Solve for pressure, volume, moles, or temperature using the ideal gas law PV = nRT.
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The ideal gas law is a fundamental equation in physical chemistry that relates the pressure, volume, number of moles, and temperature of any ideal gas, written as PV = nRT, where P is pressure (in standard atmospheres, atm), V is volume (in liters, L), n is the number of moles, T is the absolute temperature (necessarily in kelvin, K, since the equation assumes a temperature scale starting from absolute zero), and R is the universal gas constant (0.08206 liter·atmospheres per mole·kelvin in these units). This law assumes gas particles have no volume and don't interact with each other, which is a very good approximation for real gases at ordinary temperatures and pressures, though it becomes less accurate at very high pressures or very low temperatures where real gas molecules' volume and intermolecular forces start to matter. This calculator lets you find any one of the four quantities (pressure, volume, moles, or temperature) if the other three are known, making it useful in general chemistry problems, calculating the volumes of gases produced by chemical reactions, and designing gas vessels and piping.
No real gas perfectly satisfies the assumptions behind the ideal gas law — the assumption that gas particles have zero volume and exert no forces on each other is a simplification, since real molecules do occupy some actual space and do exert weak attractive forces on their neighbors. Despite this, PV=nRT remains remarkably accurate for most everyday chemistry and engineering calculations.
The reason the idealization works so well in practice comes down to typical conditions: at ordinary temperatures and pressures, gas molecules are spread far enough apart, and moving fast enough, that the actual volume they occupy is a tiny fraction of the total container volume, and the brief, weak intermolecular attractions have negligible effect compared to the particles' kinetic energy. Under these common conditions, treating molecules as point particles with no interactions introduces only a small error.
The equation breaks down more noticeably under extreme conditions: at very high pressure, gas molecules are forced close enough together that their actual physical volume becomes a meaningful fraction of the total volume, no longer negligible. At very low temperature, molecules move slowly enough that the weak intermolecular attractive forces become significant relative to their reduced kinetic energy, causing real gas behavior to deviate from the ideal prediction — behavior more accurately captured by more complex equations of state like the van der Waals equation.
Requiring absolute temperature (kelvin) rather than Celsius or Fahrenheit isn't an arbitrary convention — the entire relationship in PV=nRT assumes temperature is proportional to the average kinetic energy of gas molecules, a relationship that only holds true starting from absolute zero, the temperature at which molecular motion theoretically stops entirely. Using Celsius, which has an arbitrary zero point unrelated to molecular motion, would break this proportionality and make the equation give incorrect results.
Practically, the ideal gas law is genuinely useful across an enormous range of real applications: calculating how much gas a storage tank of known volume can hold at a given pressure, predicting the volume of gas produced by a chemical reaction before it's actually run, and designing piping and vessels that must safely contain gas at specified pressure and temperature conditions — all standard calculations in chemical engineering that rely on this one relatively simple equation holding true closely enough for practical design purposes.
The ideal gas law requires an absolute temperature scale starting at true zero (absolute zero); Celsius or Fahrenheit have arbitrary zero points that would give incorrect (or even negative volume/pressure) results in this formula.
It uses R = 0.08206 L·atm/(mol·K), which matches the units used here (pressure in atmospheres, volume in litres) — R has other numerical values (like 8.314 J/(mol·K)) when different units are used.
It's an excellent approximation for most real gases at ordinary temperatures and pressures, but it becomes less accurate at very high pressure or very low temperature, where intermolecular forces and molecular volume become significant.