Chapter 12 Moles Equilibrium Gases Liquids and Solids

Year 1 · Chemistry · G114-L3

Use moles and concentration, connect Gibbs energy with equilibrium, and compare gases, liquids and solids through worked quantitative examples.

Complementary observations used in systematic mineral identification. Original Geology Hub teaching diagram.

Learning objectives: Calculate amounts and concentrations, distinguish equilibrium from reaction rate, apply a simple gas law, and explain crystallization and intermolecular effects.

The mole connects particles with measured mass

A mole represents a specified number of elementary entities, allowing chemical equations to connect microscopic ratios with laboratory quantities. Molar mass converts mass into amount: n = m/M. Always specify the substance and units. The same mass of two substances generally contains different numbers of moles because their molar masses differ. A balanced reaction relates amounts of reactants and products, not arbitrary equal masses.

Concentration requires both an amount and a defined basis. Molarity is moles of solute per litre of solution, while mass fraction and mass-per-volume units answer related but different questions. “Ten percent” is incomplete unless the basis is clear. In water chemistry, inconsistent units can create apparent trends that disappear after conversion. Keep original observations and document every transformation.

Energy, equilibrium and reaction direction

A thermodynamic system is the part of the world chosen for study; its surroundings lie outside the defined boundary. The first law accounts for energy transfers, while the second constrains spontaneous change. At constant temperature and pressure, Gibbs free-energy change helps determine whether a process is thermodynamically favoured under specified conditions. A negative change does not imply a fast reaction: kinetic barriers may make an allowed transformation extremely slow.

At chemical equilibrium, forward and reverse processes balance at the macroscopic scale. Equilibrium does not mean molecular activity has stopped. Temperature, pressure and composition influence equilibrium, which matters when considering mineral stability or dissolved constituents. A laboratory observation lasting a few minutes need not represent equilibrium if dissolution or crystallization is slow.

Gases, liquids and solids

The ideal gas relation PV = nRT connects pressure, volume, amount and absolute temperature. It is an approximation and becomes less adequate under conditions where molecular interactions and finite molecular size matter strongly. Use kelvin, not degrees Celsius, in this equation. Diffusion spreads particles through random motion, while osmosis concerns solvent transfer across a suitable selective barrier. Dissolved-gas behaviour can be described using relationships such as Henry’s law under specified assumptions and conventions.

In liquids, intermolecular interactions influence viscosity, surface tension and vapour pressure. Density is mass per volume, not resistance to flow. Colligative properties depend on the number of dissolved particles in an appropriate dilute-solution model, whereas other properties depend strongly on chemical identity. A substance may crystallize into an ordered solid, remain amorphous or form distinct structures under different conditions. Supercooling illustrates that the observed state can depend on transformation kinetics as well as temperature.

Balanced equations connect amounts rather than equal masses

A reaction equation specifies stoichiometric ratios between chemical entities. Those ratios become mole ratios, while molar masses convert them into measured masses. Equal coefficients therefore do not generally mean equal masses. Concentration needs a stated denominator: a mass fraction divides by solution mass, whereas molarity uses final solution volume. Diluting a solution changes concentration without necessarily changing the total solute amount. Record whether a percentage refers to mass, volume or another basis before using it in a geological calculation.

Thermodynamics separates boundaries from behaviour

An open system can exchange matter with its surroundings; a closed system excludes matter exchange but may exchange energy. The first law accounts for energy, and the second constrains the direction of spontaneous overall change. At fixed temperature and pressure, Gibbs energy supplies a useful reaction criterion. Equilibrium is dynamic balance rather than inactivity. A natural mineral assemblage may persist because reaction is slow, so its mere presence is not proof that the current temperature, pressure and fluid composition match equilibrium conditions.

Gas and dissolved transport have different models

Boyle’s relation describes inverse pressure–volume behaviour for fixed amount and temperature in the ideal approximation. Charles-type relations compare volume with absolute temperature under suitable fixed conditions. Real gases depart from ideal behaviour when molecular interactions and volume become important. Diffusion follows random molecular motion toward a more dispersed distribution; osmosis concerns solvent movement across a selective barrier. Henry’s law relates dissolved gas to gas pressure under specified conventions and conditions, so its coefficient and units must accompany any numerical use.

Liquid properties should not be collapsed into one label

Density compares mass with volume; viscosity concerns resistance to flow-related deformation; surface tension concerns interfaces; vapour pressure reflects equilibrium with vapour under stated conditions. Dissolved particles can change freezing, boiling and osmotic behaviour in appropriate dilute-solution models. These colligative effects depend on particle number, while many other properties depend strongly on chemical identity. A dense liquid need not be the most viscous, and a clear liquid need not be pure.

Solid formation and analysis require structural evidence

Crystallization produces ordered arrangements through nucleation and growth. Rapid cooling or slow nucleation can produce a supercooled liquid or an amorphous solid instead of the expected crystal at once. Liquid crystals retain forms of orientational order while retaining fluid-like behaviour. In analytical work, qualitative tests ask which constituents are present; quantitative tests ask how much. Identifying a mixed rock requires recognizing that several mineral phases may contribute signals. A single positive test does not establish the whole composition or justify preparing unknown salts outside a supervised laboratory.

Worked amount and gas calculations

Using a rounded molar mass of 100 grams per mole for calcium carbonate, a 25-gram specimen would contain 0.25 moles if it were pure CaCO₃. A natural rock may contain other minerals, so composition is an explicit assumption. Dissolving 0.010 moles of a hypothetical solute to a final solution volume of 0.50 litres gives 0.020 moles per litre, not 0.005.

For a fixed amount of ideal gas at constant temperature, doubling volume halves pressure. If an initial 100-kilopascal gas occupies two litres, expanding to four litres predicts 50 kilopascals. Absolute pressures are required. Finish by writing one reason a real gas or an impure mineral sample could differ from these ideal results. Home study should use calculations and diagrams; unknown salts, acids and metal-bearing solutions require a supervised laboratory and proper disposal.

Self-check

Does a negative Gibbs-energy change guarantee rapid reaction?

No. Thermodynamic favourability and reaction rate are distinct.

Which temperature scale belongs in PV = nRT?

Use absolute temperature in kelvin.

What is the molarity of 0.010 mol in 0.50 L?

It is 0.020 mol/L, obtained by amount divided by final solution volume.

Sources and further study

Topic framework: the supplied University of Peshawar BS Geology curriculum, session 2004–05 onward. This independently authored learning resource is not affiliated with the university and does not confer a degree or accreditation.

Chapter 12 multiple choice questions

Choose one best answer for each question. Open each answer panel after making your choice.

A pure CaCO₃ sample has mass 25 g. Using a rounded molar mass of 100 g/mol, how much substance is present?
1. 4 mol
2. 0.25 mol
3. 2.5 mol
4. 2,500 mol
Answer and explanation
B. 0.25 mol Amount is mass divided by molar mass: 25/100 = 0.25 mol.
A solution contains 0.010 mol of solute in a final volume of 0.50 L. What is its molarity?
1. 0.005 mol/L
2. 0.50 mol/L
3. 50 mol/L
4. 0.020 mol/L
Answer and explanation
D. 0.020 mol/L Molarity is amount divided by final solution volume: 0.010/0.50 = 0.020 mol/L.
A process has negative Gibbs free-energy change under specified constant-temperature and pressure conditions. What can still prevent a rapid observable change?
1. Negative free energy requires every reaction to finish instantly.
2. The sign removes all dependence on reaction mechanism.
3. A kinetic barrier can make the process slow.
4. A negative value means particles stop moving.
Answer and explanation
C. A kinetic barrier can make the process slow. Thermodynamic favourability does not specify reaction speed.
An ideal gas expands from 2 L to 4 L at constant amount and temperature. If its initial absolute pressure is 100 kPa, what is the predicted final pressure?
1. 50 kPa
2. 200 kPa
3. 100 kPa
4. 25 kPa
Answer and explanation
A. 50 kPa At fixed amount and temperature, pressure is inversely proportional to volume.
A liquid remains uncrystallized below its usual freezing temperature. Which lesson concept helps explain this observation?
1. The absence of intermolecular interactions
2. The requirement that every solid be a liquid crystal
3. The conversion of all atoms into isotopes
4. Supercooling and transformation kinetics
Answer and explanation
D. Supercooling and transformation kinetics Observed state can depend on the kinetics of nucleation and transformation as well as temperature.

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