2}\mathrm{O}(l)$

Half-equations Used for redox processes and electrolysis to show electron transfer. For example, in the electrolysis of molten sodium chloride: At the cathode: $\mathrm{Na}^{+} + e^{-} \rightarrow \mathrm{Na}$ At the anode: $2\mathrm{Cl}^{-} \rightarrow \mathrm{Cl}_{2} + 2e^{-}$

Reversible Reactions and Equilibrium

Many reactions are reversible ($\rightleftharpoons$). In a closed system, they reach dynamic equilibrium, where the forward and reverse reactions occur at the same rate.

Le Chatelier's Principle states that if a system at equilibrium is changed, the position of equilibrium moves to oppose that change.

1. Concentration: Adding a reactant moves the equilibrium to the right.
2. Temperature: Increasing temperature favours the endothermic direction (positive $\Delta H$). Decreasing temperature favours the exothermic direction (negative $\Delta H$).
3. Pressure: Increasing pressure moves the equilibrium to the side with fewer gas molecules.

Quantitative Chemistry: The Mole

The mole is the unit for the amount of a substance. One mole contains $6.022 \times 10^{23}$ particles (Avogadro's constant, $N_{\mathrm{A}}$).

Key relationship: $\text{Amount (mol)} = \frac{\text{Mass (g)}}{\text{Molar Mass (g mol}^{-1})}$

Empirical and Molecular Formulae The empirical formula is the simplest integer ratio of atoms. The molecular formula is the actual number of atoms and is a multiple of the empirical formula.

Worked Example: Empirical Formula A compound is 36% Beryllium ($A_{\mathrm{r}}=9$) and 64% Oxygen ($A_{\mathrm{r}}=16$). Moles Be = $36/9 = 4$; Moles O = $64/16 = 4$. Ratio is 1:1, so the formula is $\mathrm{BeO}$.

Reacting Masses and Yield Calculations often require identifying a limiting reactant. The percentage yield is calculated as: $\text{Percentage Yield} = \frac{\text{Actual Yield}}{\text{Predicted Yield}} \times 100$

Gases and Solutions At room temperature and pressure (rtp), 1 mole of any gas occupies $24.0 \text{ dm}^{3}$. Concentration ($c$) is measured in $\text{mol dm}^{-3}$ or $\text{g dm}^{-3}$: $n = c \times V$ (where $V$ is in $\text{dm}^{3}$)

Solubility A saturated solution contains the maximum mass of solute that can dissolve at a specific temperature. Solubility curves show how this changes with temperature.

Oxidation, Reduction, and Oxidation States

Oxidation is the gain of oxygen or the loss of electrons. Reduction is the removal of oxygen or the gain of electrons. Remember OIL RIG.

Oxidation States are used to track electron transfer in covalent molecules.

• Elements = 0.
• Monatomic ions = Charge of ion.
• Oxygen = -2 (except in peroxides or with Fluorine).
• Hydrogen = +1 (except in metal hydrides).
• Sum in a neutral compound = 0.
• Sum in a polyatomic ion = Charge of ion.

An increase in oxidation state indicates oxidation; a decrease indicates reduction.