ideal gas equation
Summary
The ideal gas equation, PV = nRT, links the pressure, volume, moles and absolute temperature of a gas modeled as having negligible particle volume and no intermolecular forces. The most testable point is that T must be in kelvins. Real gases deviate at high pressure and low temperature.
Detail
Meaning: The equation describes a model gas whose particles have negligible volume, exert no attractive or repulsive forces on each other, and collide elastically. For such a gas, pressure is proportional to moles and to temperature, and inversely proportional to volume. Real gases behave nearly ideally at low pressure and high temperature. They deviate at high pressure, where particle volume matters, and at low temperature, where attractions matter.
Equation: PV = nRT, where P is pressure (Pa), V is volume (m³), n is amount of gas (mol), R is the gas constant (8.314 J/(mol·K)), and T is absolute temperature (K). With liters and atmospheres, R = 0.0821 L·atm/(mol·K).
On the MCAT: Expect questions that change one variable and ask for the direction of another. At constant n and V, doubling T doubles P. For a fixed amount of gas, the combined form P₁V₁/T₁ = P₂V₂/T₂ is faster. Rearranging gives density d = PM/RT and molar mass M = dRT/P, where M is molar mass. Graphs of V against T (a straight line that extrapolates to zero volume at 0 K) and P against 1/V (also a straight line) are common.
Common confusion: Students substitute Celsius temperature. T must be in kelvins (K = °C + 273.15). Also match R to the units used for P and V.
Sources
- Chemistry: The Central Science
- General Chemistry: Principles and Modern Applications
- Chemistry (Zumdahl)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.