Moles and Molar Masses

Moles, Molar Masses, and Amounts of Substance

• One mole is equivalent to 6.022 137 x 10^23 entities, with 6.022 137 x 10^23 being Avogadro's constant (Nₐ).
• The amount of substance n (number of moles) of a chemical species X in a sample containing N elements is given by n = N/Nₐ.

Atomic, Ionic, and Molecular Molar Mass Determination

• The atomic molar mass of an element is the mass of one mole of atoms, noted as M, and is generally expressed in g/mol.
• Molecular molar mass refers to the mass of one mole of molecules.
• To determine molecular mass, sum the atomic molar masses of the atoms constituting the molecule, considering the coefficients in the molecular formula.
• Electric charges are not accounted for when determining an ionic molar mass.

Avogadro-Ampere's Law and Molar Volume Definition

• Equal volumes of different gases, measured under the same temperature and pressure conditions, contain the same number of molecules or atoms N, and thus, the same amount of substance n.
• The molar volume Vₘ of a gas is the volume occupied by 1 mole of that gas.
• All gases have the same molar volume Vₘ under the same temperature and pressure conditions.
• At 0°C, under 10.13 hPa: Vₘ = 22.4 L/mol; at 20°C, under 10 hPa: Vₘ = 24 L/mol.

Determining the Amount of Substance

• To determine the amount of substance n from a mass m, a liquid volume Vliq, or a gas volume Vgaz.
• n (solid) = m/M
• n (liquid) = p.Vliq/M = d. peau. Vliq/M; where p = m/V is the volumetric mass of the liquid, and d = p/peau is the liquid's density.
• n (gas) = Vgaz/Vₘ

Solutions and Concentrations

• A solution is formed when a solute (solid, liquid, or gas) is introduced into a solvent.
• The mass concentration Cm of a dissolved chemical species equals the ratio between the mass m of the introduced species and the solution volume V: Cm = m/V.
• The amount of substance concentration C of a dissolved chemical species is equal to the ratio between the amount of substance nX of the introduced species X and the solution volume V: C = [X] = nX/V.
• Relationship between Cm and C: Cm = CxM

Solution Preparation

• Calculating and preparing a volume V of a solution with a concentration in the amount of substance C through the dissolution of a solid compound.
• Amount of substance to be taken: n = CxV.
• Mass of compound to be taken: m = nxM = CxVxM.
• Introduce a mass m of solid into a volumetric flask of volume V, half-filled with distilled water. Dissolve the solid, complete with distilled water up to the calibration mark, and homogenize.

Preparing a Daughter Solution

• Calculating and preparing a daughter solution of volume V and concentration in the amount of substance C through dilution of a stock solution of concentration Cm.
• Volume Vp of stock solution to be taken:
  • Method 1: CmxVmP = CfxVf, thus Vmp = CfxVf / Cm.
  • Method 2: Determine the dilution factor F = Cm/Cf, then Vmp = Vf / F.
• Using a volumetric pipette (or graduated pipette or burette), take a volume Vmp of stock solution, which is introduced into a volumetric flask of volume Vf. Complete with distilled water up to the calibration mark and homogenize.

Chemical Reaction, Stoichiometry Table, and Molar Balance

• Chemical Equation, Reactants, Products, Adjustment
• Chemical equations indicate the proportions in which reactants disappear and products appear.
• Adjusted chemical reaction equations provide a balance in the amount of substance (number of moles) between the reactants consumed and the products formed.

Advancement Table Type

• Initial system: x = 0, n1 = 0.1, n2 = 0.6, 0, 0.
• Intermediate system: x, n1 - x, n2 - 3x, 2x, 3x.
• Final system: xmax = 0.1, n1 - xmax = 0, n2 - 3xmax = 0.3, 2xmax = 0.2, 3xmax = 0.3.

Maximum Advancement, Limiting and Excess Reactants, Stoichiometric Proportions

• When a chemical reaction is complete, the chemical system no longer evolves because the limiting reactant has completely disappeared.
  • Advancement is then maximal x = Xmax, and the system is in its final state.
  • Other unconsumed reactants are said to be in excess.
• To determine the maximum advancement Xmax, writing that each of the amounts of reactant in the final state is zero:
  • n1 - Xmax = 0 or n2 - 3Xmax = 0 and keeping the smallest value of xmax then found; Here Xmax = 0.1 mol.
• When all reactants are completely consumed, the proportions are said to be stoichiometric.