The Concept of the Mole and Physical Chemistry Fundamentals

Fundamental Atomic and Molecular Masses

• Atomic Mass Unit (amu): Defined as exactly $1/12^{th}$ the mass of a carbon-12 atom. $1\,amu = 1.6603 \times 10^{-24}\,g$.
• Relative Atomic Mass ($A_r$): The average mass of one atom of an element compared to $1/12^{th}$ of the mass of one atom of carbon-12. It accounts for isotopic abundance and has no units.
• Relative Molecular Mass ($M_r$): The average mass of one molecule of a substance compared to $1/12^{th}$ the mass of one atom of carbon-12. It is calculated by summing the $A_r$ of all atoms in the chemical formula.
• Relative Formula Mass: The term used for the relative mass of ionic compounds (e.g., $NaCl$), as they do not exist as distinct molecules.

The Mole and Avogadro's Constant

• The Mole (mol): The base unit for the amount of substance. One mole contains as many elementary entities (atoms, molecules, ions, etc.) as there are atoms in $12\,g$ of carbon-12.
• Avogadro’s Constant ($N_A$ or $L$): Defined as $6.022 \times 10^{23}\,particles\,mol^{-1}$.
• Relationship Formula:$n = \frac{N}{L}$   Where $n$ is the amount of substance in moles, $N$ is the number of entities, and $L$ is Avogadro's constant.

Molar Mass and Molar Volume

• Molar Mass ($M$): The mass of one mole of a substance expressed in $g\,mol^{-1}$. It is numerically equal to the $A_r$ or $M_r$.
• Mass-Mole Relationship:$n = \frac{m}{M}$   Where $m$ is mass in grams.
• Molar Volume ($V_m$): The volume occupied by one mole of any gas at standard temperature and pressure (s.t.p. = $273\,K$ and $101.3\,kPa$). At s.t.p., $V_m = 22.4\,dm^3\,mol^{-1}$.
• Gas Volume Relationship:$n = \frac{V}{V_m}$   Where $V$ is the volume of the gas in $dm^3$.

Concentration and Solution Preparation

• Molarity (C): The quantity of solute (moles) dissolved in one cubic decimetre of solution, expressed in $mol\,dm^{-3}$.   $C = \frac{n}{V}$
• Mass Concentration (\rho): The mass of solute dissolved in one cubic decimetre of solution, expressed in $g\,dm^{-3}$.   $\rho = \frac{m}{V}$
• Relationship Between Concentrations:$C = \frac{\rho}{M}$
• Standard Solution: A solution with an accurately known concentration.
• Primary Standard: A high-purity, stable substance used to prepare standard solutions (e.g., sodium carbonate or potassium iodate).
• Dilution Formula: Used to prepare solutions from concentrated stocks.   $C_1 V_1 = C_2 V_2$
• Stock Solution Concentration Formula:$C = \frac{\text{Density}(\rho) \times 1000 \times \text{percentage purity}(\%)}{M \times 100}$

Questions & Discussion

Q: How do you determine the relative atomic mass of Oxygen if the average mass of an atom is $2.65659 \times 10^{-23}\,g$?A: Use the formula $A_r(O) = \frac{2.65659 \times 10^{-23}\,g}{1.6603 \times 10^{-24}\,g} = 16.0$.

Q: How many moles are contained in $9.5 \times 10^{23}$ molecules of oxygen?A: $n = \frac{9.5 \times 10^{23}}{6.02 \times 10^{23}} = 1.58\,mol$.

Q: Calculate the volume occupied by $0.75\,mol$ of ammonia gas ($NH_3$) at s.t.p.A: $V = n \times V_m = 0.75\,mol \times 22.4\,dm^3\,mol^{-1} = 16.8\,dm^3$.

Q: Do $1\,mol$ of $H_2O$ and $1\,mol$ of $NaCl$ have the same mass?A: No, their molar masses differ ($H_2O \approx 18\,g\,mol^{-1}$, $NaCl \approx 58.5\,g\,mol^{-1}$), though they contain the same number of particles.

Q: What are the properties of a primary standard?A: It must be available in high purity, stable (no weight loss or water gain during weighing), have a high relative formula mass, be highly soluble, and react rapidly and specifically.