States of Matter

Kinetic molecular theory (KMT) for gases:

1. Gas particles are in constant, random motion.
2. The volume of individual particles is negligible relative to the container.
3. No attractive or repulsive forces between particles.
4. Collisions are perfectly elastic (kinetic energy is conserved).
5. Average kinetic energy is proportional to absolute temperature: KE_avg = (3/2)kT.

Assumptions 2 and 3 define an ideal gas. Real gases deviate at high pressure (particle volume matters) and low temperature (intermolecular forces matter).

Gas Laws

Worked Example: Ideal Gas Law

Problem. What volume does 2.50 mol of N2 occupy at 25.0 C and 1.25 atm?

V = nRT / P = (2.50)(0.08206)(298.15) / 1.25 = 49.0 L.

Worked Example: Dalton's Law

Problem. A gas mixture contains 0.40 atm N2, 0.20 atm O2, and 0.10 atm CO2. What is the total pressure and the mole fraction of N2?

P_total = 0.40 + 0.20 + 0.10 = 0.70 atm.

Mole fraction of N2: X_N2 = P_N2 / P_total = 0.40 / 0.70 = 0.571.

Real Gases: Van der Waals Equation

(P + a(n/V)^2)(V - nb) = nRT

The a-term corrects for intermolecular attractions. The b-term corrects for particle volume. Gases with strong IMFs (H2O, NH3) have large a values. Gases with large molecules have large b values.

Phase Transitions

Heating curve. When heating a substance at constant pressure: temperature rises through the solid phase, plateaus at the melting point (energy goes to breaking lattice, not raising T), rises through the liquid phase, plateaus at the boiling point (energy goes to overcoming IMFs), then rises through the gas phase.

Worked example. How much energy is needed to convert 36.0 g of ice at -10.0 C to steam at 110.0 C?

Step 1. Heat ice from -10 to 0 C: q1 = m x c_ice x delta-T = 36.0 x 2.09 x 10.0 = 752 J.

Step 2. Melt ice at 0 C: q2 = m x delta-H_fus = 36.0 x 334 = 12,024 J.

Step 3. Heat water from 0 to 100 C: q3 = 36.0 x 4.184 x 100 = 15,062 J.

Step 4. Boil water at 100 C: q4 = 36.0 x 2260 = 81,360 J.

Step 5. Heat steam from 100 to 110 C: q5 = 36.0 x 2.01 x 10.0 = 724 J.

Total: 752 + 12,024 + 15,062 + 81,360 + 724 = 109,922 J = 110 kJ.

Note: the vaporization step dominates (74% of total energy). This is why steam burns are far more severe than hot water burns — the condensation of steam releases enormous energy.

Phase Diagrams

A phase diagram maps the stable phase as a function of temperature and pressure.

Key features:

• Triple point: The unique temperature and pressure where solid, liquid, and gas coexist in equilibrium. For water: 0.01 C, 0.006 atm.
• Critical point: Above this temperature and pressure, the liquid-gas boundary disappears — the substance becomes a supercritical fluid. For water: 374 C, 218 atm. For CO2: 31 C, 73 atm.
• Normal boiling point: Temperature where liquid-gas curve crosses 1 atm.
• Normal melting point: Temperature where solid-liquid curve crosses 1 atm.

Water's anomaly. Water's solid-liquid line slopes to the left (negative slope), meaning increasing pressure on ice at certain temperatures causes melting. This is because ice is less dense than liquid water — pressure favors the denser phase. Most substances have a positive-sloping solid-liquid line.

Worked Example: Reading a Phase Diagram

Problem. CO2 at 1 atm and -78.5 C is a solid (dry ice). What happens when you warm it at 1 atm?

At 1 atm, CO2's triple point is at 5.1 atm — well above 1 atm. Therefore, the 1 atm line passes only through solid and gas regions. CO2 sublimes directly from solid to gas at -78.5 C without ever becoming liquid. This is why dry ice "smokes" but never forms a puddle.

To get liquid CO2: you must exceed 5.1 atm. CO2 fire extinguishers operate at about 60 atm, where CO2 exists as a liquid.

Vapor Pressure and Clausius-Clapeyron

Vapor pressure is the pressure exerted by a substance's vapor in equilibrium with its liquid. It increases with temperature (more molecules have enough energy to escape the liquid).

Clausius-Clapeyron equation: ln(P2/P1) = -(delta-H_vap/R)(1/T2 - 1/T1)

Worked example. The vapor pressure of ethanol is 44 mmHg at 20 C and 222 mmHg at 50 C. Calculate delta-H_vap.

ln(222/44) = -(delta-H_vap / 8.314)(1/323.15 - 1/293.15)

ln(5.045) = -(delta-H_vap / 8.314)(-3.17 x 10^-4)

1.618 = delta-H_vap x 3.81 x 10^-5

delta-H_vap = 1.618 / 3.81 x 10^-5 = 42,500 J/mol = 42.5 kJ/mol.

Literature value: 42.3 kJ/mol. Excellent agreement.

Atmospheric Chemistry

Earth's atmosphere is a giant chemical reactor. Understanding its composition and reactions is essential for environmental chemistry.

Composition

Ozone Chemistry

Stratospheric ozone (beneficial). The Chapman cycle:

1. O2 + UV-C -> 2 O (photodissociation)
2. O + O2 + M -> O3 + M (ozone formation; M = third body absorbs energy)
3. O3 + UV-B -> O2 + O (ozone absorbs harmful UV — the protective function)
4. O + O3 -> 2 O2 (natural ozone destruction)

This steady-state cycle maintains the ozone layer at approximately 15-35 km altitude.

Ozone depletion. Chlorofluorocarbons (CFCs) catalytically destroy ozone:

Cl + O3 -> ClO + O2 ClO + O -> Cl + O2 Net: O3 + O -> 2 O2

One Cl atom can destroy approximately 100,000 ozone molecules before being removed. The Montreal Protocol (1987) phased out CFCs — one of the most successful international environmental agreements. The ozone layer is recovering but will not fully heal until approximately 2060-2070.

Tropospheric ozone (harmful). Ground-level ozone is a secondary pollutant formed by:

NO2 + UV -> NO + O O + O2 -> O3

This ozone is a lung irritant and a key component of photochemical smog. Volatile organic compounds (VOCs) from vehicles and industry drive NO2 regeneration, sustaining the cycle.

Greenhouse Effect

Mechanism. Earth absorbs solar radiation (mostly visible) and re-emits it as infrared. Greenhouse gases (CO2, H2O, CH4, N2O, O3) absorb and re-radiate some of this IR, warming the surface.

Without the greenhouse effect: Earth's average temperature would be approximately -18 C instead of +15 C. The natural greenhouse effect is essential for life. The problem is the enhanced greenhouse effect from anthropogenic emissions increasing CO2 from 280 ppm (pre-industrial) to 420+ ppm.

Worked example. A power plant burns 1000 tonnes of coal (assume pure carbon) per day. How many tonnes of CO2 does it produce?

C + O2 -> CO2. Molar mass C = 12, CO2 = 44.

Mass CO2 = 1000 x (44/12) = 3,667 tonnes CO2 per day.

Every tonne of carbon burned produces 3.67 tonnes of CO2 — the mass increases because two oxygen atoms from the atmosphere are incorporated. This is a key concept in carbon accounting.

Acid Rain

SO2 and NOx emissions react with water vapor:

SO2 + H2O -> H2SO3 (sulfurous acid) 2 SO2 + O2 -> 2 SO3 (catalyzed oxidation) SO3 + H2O -> H2SO4 (sulfuric acid) 2 NO2 + H2O -> HNO3 + HNO2

Normal rain is pH 5.6 (dissolved CO2 forms carbonic acid). Acid rain can reach pH 4.0 or lower, damaging aquatic ecosystems, forests, and stone buildings.

Green Chemistry

Green chemistry is the design of chemical products and processes that reduce or eliminate hazardous substances. It is not "environmental chemistry" (which studies existing pollution) — it is prevention at the molecular design level.

The 12 Principles of Green Chemistry (Anastas & Warner, 1998)

Atom Economy

Atom economy = (molecular weight of desired product / total molecular weight of all products) x 100%.

Worked example. Compare the atom economy of two routes to styrene oxide.

Route A (traditional). Styrene + mCPBA (meta-chloroperoxybenzoic acid) -> styrene oxide + mCBA (meta-chlorobenzoic acid).

MW desired product (styrene oxide) = 120. MW all products = 120 + 156.5 = 276.5. Atom economy = 120 / 276.5 x 100% = 43.4%.

Route B (green). Styrene + H2O2 (catalyst: methyltrioxorhenium) -> styrene oxide + H2O.

MW all products = 120 + 18 = 138. Atom economy = 120 / 138 x 100% = 87.0%.

Route B doubles the atom economy and replaces a hazardous stoichiometric oxidant with hydrogen peroxide (byproduct: water). This exemplifies principles 1, 2, 5, and 9.

Solvent Selection

Solvents account for 80-90% of mass in a typical chemical process. Green solvent alternatives:

Supercritical CO2. Above 31 C and 73 atm, CO2 becomes a supercritical fluid with liquid-like density but gas-like diffusivity. It dissolves nonpolar substances, is non-toxic, non-flammable, and easily removed by depressurization. Used commercially for decaffeinating coffee and dry cleaning.

Catalysis for Sustainability

Catalysts lower activation energy without being consumed. Green chemistry strongly favors catalytic over stoichiometric reagents because catalysts are used in small amounts and regenerated.

Worked example. The Haber process (N2 + 3 H2 -> 2 NH3) uses an iron catalyst at 400-500 C and 150-300 atm. Why is this considered partially green?

Green aspects: catalytic process (principle 9), uses N2 from air (renewable feedstock, principle 7), atom economy is 100% (all atoms end in NH3, principle 2).

Non-green aspects: extreme temperature and pressure (violates principle 6), H2 is currently produced from natural gas via steam reforming (fossil feedstock). Green hydrogen from water electrolysis powered by renewables would address this. Research into ambient-temperature nitrogen fixation (mimicking nitrogenase enzyme) aims to solve the energy problem.

Crystalline vs. Amorphous Solids

Unit cells. Crystalline solids have repeating unit cells: simple cubic (1 atom/cell, 52% packing), body-centered cubic (2 atoms/cell, 68%), face-centered cubic (4 atoms/cell, 74%). Most metals adopt BCC or FCC structures.

Common Mistakes

Cross-References

• franklin agent: Materials science, polymer properties, applied chemistry, green chemistry. Primary agent for this skill.
• chemical-bonding skill: Intermolecular forces determine phase behavior, boiling points, and material properties.
• reactions-stoichiometry skill: Thermochemistry (enthalpy changes in phase transitions) and stoichiometry of atmospheric reactions.
• organic-chemistry skill: Polymer chemistry and sustainable synthesis connect organic mechanisms to materials applications.
• analytical-methods skill: Characterization of materials by spectroscopy, diffraction, and thermal analysis.
• atomic-structure skill: Nuclear chemistry connects to radioactive materials and isotope applications.

References

• Zumdahl, S. S. & Zumdahl, S. A. (2017). Chemistry. 10th edition. Cengage Learning.
• Anastas, P. T. & Warner, J. C. (1998). Green Chemistry: Theory and Practice. Oxford University Press.
• Seinfeld, J. H. & Pandis, S. N. (2016). Atmospheric Chemistry and Physics. 3rd edition. Wiley.
• Callister, W. D. & Rethwisch, D. G. (2018). Materials Science and Engineering. 10th edition. Wiley.
• IPCC. (2023). AR6 Synthesis Report: Climate Change 2023. Intergovernmental Panel on Climate Change.
• Molina, M. J. & Rowland, F. S. (1974). "Stratospheric Sink for Chlorofluoromethanes: Chlorine Atom-Catalysed Destruction of Ozone." Nature, 249, 810-812.
• Sheldon, R. A. (2012). "Fundamentals of Green Chemistry." Chemical Society Reviews, 41, 1437-1451.