General Chemistry Study Guide: Gases, Liquids & Phase Changes, and Kinetics

Gases

How Gases Behave

Gases are characterized by their unique physical properties, which distinguish them from solids and liquids.

• Compressibility: Gas volume changes significantly with pressure and temperature.

• Fluidity: Gases flow freely and fill any container.

• Low Density: Gases have much lower densities (g/L) compared to liquids and solids.

• Mixing: Gases mix in any proportion to form homogeneous solutions.

Pressure

Pressure is defined as force per unit area. For a column of fluid, pressure depends on the fluid's density, height, and gravity:

• Formula: $P = \text{density} \times \text{height} \times g$

• Unit Conversions:

Unit	Equivalent
1 atm	760 mm Hg = 760 torr
1 atm	101,325 Pa = 101.325 kPa
1 atm	14.7 psi = 1.01325 bar

• Example: Convert 1.50 atm to mm Hg: $1.50 \times (760/1) = 1140$ mm Hg.

The Gas Laws

Gas behavior is described by several fundamental laws:

• Boyle's Law: $PV = \text{constant}$ (at constant T, n). Pressure and volume are inversely proportional.

• Charles's Law: $V/T = \text{constant}$ (at constant P, n). Volume is directly proportional to temperature (in Kelvin).

• Avogadro's Law: $V/n = \text{constant}$ (at constant P, T). Volume is proportional to moles of gas.

• Combined Gas Law: $\frac{P_1V_1}{n_1T_1} = \frac{P_2V_2}{n_2T_2}$

• Ideal Gas Law: $PV = nRT$ (R = 0.08206 L·atm/(mol·K); T in K)

Note: Always use Kelvin for temperature in gas equations: $T(K) = T(°C) + 273.15$.

Rearrangements of the Ideal Gas Law

• Moles: $n = \frac{PV}{RT}$

• Density: $d = \frac{PM}{RT}$ (M = molar mass)

• Molar Mass: $M = \frac{dRT}{P}$

• Molar Mass from Mass and Volume: $M = \frac{mRT}{PV}$

Standard Temperature and Pressure (STP)

• STP: 0 °C (273.15 K) and 1 atm.

• Standard Molar Volume: 1 mol of any ideal gas occupies 22.4 L at STP.

Gas Stoichiometry

• Use molar volume at STP for quick calculations.

• For reactions, convert each reactant to moles of the same product to identify the limiting reagent.

Dalton's Law of Partial Pressures

• Total Pressure: $P_{\text{total}} = P_A + P_B + P_C + \ldots$

• Partial Pressure: $P_A = X_A \cdot P_{\text{total}}$ where $X_A = \frac{\text{moles of A}}{\text{total moles}}$

Kinetic Molecular Theory (KMT)

• Gas molecules move in constant, random, straight-line motion.

• Their volume is negligible compared to the container.

• Collisions are perfectly elastic.

• No intermolecular forces are present.

• Average kinetic energy depends only on temperature (K).

Root-mean-square speed: $u_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ (R = 8.314 J/(mol·K), M in kg/mol)

Real Gases and Deviations from Ideal Behavior

• Deviations occur at high pressure (molecular volume matters) and low temperature (attractive forces matter).

• van der Waals Equation: $[P + a(n/V)^2](V - nb) = nRT$

• a(n/V)^2: Corrects for intermolecular attractions (raises P above measured).

• nb: Corrects for finite molecular volume (reduces free V).

Liquids, Solids, and Intermolecular Forces

States of Matter

State	Shape	Volume
Solid	Definite	Definite
Liquid	Indefinite (container shape)	Definite
Gas	Indefinite	Indefinite

• Density changes dramatically between phases. For water, gas is ~1,700× less dense than liquid.

• Ice is less dense than liquid water due to its open hydrogen-bonded structure.

Crystalline vs. Amorphous Solids

Type	Description	Examples
Crystalline	Regular, repeating, long-range order	NaCl, diamond, ice, sugar, metals
Amorphous	No long-range order; disordered	Glass, rubber, plastics, wax

• Crystalline solids have sharp melting points; amorphous solids soften over a range.

Intramolecular vs. Intermolecular Forces

• Intramolecular forces: Covalent and ionic bonds within molecules; very strong (150–1000 kJ/mol).

• Intermolecular forces (IMFs): Forces between molecules; much weaker (1–40 kJ/mol).

• IMFs determine boiling/melting points, viscosity, surface tension, vapor pressure.

Types of Intermolecular Forces

IMF	Description	When Present
Dispersion (London)	Temporary dipoles; always present	All molecules
Dipole-induced dipole	Polar induces dipole in nonpolar	Polar + nonpolar
Dipole-dipole	Permanent dipoles attract	Two polar molecules
Hydrogen bond	Special strong dipole-dipole (H with F, O, N)	H–F, H–O, H–N bonds
Ion-dipole	Ion and polar molecule	Ionic compounds in polar solvents
Ion-ion	Between two ions (not an IMF)	Ionic compounds

Ranking (strongest to weakest): Ion-ion > Ion-dipole > H-bond > Dipole-dipole > Dispersion

Dispersion Forces (London Forces)

• Present in all molecules; arise from instantaneous dipoles.

• Strength increases with polarizability (more electrons, larger size, greater surface area).

• Example: Noble gas boiling points increase with molar mass due to stronger dispersion forces.

• Example: n-Pentane (linear) has a higher boiling point than neopentane (spherical) due to greater surface contact.

Dipole-Dipole Forces

• Occur between polar molecules with permanent dipoles.

• Stronger than dispersion for similar-sized molecules.

• Example: Acetone (polar) has a much higher boiling point than butane (nonpolar) of similar mass.

Hydrogen Bonds

• Special strong dipole-dipole interaction; requires H bonded to F, O, or N.

• Donor: H–F, H–O, or H–N; Acceptor: lone pair on F, O, or N.

• Strength: 10–40 kJ/mol (strongest IMF, but weaker than covalent bonds).

• Water: Each H2O can form up to four H-bonds, leading to high boiling point, surface tension, and unique solid structure (ice floats).

• Biological importance: H-bonds stabilize DNA, proteins, and enzyme-substrate interactions.

Ion-Dipole and Induced-Dipole Forces

• Ion-dipole: Full charge on ion attracts partial charge on polar molecule; critical for dissolving ionic compounds in water.

• Dipole-induced dipole: Polar molecule induces dipole in nonpolar molecule (e.g., O2 in water).

• Ion-induced dipole: Ion induces dipole in nonpolar molecule (e.g., O2 with Fe2+ in hemoglobin).

Ranking IMFs in Practice

• Identify the strongest IMF present in each molecule.

• If IMFs are the same, compare molar mass and shape (more mass/surface area = stronger dispersion).

• Straight-chain isomers have higher boiling points than branched isomers of the same formula.

Properties Driven by IMFs

Property	Effect of Stronger IMFs
Boiling point	Higher
Vapor pressure	Lower
Surface tension	Higher
Viscosity	Higher
Capillary action	Adhesive > cohesive forces

Phase Changes and Enthalpy

Name	Direction	ΔH sign	Example
Melting (fusion)	Solid → Liquid	+ΔH (endothermic)	Ice → water
Freezing	Liquid → Solid	−ΔH (exothermic)	Water → ice
Vaporization	Liquid → Gas	+ΔH (endothermic)	Water → steam
Condensation	Gas → Liquid	−ΔH (exothermic)	Steam → water
Sublimation	Solid → Gas	+ΔH (endothermic)	Dry ice → CO2 gas
Deposition	Gas → Solid	−ΔH (exothermic)	Frost formation

• Endothermic: melting, vaporization, sublimation (heat absorbed).

• Exothermic: freezing, condensation, deposition (heat released).

• Magnitude of ΔH is the same for a phase change and its reverse, but the sign is opposite.

Calculating Heat for Phase Changes

• Within a phase: $q = m \cdot C_s \cdot \Delta T$

• At a phase change: $q = n \cdot \Delta H_{\text{phase}}$

• ΔHsub = ΔHfus + ΔHvap (Hess's law)

Water values:

Quantity	Per gram	Per mole
Specific heat, ice	2.09 J/(g·°C)	—
ΔHfusion	333 J/g	6.02 kJ/mol
Specific heat, liquid	4.18 J/(g·°C)	—
ΔHvaporization	2260 J/g	40.7 kJ/mol
Specific heat, steam	2.01 J/(g·°C)	—

Heating/Cooling Curves

• Five segments: heat solid, melt, heat liquid, vaporize, heat gas.

• Each segment requires a separate q calculation.

Vapor Pressure and Clausius–Clapeyron Equation

• Vapor pressure: pressure exerted by vapor in equilibrium with its liquid/solid.

• Stronger IMFs → lower vapor pressure at a given T.

• Vapor pressure increases exponentially with temperature.

• Boiling occurs when vapor pressure equals atmospheric pressure.

• Clausius–Clapeyron Equation: $\ln(P) = -\frac{\Delta H_{\text{vap}}}{R} \cdot \frac{1}{T} + C$

• Two-point form: $\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{\text{vap}}}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

Phase Diagrams

• X-axis: temperature; Y-axis: pressure.

• Regions: solid, liquid, gas.

• Curves: fusion (solid-liquid), vaporization (liquid-gas), sublimation (solid-gas).

• Triple point: all three phases coexist.

• Critical point: above this, no distinction between liquid and gas.

• Water's fusion curve has a negative slope (ice less dense than liquid).

Kinetics — Rates and Rate Laws

Reaction Rate from Stoichiometry

For a reaction $aA + bB \rightarrow cC + dD$:

• $\text{Rate} = -\frac{1}{a} \frac{\Delta [A]}{\Delta t} = -\frac{1}{b} \frac{\Delta [B]}{\Delta t} = +\frac{1}{c} \frac{\Delta [C]}{\Delta t} = +\frac{1}{d} \frac{\Delta [D]}{\Delta t}$

• Reactants have a negative sign (disappearing); products have a positive sign (appearing).

• Divide by stoichiometric coefficients for consistent rate values.

Rate Laws and Reaction Order

• General form: $\text{Rate} = k [A]^m [B]^n$

• m, n: orders with respect to A and B (determined experimentally).

• Overall order = m + n.

• Units of k depend on overall order:

Order	Units of k
0	M·s−1
1	s−1
2	M−1·s−1
3	M−2·s−1

Effect of Concentration Changes

• If [A] is multiplied by f, rate is multiplied by $f^{\text{order in A}}$.

• Examples:

  • Double [A], first order: rate ×2

  • Double [A], second order: rate ×4

  • Halve [A], second order: rate ×1/4

  • Quadruple [A], second order: rate ×16

  • Halve [A], third order: rate ×1/8

Finding the Rate Law from Initial-Rate Data

• Compare experiments where only one reactant changes to determine order in that reactant.

• Repeat for each reactant.

• Plug values into the rate law to solve for k.

Integrated Rate Laws

Order	Integrated Rate Law	Linear Plot
Zero	$[A] = -kt + [A]_0$	[A] vs. t
First	$\ln[A] = -kt + \ln[A]_0$	ln[A] vs. t
Second	$1/[A] = kt + 1/[A]_0$	1/[A] vs. t

• First-order half-life: $t_{1/2} = 0.693 / k$ (independent of [A]0)

• Zero-order half-life: $t_{1/2} = [A]_0 / (2k)$

• Second-order half-life: $t_{1/2} = 1 / (k[A]_0)$

Arrhenius Equation — Temperature Dependence of k

• $k = A e^{-E_a / RT}$

• Two-point form: $\ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

• Use R = 8.314 J/(mol·K); Ea in J/mol.

Last-Minute Review — Key Facts to Memorize

• R = 0.08206 L·atm·mol−1·K−1 (ideal gas law)

• R = 8.314 J·mol−1·K−1 (kinetic/Arrhenius)

• STP: 0 °C, 1 atm, 22.4 L/mol

• 1 atm = 760 mm Hg = 760 torr = 101.325 kPa

• T(K) = T(°C) + 273.15

• Order of reaction is determined experimentally, not from coefficients.

• First-order half-life is independent of [A]0; zero and second order depend on [A]0.

• Stronger IMF → higher BP, higher viscosity, higher surface tension, lower vapor pressure.

• Vapor pressure increases with temperature.

• Covalent bonds (intramolecular) are much stronger than any IMF.

• Condensation releases heat (exothermic); vaporization absorbs heat (endothermic).

• For Arrhenius, use R in J/(mol·K); check units for Ea (J/mol or kJ/mol).