Chemical Equations, Moles, and Solution Concentration: Core Concepts in Chemical Accounting

Chemical Equations and the Law of Conservation of Mass

Law of Conservation of Mass

The Law of Conservation of Mass states that matter is neither created nor destroyed in a chemical reaction. This principle, established by Antoine Lavoisier, is foundational to all chemical equations and calculations.

• Reactants are substances present before the reaction; products are substances formed as a result.

• The total mass and number of atoms for each element must be the same on both sides of the equation.

Chemical Equations: Structure and Balancing

Chemical equations are concise representations of chemical reactions, showing the identities and quantities of reactants and products.

• Subscripts indicate the number of atoms of each element in a molecule.

• Coefficients indicate the number of molecules or moles involved.

• States of matter are denoted as (s) for solid, (l) for liquid, (g) for gas, and (aq) for aqueous.

To balance an equation, adjust only the coefficients, never the subscripts.

Balancing Chemical Equations: Stepwise Approach

Balancing ensures the same number of each type of atom on both sides of the equation. The process involves:

1. Writing correct formulas for all reactants and products.

2. Counting the number of atoms of each element on both sides.

3. Balancing one element at a time using coefficients.

4. Checking that all elements are balanced.

Example: Balancing Sodium Azide Decomposition

Consider the decomposition of sodium azide, used in airbags:

Balancing requires ensuring equal numbers of sodium and nitrogen atoms on both sides.

Volume Relationships and Avogadro's Hypothesis

Law of Combining Volumes

When gases react at constant temperature and pressure, their volumes are in simple whole-number ratios.

Avogadro's Hypothesis

Equal volumes of gases, at the same temperature and pressure, contain equal numbers of molecules. This leads to the concept of molar volume:

• At standard temperature and pressure (STP: 0°C, 1 atm), 1 mole of any gas occupies 22.4 L.

The Mole and Avogadro's Number

Definition of the Mole

A mole (mol) is the amount of substance containing as many particles (atoms, molecules, ions) as there are in exactly 12 g of carbon-12. This number is Avogadro's number:

• Avogadro's number: $6.02 \times 10^{23}$ particles/mol

Using Avogadro's Number

Avogadro's number allows conversion between moles and number of particles:

• 1 mole = $6.02 \times 10^{23}$ particles

Molar Mass and Formula Mass

Molar Mass

The molar mass of a substance is the mass of one mole of its entities (atoms, molecules, or formula units), expressed in grams per mole (g/mol). For elements, this is the atomic mass from the periodic table.

• For compounds, add the atomic masses of all atoms in the formula.

Formula Mass and Molecular Mass

Formula mass is used for ionic compounds; molecular mass for covalent molecules. Both are calculated by summing atomic masses.

Stoichiometry: Quantitative Chemical Relationships

Stoichiometric Calculations

Stoichiometry uses balanced equations to relate amounts of reactants and products. The coefficients provide the mole ratios needed for conversions.

• General plan: mass A → moles A → moles B → mass B

Example: Mass Relationships in Reactions

To find the mass of oxygen needed to react with a given mass of carbon:

• Convert grams of C to moles of C

• Use the mole ratio from the balanced equation

• Convert moles of O2 to grams

Solutions and Concentration

Solutions: Definitions

A solution is a homogeneous mixture of two or more substances. The solute is dissolved in the solvent, which is present in greater amount.

Concentration of Solutions

Concentration expresses the amount of solute in a given amount of solution. Common units include:

• Percent by mass: $(\text{mass solute}/\text{mass solution}) \times 100\%$

• Percent by volume: $(\text{volume solute}/\text{volume solution}) \times 100\%$

• Molarity (M): $\text{moles solute}/\text{liters solution}$

Preparing Solutions of Known Molarity

To prepare a solution of known molarity:

1. Weigh the required mass of solute.

2. Dissolve in a volumetric flask.

3. Add solvent to the calibration mark.

Calculating Molarity and Related Quantities

Example: To find the molarity of a solution, convert grams of solute to moles, then divide by the volume in liters.

To find the mass of solute needed for a given volume and molarity, multiply volume (L) by molarity (mol/L), then by molar mass (g/mol).

To find the volume of solution needed for a given amount of solute and molarity, divide moles by molarity.

Percent Concentration Calculations

Percent by mass and percent by volume are alternative ways to express concentration, useful for practical laboratory and industrial applications.