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Solve PV = nRT for any unknown: pressure, volume, moles, or temperature. Includes pressure unit conversions (atm, kPa, mmHg, psi), STP/SATP reference conditions, and explanations of all four gas laws.
PV = nRT relates pressure, volume, moles, and temperature. R = 0.08206 L·atm/mol·K. Describes ideal gas behavior — a good approximation for real gases at moderate conditions.
| Law | Equation | Condition |
|---|---|---|
| Boyle | P₁V₁=P₂V₂ | Const T,n |
| Charles | V₁/T₁=V₂/T₂ | Const P,n |
| Gay-Lussac | P₁/T₁=P₂/T₂ | Const V,n |
| Avogadro | V∝n | Const P,T |
| Ideal Gas | PV=nRT | All variables |
| Combined | P₁V₁/T₁=P₂V₂/T₂ | Fixed amount |
STP (0°C, 1 atm): 1 mol = 22.414 L. SATP (25°C, 100 kPa): 1 mol = 24.790 L. Always use Kelvin: K = °C + 273.15.
High pressure (molecules occupy volume) and low temperature (intermolecular attractions) cause deviations. Noble gases behave most ideally. Use van der Waals for extreme conditions.
The Ideal Gas Law PV = nRT is one of the most powerful equations in chemistry and physics. It allows calculation of any one gas property when the other three are known, and it underlies thermodynamics, atmospheric science, respiratory physiology, and chemical engineering.
Breathing is driven by gas law principles. Inhalation: diaphragm contracts, chest volume increases (V↑), pressure decreases (P↓) below atmospheric, air flows in. Exhalation: diaphragm relaxes, chest volume decreases (V↓), pressure increases (P↑), air flows out. This is Boyle's Law (PV = constant at fixed T and n). Altitude: at 5500m altitude, atmospheric pressure ≈ 0.5 atm — inspired O₂ partial pressure halved. Mountaineers must acclimatize because reduced O₂ partial pressure impairs oxygen loading onto hemoglobin.
Real gases deviate from ideal behavior for two reasons: molecular volume (molecules are not point particles — they occupy space, so volume at high pressure is higher than ideal) and intermolecular attractions (molecules attract each other, reducing the pressure they exert on container walls, especially at low temperature). The van der Waals equation corrects for both: (P + an²/V²)(V - nb) = nRT. Constants a and b are gas-specific. CO₂ deviates significantly from ideal (large a due to quadrupole moment), while He and H₂ behave nearly ideally.
Industrial processes rely on gas law calculations. Haber process (N₂ + 3H₂ → 2NH₃ for fertilizer production): run at 150-300 atm to maximize yield (Le Chatelier — high pressure favors fewer moles of gas). Liquefied natural gas (LNG): methane compressed and cooled to -162°C, volume reduced approximately 600× compared to gas at STP. Scuba diving: compressed air tanks at 200 bar contain the equivalent of about 2000 liters of air at atmospheric pressure.
This type of calculation is used daily by chemists, pharmacists, environmental scientists, and engineers worldwide. In pharmaceutical manufacturing, precise concentration and yield calculations ensure drug potency and patient safety. In environmental monitoring, accurate concentration calculations are critical for comparing samples to regulatory limits. In research laboratories, reproducible solution preparation forms the foundation of any valid experiment. Understanding these core calculations is essential for any scientist working in a quantitative field.
The most frequent calculation errors include: confusing molarity (mol/L solution) with molality (mol/kg solvent), forgetting to convert Celsius to Kelvin for gas calculations, failing to account for solute dissociation in colligative property calculations, using molar mass instead of equivalent weight for normality calculations, and mixing up percent by mass vs percent by volume. Always double-check your units at every step of a calculation. Dimensional analysis — tracking units through the calculation — is the most reliable way to catch errors before they propagate.
Scientific calculations require attention to significant figures. The result of a calculation can never be more precise than the least precise measurement used as input. Molar mass values (from the periodic table) are typically known to 4-5 significant figures. Volumetric glassware accuracy: Class A volumetric flasks ±0.02-0.05%, Class A pipettes ±0.01-0.05%. Analytical balances: ±0.1 mg (4-5 significant figures for mg range samples). When reporting results in lab reports, always match your significant figures to the precision of your instrumentation.
The Ideal Gas Law PV = nRT is one of the most powerful and universally applicable equations in chemistry and physics. It relates four fundamental properties of any gas sample: pressure (P), volume (V), number of moles (n), and absolute temperature (T), through the universal gas constant R = 0.08206 L·atm/mol·K = 8.314 J/mol·K. Knowing any three of these quantities allows calculation of the fourth.
The ideal gas law combines three earlier empirical observations: Boyle's Law (P∝1/V at constant T,n), Charles's Law (V∝T at constant P,n), and Avogadro's Law (V∝n at constant P,T). These observations were unified into a single equation that describes the behavior of gases with reasonable accuracy under normal conditions of moderate pressure and temperature.
STP (Standard Temperature and Pressure, 0°C and 1 atm): one mole of ideal gas occupies exactly 22.414 L. This molar volume is used constantly in gas stoichiometry. SATP (Standard Ambient Temperature and Pressure, 25°C and 100 kPa): one mole occupies 24.790 L — used in modern IUPAC standard. NTP (Normal Temperature and Pressure, 20°C and 1 atm): one mole = 24.055 L. Always specify which standard conditions you are using to avoid confusion.
Stoichiometry with gases: 2H₂(g) + O₂(g) → 2H₂O(g). How many liters of H₂ at STP react with 11.2 L of O₂ at STP? Moles O₂ = 11.2/22.4 = 0.500 mol. Moles H₂ = 2 × 0.500 = 1.00 mol. Volume H₂ = 1.00 × 22.4 = 22.4 L. Gas density: d = PM/(RT) where M = molar mass. Density of CO₂ at 25°C, 1 atm: d = (1 × 44.009)/(0.08206 × 298) = 1.799 g/L. Much denser than air (average M ≈ 29 g/mol, density = 1.184 g/L).
Breathing operates by Boyle's Law. Inhalation: diaphragm contracts and flattens, chest cavity volume increases (V↑), intrapulmonary pressure drops below atmospheric (P↓), air flows in. Exhalation: diaphragm relaxes, chest volume decreases (V↓), pressure rises (P↑), air flows out. At high altitude (5500m): atmospheric pressure ≈ 380 mmHg (half sea level). Inspired O₂ partial pressure: 0.21 × 380 = 79.8 mmHg vs 159 mmHg at sea level — nearly half. Mountaineers must acclimatize because reduced O₂ partial pressure impairs hemoglobin saturation, requiring increased red blood cell production.
Ideal gas behavior assumes point-particle molecules with no intermolecular forces. Real gases deviate because: (1) Molecules occupy volume — at high pressure, the actual volume of gas molecules is significant compared to the container volume, making real volume larger than ideal. (2) Intermolecular attractions — at low temperature and high pressure, attractive forces between molecules reduce the effective pressure. The van der Waals equation corrects both effects: (P + an²/V²)(V - nb) = nRT. Constants a (measures intermolecular attraction) and b (measures molecular volume) are gas-specific. CO₂ deviates strongly from ideal (a = 3.59 L²·atm/mol²). Noble gases (He, Ne, Ar) behave most ideally because they are small and have minimal intermolecular forces.
Dalton's Law of Partial Pressures: the total pressure of a gas mixture equals the sum of the partial pressures of all component gases. Pₜₒₜₐₗ = P₁ + P₂ + P₃ + ... Each gas exerts its partial pressure independently: Pᵢ = nᵢRT/V. In a 10 L vessel at 300 K containing 1 mol N₂ and 2 mol O₂: P(N₂) = 1×0.08206×300/10 = 2.46 atm. P(O₂) = 2×0.08206×300/10 = 4.92 atm. Total = 7.38 atm. Collecting gas over water: subtract water vapor pressure (temperature-dependent) from total pressure to find partial pressure of collected gas.