Mass Relations in Chemistry: Stoichiometry

The Mole and Avogadro's Number

The concept of the mole is fundamental in chemistry for relating the mass of substances to the number of particles they contain. Avogadro's number defines the number of items in one mole.

• Mole (mol): The amount of substance containing as many entities (atoms, molecules, ions, etc.) as there are atoms in exactly 12 grams of carbon-12.

• Avogadro's Number (NA): items per mole.

• Significance: The mole allows chemists to count particles by weighing them, as laboratory measurements are typically made in grams.

• Example: 1 mole of Ca contains Ca atoms.

Molar Mass

Molar mass (MM) is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is numerically equal to the sum of the atomic masses (in amu) of the atoms in a chemical formula.

• Formula:

• Example: For H2O: g/mol

Mole-Gram Conversions

Conversions between mass and moles use the molar mass as a conversion factor.

• Formula:

• Conversion factors: and

• Example: To find the mass of 4.05 mol of N2O, multiply by its molar mass.

Interconverting Particles, Moles, and Mass

Stoichiometric calculations often require converting between the number of particles, moles, and mass.

• To convert particles to moles: Divide by Avogadro's number.

• To convert moles to mass: Multiply by molar mass.

• To convert mass to moles: Divide by molar mass.

• To convert moles to particles: Multiply by Avogadro's number.

Flowchart: Number of particles ↔ (Avogadro's number) ↔ Moles ↔ (Molar mass) ↔ Mass

Solute Concentrations – Molarity

Molarity (M) is the most common unit of concentration in chemistry, defined as moles of solute per liter of solution.

• Formula:

• Symbol: M

• Example: If 1.20 mol of a substance is dissolved to make 2.50 L of solution, M

• Square brackets, e.g., [Na+], indicate molar concentration.

Preparation of Molar Solution

Preparing solutions of known molarity involves dissolving a measured amount of solute in a volumetric flask and diluting to a precise volume.

• Use volumetric glassware for accuracy.

• Ensure the solute is fully dissolved before making up to the final volume.

Molarity as a Conversion Factor

Molarity can be used to calculate the number of moles of solute in a given volume or the volume needed for a given number of moles.

• To find moles:

• To find volume:

• Example: What volume of 12 M HCl is needed to obtain 0.10 mol HCl? L = 8.3 mL

Chemical Equations

Chemical equations represent chemical reactions, showing reactants and products. Equations must be balanced to obey the law of conservation of mass.

• Reactants: Substances on the left side of the equation.

• Products: Substances on the right side.

• Balancing: The number of atoms of each element must be the same on both sides.

Writing Chemical Equations

Steps for writing and balancing chemical equations:

1. Write a skeleton equation for the reaction.

2. Indicate the physical state of each reactant and product: (g) gas, (l) liquid, (s) solid, (aq) aqueous.

3. Balance the equation by adjusting coefficients (not subscripts).

Reactions in the Laboratory

Most chemical reactions in the laboratory occur in aqueous solution, with water as the universal solvent. Common types of reactions include:

• Precipitation reactions

• Acid-base reactions

• Oxidation-reduction reactions

Example Problems

• How many Ca atoms are in a 0.6000-mol sample of Ca?

• Calculate the molar mass of CH4 and HNO3.

• What is the molar mass of tungsten(IV) oxide (WO2)?

• What is the mass of a 4.05-mol sample of N2O?

• How many moles are in 2.37 g of C7H8O?

• What is the molarity of a solution with 7.85 g methanol (CH3OH) in 153 mL solution?

• What volume of 12 M HCl is needed to obtain 0.10 mol HCl?

• Balance the following equations:

  • P2O5 + H2O → H3PO4

  • B2N3H14 + O2 → N2O5 + B2O3 + H2O

Additional info: For all calculations, use atomic masses from the periodic table and ensure units are consistent. Practice with example problems to master stoichiometric conversions and balancing equations.