Chapter 6: Stoichiometry

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Chapter Overview & SLOs

What is stoichiometry? Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. It involves calculations of mass, moles, and number of particles.

What is the mole concept?

• A mole is the amount of substance that contains exactly $6.022 \times 10^{23}$ particles (atoms, molecules, ions, or formula units).
• This number is called Avogadro's number ($N_A$).
• One mole of any substance has a mass equal to its atomic/molecular/formula mass in grams (molar mass).
• Example: 1 mole of $H_2O$ = 18.015 g = $6.022 \times 10^{23}$ molecules

How do we calculate formula mass and molar mass? Formula mass is the sum of the atomic masses of all atoms in a chemical formula (in amu). Molar mass is the same numerical value expressed in g/mol.

• Example: $CuSO_4 \cdot 5H_2O$ (Copper(II) sulfate pentahydrate)
  • $Cu = 63.5$, $S = 32$, $O_4 = 64$, $5H_2O = 5 \times 18 = 90$
  • Formula mass = $63.5 + 32 + 64 + 90 = 249.5$ amu
  • Molar mass = $249.5$ g/mol

What is the difference between empirical and molecular formulas?

• Empirical formula: The simplest whole-number ratio of atoms in a compound.
• Molecular formula: The actual number of atoms of each element in a molecule.
• Example: Glucose
  • Empirical formula: $CH_2O$ (ratio C:H:O = 1:2:1)
  • Molecular formula: $C_6H_{12}O_6$ (actual atoms)
  • Relation: Molecular formula = $(\text{Empirical formula})_n$ where $n = \frac{\text{Molecular mass}}{\text{Empirical formula mass}}$

How do we perform mole-mass-particle conversions? Use the following relationships:

• $$\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}}$$
• $$\text{Mass (g)} = \text{Moles} \times \text{Molar mass (g/mol)}$$
• $$\text{Number of particles} = \text{Moles} \times 6.022 \times 10^{23}$$
• $$\text{Moles} = \frac{\text{Number of particles}}{6.022 \times 10^{23}}$$

How do we perform stoichiometric calculations? Stoichiometry uses balanced chemical equations to relate quantities of reactants and products.

• Mass-to-mass conversion: Mass $\rightarrow$ moles $\rightarrow$ mole ratio $\rightarrow$ mass
• Mass-to-mole conversion: Mass $\rightarrow$ moles $\rightarrow$ mole ratio $\rightarrow$ moles
• Example: Potassium reacting with water: $$2K + 2H_2O \rightarrow 2KOH + H_2$$
• From the balanced equation, 2 moles of K produce 1 mole of $H_2$

How do we calculate particle counts using Avogadro's number?

• Example: Calculate the number of molecules in 2 moles of hydrogen gas ($H_2$).
• Number of molecules = $2 \times 6.022 \times 10^{23} = 1.2044 \times 10^{24}$ molecules
• Number of hydrogen atoms = $2 \times (2 \times 6.022 \times 10^{23}) = 2.4088 \times 10^{24}$ atoms

What are the different chemical species?

• Ions: Charged atoms or molecules (e.g., $Na^+$, $Cl^-$, $SO_4^{2-}$)
• Molecular ions (polyatomic ions): Groups of covalently bonded atoms with an overall charge (e.g., $NH_4^+$, $CO_3^{2-}$)
• Free radicals: Atoms or molecules with unpaired electrons (e.g., $OH\cdot$, $Cl\cdot$)
• Formula units: The simplest whole-number ratio of ions in an ionic compound (e.g., NaCl formula unit)

What is molar volume? At standard temperature and pressure (STP: $0^\circ C$, 1 atm), 1 mole of any gas occupies 22.4 L (molar volume).

Key formulas summary:

• $\text{Avogadro's number} = 6.022 \times 10^{23} \text{ particles/mol}$
• $$\text{Moles} = \frac{\text{Mass}}{\text{Molar mass}}$$
• $$\text{Particles} = \text{Moles} \times 6.022 \times 10^{23}$$
• $\text{Molar volume (STP)} = 22.4 \text{ L/mol}$
• $$\text{Empirical formula mass} \times n = \text{Molecular mass}$$

Important note for diatomic gases: Remember that 1 mole of hydrogen gas ($H_2$) has a mass of 2 g, while 1 mole of hydrogen atoms ($H$) is 1 g. The same applies to $O_2$, $N_2$, $F_2$, $Cl_2$.

These notes are strictly aligned with the Student Learning Outcomes (SLOs) for the FBISE 2026 annual examination.

• How do we relate mass to the mole? Use the atomic or molecular mass of elements and compounds to calculate the number of moles in a given mass, such as determining that 16 g of oxygen ($O_2$) contains 0.5 moles of $O_2$ molecules (since molar mass of $O_2$ is 32 g/mol).
• How do we determine chemical formulas from data? Distinguish between empirical formulas (simplest whole-number ratio, e.g., $CH_2O$ for glucose) and molecular formulas (actual atom count, e.g., $C_6H_{12}O_6$), and use the 'n' factor $n = \frac{\text{Molecular Mass}}{\text{Empirical Formula Mass}}$ to convert between them.
• How do we use Avogadro's number in calculations? Calculate the total number of atoms or molecules in a sample by multiplying the number of moles by $6.022 \times 10^{23}$, applied to substances like hydrogen gas ($H_2$), carbon, or benzene ($C_6H_6$).
• How do we solve mass-to-mass and particle-count problems? Apply stoichiometric principles using balanced chemical equations to calculate the grams of a substance required or produced in a reaction, and determine the corresponding number of particles involved, using the mole concept as the bridge.

Frequently Asked Questions (FAQ)