Stoichiometry: The Mole Concept, Molar Mass, and Chemical Formulae

Calculation of Formula Mass and Molecular Mass

• Formula Mass of Sodium Chloride ($NaCl$)   - To calculate the formula mass of sodium chloride, the atomic masses of its constituent elements are summed.   - Atomic mass of sodium ($Na$) = $23.0\,\text{u}$   - Atomic mass of chlorine ($Cl$) = $35.5\,\text{u}$   - Formula mass = $23.0\,\text{u} + 35.5\,\text{u} = 58.5\,\text{u}$

• Problem 1.1: Molecular Mass of Glucose ($C_6H_{12}O_6$)   - The molecular mass is determined by calculating the total mass of all atoms present in the molecule using their individual atomic masses.   - Calculation Steps:     - Six atoms of Carbon: $6 \times (12.011\,\text{u}) = 72.066\,\text{u}$     - Twelve atoms of Hydrogen: $12 \times (1.008\,\text{u}) = 12.096\,\text{u}$     - Six atoms of Oxygen: $6 \times (16.00\,\text{u}) = 96.00\,\text{u}$   - Total Molecular Mass:     - $72.066\,\text{u} + 12.096\,\text{u} + 96.00\,\text{u} = 180.162\,\text{u}$

The Mole Concept and Avogadro Constant

• Need for a Convenient Unit   - Atoms and molecules exhibit extremely small sizes.   - Even a minute amount of any substance contains a very large number of these entities.   - To manage these quantities, the concept of a "mole" is utilized, similar to other collective units:     - One dozen = $12\,\text{items}$     - One score = $20\,\text{items}$     - One gross = $144\,\text{items}$

• SI Definition of the Mole   - In the SI system, the mole (symbol: mol) is the seventh base quantity designated for the amount of a substance.   - One mole contains exactly $6.02214076 \times 10^{23}$ elementary entities.   - This fixed numerical value is known as the Avogadro constant ($N_A$) when expressed in the unit $\text{mol}^{-1}$.   - The amount of substance (symbol: $n$) represents the measure of the number of specified elementary entities in a system.   - Elementary entities can include an atom, a molecule, an ion, an electron, any other particle, or a specific group of particles.   - A mole of any substance always contains the same number of entities, regardless of what the substance is.

• Determination of the Avogadro Number   - The precision of this number was established using mass spectrometry to find the mass of a carbon-12 ($^{12}C$) atom.   - Mass of one $^{12}C$ atom = $1.992648 \times 10^{-23}\,g$   - One mole of carbon weighs exactly $12\,g$.   - Number of atoms in 1 mole of carbon = $\frac{12\,g/mol\,^{12}C}{1.992648 \times 10^{-23}\,g/^{12}C\,atom} = 6.0221367 \times 10^{23}\,\text{atoms/mol}$   - Written without powers of ten, the number is: $602,213,670,000,000,000,000,000$.   - Named the 'Avogadro constant' or 'Avogadro number' after Amedeo Avogadro.

• Examples of Molar Quantities   - 1 mol of hydrogen atoms = $6.022 \times 10^{23}\,\text{atoms}$   - 1 mol of water molecules = $6.022 \times 10^{23}\,\text{water molecules}$   - 1 mol of sodium chloride = $6.022 \times 10^{23}\,\text{formula units of sodium chloride}$

Molar Mass

• Definition   - The mass of one mole of a substance expressed in grams is known as its molar mass.   - The molar mass in grams is numerically identical to the atomic mass, molecular mass, or formula mass when expressed in unified atomic mass units ($\text{u}$).

• Reference Values   - Molar mass of water ($H_2O$) = $18.02\,g\,mol^{-1}$   - Molar mass of sodium chloride ($NaCl$) = $58.5\,g\,mol^{-1}$

Percentage Composition

• Purpose and Utility   - Used to determine the percentage of a specific element within a compound.   - Essential for identifying the formula of unknown or new compounds.   - Serves as a purity check for known compounds by comparing the analyzed percentage of elements against a pure sample.

• Calculation Formula   - \text{Mass % of an element} = \frac{\text{mass of that element in the compound} \times 100}{\text{molar mass of the compound}}

• Percentage Composition of Water ($H_2O$)   - Molar mass of water = $18.02\,g$   - Mass % of Hydrogen:     - \text{Mass % H} = \frac{2 \times 1.008}{18.02} \times 100 = 11.18   - Mass % of Oxygen:     - \text{Mass % O} = \frac{16.00}{18.02} \times 100 = 88.79

• Percentage Composition of Ethanol ($C_2H_5OH$)   - Molecular formula: $C_2H_5OH$   - Molar mass: $(2 \times 12.01 + 6 \times 1.008 + 16.00)\,g = 46.068\,g$   - Mass per cent of Carbon:     - \text{Mass % C} = \frac{24.02\,g}{46.068\,g} \times 100 = 52.14\%   - Mass per cent of Hydrogen:     - \text{Mass % H} = \frac{6.048\,g}{46.068\,g} \times 100 = 13.13\%   - Mass per cent of Oxygen:     - \text{Mass % O} = \frac{16.00\,g}{46.068\,g} \times 100 = 34.73\%

Empirical and Molecular Formulae

• Definitions   - Empirical Formula: Represents the simplest whole number ratio of the various atoms present in a compound.   - Molecular Formula: Represents the exact number of different types of atoms present in a single molecule of a compound.

• Determining Formulae from Mass Percent   - If the mass percentage of elements is known, the empirical formula can be calculated.   - If the molar mass is also known, the molecular formula can be derived.

• Problem 1.2: Calculating Empirical and Molecular Formulae   - Given Data:     - Hydrogen ($H$) = $4.07\%$     - Carbon ($C$) = $24.27\%$     - Chlorine ($Cl$) = $71.65\%$     - Molar mass = $98.96\,g$   - Step 1: Conversion of mass per cent to grams     - Assume a $100\,g$ sample of the compound.     - Mass of Hydrogen = $4.07\,g$     - Mass of Carbon = $24.27\,g$     - Mass of Chlorine = $71.65\,g$   - Step 2: Convert into number of moles for each element     - Divide the mass of each element by its atomic mass.     - Moles of hydrogen: $\text{Moles of H} = \frac{4.07\,g}{1.008\,g} = 4.04$     - Moles of carbon: $\text{Moles of C} = \frac{24.27\,g}{12.01\,g} = 2.021$     - Moles of chlorine: $\text{Moles of Cl} = \frac{71.65\,g}{35.453\,g} = 2.021$