Ideal Gas Laws Calculator (Boyle, Charles)

Ideal Gas Laws Guide

What should I know about The Three Simple Laws?

Boyle's Law (constant T): P₁V₁ = P₂V₂. Pressure and volume are inversely proportional at constant temperature. Example: 2L gas at 101.3kPa compressed to 1L: P₂ = 101.3×2/1 = 202.6kPa. Charles' Law (constant P): V₁/T₁ = V₂/T₂ (T in Kelvin). Volume proportional to absolute temperature. Example: 2L gas at 25°C (298K) heated to 100°C (373K): V₂ = 2×373/298 = 2.50L. Gay-Lussac's Law (constant V): P₁/T₁ = P₂/T₂. Pressure proportional to absolute temperature. Car tyre pressure increases on a hot day — manufacturers recommend checking and adjusting tyre pressure when tyres are cold, since a hot-day reading will be several psi higher than the true cold-tyre pressure purely due to the temperature effect, not an actual change in the amount of air.

What do I need to know about PV = nRT?

R = 8.314 J/mol·K (universal gas constant). T must be in Kelvin (°C + 273.15). P in Pascals (1 kPa = 1000 Pa). V in m³ (1 L = 0.001 m³). n = number of moles. Example: 1 mol of ideal gas at STP (0°C, 101.325 kPa): V = nRT/P = 1×8.314×273.15/101325 = 0.02241 m³ = 22.41 L. Standard molar volume at STP: 22.4 L/mol. At room temperature (25°C, 101.325 kPa): 24.5 L/mol. Real gases deviate from ideal at high pressures and low temperatures — the van der Waals equation corrects for intermolecular forces and the finite size of gas molecules, both of which the ideal gas model ignores. The correction becomes most noticeable for gases that are close to condensing (high pressure, low temperature) or that have strong intermolecular attractions, such as ammonia or carbon dioxide.

What's the key thing to understand about Deviations from Ideal Behaviour?

Ideal gas assumptions: molecules have negligible volume. No intermolecular forces (except during collisions). Elastic collisions. Real gases deviate most at: high pressure (molecular volume becomes significant). Low temperature (intermolecular attractive forces matter). Van der Waals equation: (P + an²/V²)(V − nb) = nRT. a accounts for attractive forces, b accounts for molecular volume. Noble gases (He, Ne, Ar): closest to ideal. CO₂: significant deviation at high pressure. NH₃: strong hydrogen bonding, causing it to deviate more from ideal behaviour than non-polar gases of similar molar mass. In general, the more polar a gas molecule and the closer it is to its liquefaction point, the further its real behaviour departs from the ideal gas law's predictions.

What should I know about Gas Law Applications?

Weather balloons: as altitude increases, atmospheric pressure decreases. Balloon expands (Boyle's Law). Eventually bursts when external pressure too low. SCUBA tanks: compressed air at 200-300 bar, ~0.01 L/bar volume. At depth, partial pressure of N₂ increases — causes narcosis at great depths. Nitrogen narcosis is essentially alcohol-like impairment. Breathing at depth: air consumption rate increases proportionally with depth pressure (1 tank lasts half as long at 10m as at surface). Autoclaves (used to sterilise medical and laboratory equipment) rely on the same pressure-temperature relationship in reverse: sealing steam in a chamber and letting pressure build raises its temperature well above 100°C, since boiling point rises with pressure — this higher temperature is what kills heat-resistant bacterial spores that survive ordinary boiling.

What should I know about The Combined Gas Law?

When pressure, volume, and temperature of a fixed amount of gas all change simultaneously, Boyle's, Charles', and Gay-Lussac's laws combine into: P1V1/T1 = P2V2/T2 (temperature in Kelvin). Example: a gas occupies 3.0 L at 100 kPa and 20°C (293K). What is its volume at 150 kPa and 50°C (323K)? V2 = (P1V1T2)/(T1P2) = (100 x 3.0 x 323)/(293 x 150) = 2.20 L. This combined form is especially useful for weather balloons, scuba diving calculations, and any situation where a gas sample moves between two sets of conditions without gas being added or removed, since it avoids calculating each simple law in sequence. Where the amount of gas does change, PV = nRT must be used directly, comparing states via P1V1/(n1T1) = P2V2/(n2T2), which reduces to the combined gas law whenever n1 = n2.

What's the key thing to understand about Dalton's Law of Partial Pressures?

In a mixture of non-reacting gases, each gas exerts a partial pressure as if it alone occupied the total volume, and the total pressure is the sum of all partial pressures: Ptotal = P1 + P2 + P3... Each gas's partial pressure is proportional to its mole fraction: P(gas) = mole fraction x Ptotal. Example: dry air at 101.3 kPa is approximately 78% N2 and 21% O2 by mole fraction, so the partial pressure of O2 at sea level is about 0.21 x 101.3 = 21.3 kPa. This is central to diving physiology: as a diver descends, total pressure increases (about 1 atm per 10m of seawater), and the partial pressure of every gas in the breathing mixture increases proportionally — elevated nitrogen partial pressure at depth drives more N2 into tissues (causing nitrogen narcosis, and decompression sickness on rapid ascent), while elevated oxygen partial pressure beyond about 1.4-1.6 atm becomes toxic, which is why technical divers use custom gas mixtures rather than ordinary air at depth.

What's the difference between Old and Current STP Conventions?

'Standard temperature and pressure' hasn't always meant the same thing. The traditional definition (0°C, 1 atm = 101.325 kPa) gives a molar volume of 22.4 L/mol and is still the one most commonly taught and used in introductory chemistry. IUPAC's current definition (since 1982: 0°C, 100 kPa) gives a slightly different molar volume of 22.7 L/mol. The difference is small but real, and it's worth checking which convention a textbook, exam board, or problem set is using before quoting '22.4 L/mol' as if it were the only correct answer — both are 'STP,' just defined at slightly different reference pressures.

Worked Example: Combined Gas Law Across a Temperature and Volume Change

A gas sample at P₁ = 1.5 atm, V₁ = 2.0 L, T₁ = 300 K is compressed to V₂ = 1.2 L while being heated to T₂ = 360 K. Find the new pressure using the combined gas law, (P₁V₁)/T₁ = (P₂V₂)/T₂: P₂ = P₁ × (V₁/V₂) × (T₂/T₁) = 1.5 × (2.0/1.2) × (360/300) = 1.5 × 1.6667 × 1.2 = 3.0 atm The pressure doubles from 1.5 atm to 3.0 atm — driven by both the volume shrinking (which alone would push pressure up by a factor of 2.0/1.2 ≈ 1.667) and the temperature rising (which alone would push it up by a factor of 1.2). Multiplying those two factors together (1.667 × 1.2 = 2.0) gives the combined effect directly, which is a useful way to sanity-check a combined gas law answer without plugging through the full formula.

Ideal Gas Law Constant in Different Unit Systems

Choosing the wrong value of R for the units you're working in is one of the most common sources of error in ideal gas law problems — the physics doesn't change, but plugging pressure in atm into a formula expecting pascals (or vice versa) with the wrong R value gives an answer off by several orders of magnitude. A reliable habit is to convert all given quantities into SI units (pascals, cubic metres, kelvin) first and use R = 8.314 J/(mol·K) consistently, only converting the final answer back to more familiar units like litres or atmospheres if needed for the context.

Worked Example: Moles of Gas From the Ideal Gas Law

A gas sample occupies V = 25 L (0.025 m³) at P = 101,325 Pa (1 atm) and T = 298 K. Using PV = nRT with R = 8.314 J/(mol·K): n = PV/RT = (101,325 × 0.025) / (8.314 × 298) = 2,533.1 / 2,477.6 ≈ 1.022 mol This is close to but not exactly 1 mole — a useful check, since 1 mole of ideal gas at standard temperature and pressure (STP, using the modern IUPAC definition of 100 kPa and 273.15 K) occupies almost exactly 22.7 L, and at the slightly different conditions given here (1 atm = 101.325 kPa and 25°C rather than 0°C), a small deviation from exactly 1 mole for 25 L is expected and confirms the calculation is in the right ballpark.

Standard Temperature and Pressure (STP): Old vs. Modern

STP has been defined slightly differently over the years, which occasionally causes confusion when comparing textbook answers. The older convention used 0°C (273.15 K) and 1 atm (101.325 kPa), giving a molar volume of 22.4 L/mol. The current IUPAC convention uses 0°C and 100 kPa exactly, giving a molar volume of about 22.7 L/mol instead. Always check which convention a question or textbook is using before quoting '22.4 litres per mole' as if it were universal — the two values differ by about 1.3%, small but enough to matter in precise calculations.