Chemical Accounting: Chapter 5 Study Notes

Learning Objectives

• Balance chemical equations by inspection.

• Relate chemical equations to determine gas volumes.

• Calculate formula/molecular, and molar masses.

• Use Avogadro's number to find number of particles.

• Convert between moles and masses.

• Perform stoichiometric calculations.

• Calculate and prepare solutions using molarity, percent by volume, or percent by mass.

Chemical Equations

Definition and Representation

Chemical equations describe chemical reactions like sentences describe thoughts. Reactants are the substances before the reaction, and products are those formed after. The arrow (→) means "yields" or "produces." States of matter are indicated by symbols:

Symbol	Meaning
(s)	solid
(l)	liquid
(g)	gas
(aq)	aqueous (dissolved in water)

• Use coefficients to balance atoms—never change subscripts in chemical formulas.

Volume Relationships in Gas Reactions

Gas Laws and Avogadro's Hypothesis

Gas volumes combine in small whole number ratios at constant temperature and pressure. Avogadro's Hypothesis: Equal gas volumes at the same temperature and pressure contain equal numbers of molecules.

• Example: $C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O$ 1 L propane reacts with 5 L oxygen.

The Mole & Avogadro's Number

Definition and Calculations

The mole is a fundamental unit for counting particles in chemistry. Avogadro's number ($N_A$) is $6.022 \times 10^{23}$ particles/mol.

• Formula: $\text{Number of particles} = \text{moles} \times N_A$

• At STP (0°C, 1 atm): 1 mol of any gas occupies 22.4 L.

• Formula for Molar Mass: $\text{Molar Mass} = \frac{\text{mass of sample}}{\text{number of moles}}$

• Example: $\text{Molar mass of SO}_2 = 32.1 + 2 \times 16.0 = 64.1$ g/mol

Mole-Mass Conversions

Conversion Formulas

Conversions between mass and moles are essential for quantitative chemical calculations.

• Formula: $\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$

• Formula: $\text{Mass} = \text{Moles} \times \text{Molar Mass}$

Stoichiometry

Quantitative Relationships

Stoichiometry involves the quantitative relationships between reactants and products in chemical reactions.

• Write and balance the equation.

• Convert masses to moles.

• Use coefficients for mole ratio.

• Convert moles to grams (if needed).

• Example: $2H_2 + O_2 \rightarrow 2H_2O$ 2 mol H2 reacts with 1 mol O2 to form 2 mol H2O.

Solutions

Definitions and Concentrations

A solution is a homogeneous mixture of solute (substance dissolved) and solvent (dissolving medium). Concentration is the amount of solute per amount of solution.

• Formula for Molarity (M): $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Example: 3.50 mol NaCl in 2.00 L = 1.75 M NaCl

Percent Concentrations

Percent concentration expresses the ratio of solute to solution as a percentage.

Type	Formula	Example
% by volume	$(\frac{\text{volume solute}}{\text{total volume}}) \times 100$	120 mL oil in 4.0 L fuel = 3.0% v/v
% by mass	$(\frac{\text{mass solute}}{\text{total mass}}) \times 100$	25.9 g NaCl in 429 g water = 5.7% w/w

Preparing Solutions

Solutions can be prepared by calculating the required mass or volume of solute and solvent.

• From molarity: $\text{mol} = M \times L$, then find mass if molar mass is known.

• From percent by mass: total mass × percent (decimal) = grams of solute.

• Example: To make 430 g of 4.85% NaNO3 solution: $430 \times 0.0485 = 20.9$ g NaNO3 + water to total 430 g.

Additional Key Points

• Always balance equations before calculations.

• Coefficients represent moles.

• Use molar mass as conversion factors.

• Mass is conserved in every reaction.

• Molarity, % by mass, and % by volume describe concentration in different ways.