General Chemistry
Gas Laws
Boyle, Charles, Avogadro — relations between P, V, T, n for ideal gases
Gas laws describe behavior of gases as relations between pressure (P), volume (V), temperature (T), and moles (n). Boyle (1662): PV = constant at fixed T (P inversely proportional to V). Charles (1787): V/T = constant at fixed P. Avogadro (1811): equal volumes contain equal moles at same T+P. Combined: ideal gas law PV = nRT (R = 8.314 J/mol·K). Real gases deviate at high P or low T (van der Waals correction). Foundation of thermodynamics, atmospheric science, engineering.
- Boyle's lawPV = constant (fixed T)
- Charles's lawV/T = constant (fixed P)
- Avogadro's lawV/n = constant (fixed T, P)
- Ideal gas lawPV = nRT
- R (gas constant)8.314 J/mol·K = 0.0821 L·atm/mol·K
- STP molar volume22.4 L/mol (0°C, 1 atm)
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Why gas laws matter
- Engineering. Gas systems, refrigeration, propulsion.
- Atmospheric science. Weather, pressure, density.
- Chemistry. Volumes in stoichiometry.
- Biology. Respiration, gas exchange.
- Industrial. Compressed gases, manufacturing.
- Diving. Pressure changes with depth.
- Aviation. Lift, density at altitude.
Common misconceptions
- T in Celsius works. Must be Kelvin.
- Gas laws are exact. Approximations; deviate at extreme conditions.
- Ideal gas exists. Theoretical; all real gases deviate.
- R has fixed value. Different units give different R.
- STP is single standard. Different definitions (IUPAC, NIST, etc.).
- Heavier gas means more pressure. Same molar volume regardless of identity.
Frequently asked questions
What's Boyle's law?
Pressure inversely proportional to volume at fixed T. PV = constant. If V halves, P doubles. Discovered by Robert Boyle (1662). Test: compress balloon — pressure increases. Useful for: scuba diving (pressure-volume changes with depth), syringes (compression injects), respiration. Mathematically: P₁V₁ = P₂V₂.
What's Charles's law?
Volume directly proportional to absolute temperature at fixed P. V/T = constant. If T doubles (in K), V doubles. Discovered by Jacques Charles (1787). Test: hot air balloon — heating gas expands volume. Math: V₁/T₁ = V₂/T₂. Important: T must be in Kelvin.
What's Avogadro's law?
At same T and P, equal volumes of any gas have equal moles. V/n = constant. Means: gas behavior depends on number of particles, not type. Important for stoichiometry — count moles by volume at STP (22.4 L = 1 mol). Allowed determination of atomic masses historically.
What's the ideal gas law?
PV = nRT. Combines Boyle + Charles + Avogadro. P (pressure), V (volume), n (moles), R (gas constant), T (Kelvin). With R = 8.314 J/mol·K (SI) or 0.0821 L·atm/mol·K (other units). Assumes: gas particles point-like, no IMFs, elastic collisions. Good approximation for most gases at normal conditions.
When does the ideal gas law fail?
At high P or low T. Real gases have: (1) Particle volume — at high pressure, this matters. (2) Intermolecular forces — at low temperature, attract particles. Van der Waals equation accounts for both: (P + a(n/V)²)(V - nb) = nRT. a, b are gas-specific. CO₂, NH₃ deviate more than He, Ne (smaller IMFs).
What about partial pressures?
Dalton's law of partial pressures. Each gas in mixture exerts its own pressure as if alone. Total = sum of partial pressures. P_total = P_A + P_B + ... + P_n. Each P = X (mole fraction) × P_total. Important: respiration (O₂, CO₂ partial pressures), industrial gas mixtures, atmospheric chemistry.
How is gas density calculated?
From PV = nRT. Density (d) = mass/volume. n/V = P/RT. Multiply by molar mass M: m/V = PM/RT. So d = PM/RT. At higher pressure: denser. At higher T: less dense. Application: hot air balloons (heat air → less dense → buoyant). Gas densities relate to molar masses at same conditions.