Chapter 15: The Mole, Gases, Solutions, and Energetics

The mole and stoichiometry

The mole is the amount of substance containing entities (, exact since 2019; BIPM, 2019). The molar mass (g mol⁻¹) links mass and amount: . Example: 5.85 g of NaCl () is mol.

A balanced equation gives mole ratios. Procedure: (1) write the balanced equation; (2) convert masses to moles; (3) use the ratio; (4) identify the limiting reagent (the one that runs out first); (5) compute the theoretical yield and percentage yield . The empirical formula is found from the percentage composition by dividing by and finding the simplest whole-number ratio.

Solutions. The concentration (mol dm⁻³). Dilution: . Titration example: 25.0 cm³ of 0.100 mol dm⁻³ NaOH is neutralized by 20.0 cm³ of HCl. Moles of NaOH mol, equal to the moles of HCl, so mol dm⁻³.

Gases

The ideal gas equation is with . Example: 2.0 g of H₂ ( mol) at 298 K and 100 kPa occupies . Dalton’s law: the total pressure is the sum of partial pressures, . Graham’s law: the rate of effusion is inversely proportional to ; hydrogen effuses times faster than oxygen. Real gases deviate from ideal behaviour at high pressure and low temperature; the van der Waals equation corrects for intermolecular attractions and molecular volume.

Thermochemistry

The enthalpy change is the heat exchanged at constant pressure; exothermic reactions have . Hess’s law: depends only on the initial and final states. Standard enthalpies are related by

Example: for CH₄ + 2O₂ → CO₂ + 2H₂O(l), using of , , and kJ mol⁻¹ for CH₄, CO₂, and H₂O(l): kJ mol⁻¹. Using bond enthalpies, . In calorimetry, , then .

Entropy and free energy

Entropy measures the number of ways energy can be distributed (disorder). The Gibbs free energy change is

and a process is spontaneous when . Example: for N₂ + 3H₂ → 2NH₃, kJ and at 298 K: kJ (spontaneous, but the rate at room temperature is low). The standard free energy and equilibrium constant are related by (Atkins et al., 2018).

Common mistakes

Using volumes in cm³ in without converting to dm³.

Forgetting to balance the equation before using mole ratios.

Taking for the wrong direction of the reaction; reversing a reaction changes its sign.

Practice questions

How many moles are in 10.0 g of CaCO₃? [0.100 mol]

What volume of CO₂ at 298 K and 100 kPa is produced by heating 10.0 g of CaCO₃? [≈2.48 dm³]

Predict the sign of for the decomposition of CaCO₃ to CaO and CO₂. [Positive]