A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
The compressibility factor Z = PV/nRT is a dimensionless measure of deviation from ideal gas behavior (Z = 1 for ideal gases). It depends on reduced temperature T_r = T/T_c and reduced pressure P_r = P/P_c, allowing data for many substances to be correlated on a single generalized chart (law of corresponding states). The compressibility factor is widely used in engineering to account for real gas behavior without solving complex equations of state.
Use generalized compressibility charts to estimate properties of real gases. Compare Z calculated from van der Waals with values from charts.
From real gas deviations you know that actual gases do not obey PV = nRT perfectly: intermolecular attractions pull molecules together (reducing pressure below the ideal prediction), while the finite volume of molecules prevents compression beyond a limit (raising pressure above ideal). The compressibility factor Z = PV/nRT is simply a number that encodes how much a real gas deviates from ideal. When Z = 1, the gas behaves ideally. When Z < 1, intermolecular attractions dominate — the gas is easier to compress than ideal (common at moderate pressures and low-to-moderate temperatures). When Z > 1, molecular volume repulsions dominate — the gas resists compression (common at very high pressures or very high temperatures).
The power of Z is that it turns a complex problem — "how does this particular gas behave?" — into a universal one via the law of corresponding states. The insight is that Z depends not on absolute T and P but on the reduced variables T_r = T/T_c and P_r = P/P_c, where T_c and P_c are the critical temperature and pressure of the substance. Two gases at the same T_r and P_r have (approximately) the same Z. This means you can construct a single generalized compressibility chart with T_r and P_r on the axes, and use it for any gas — nitrogen, methane, carbon dioxide — without knowing their detailed intermolecular potentials. The underlying reason is that all simple nonpolar molecules have intermolecular potentials of similar shape, differing mainly in the depth and range of the potential well (which is captured by T_c and P_c).
To use the chart in practice: calculate T_r and P_r from the known T, P, and tabulated critical constants. Read off Z from the chart. Then the actual molar volume is V = ZRT/P instead of just RT/P. This correction can be 5–30% for gases at high pressures, which matters enormously in engineering calculations for pipelines, compressors, and storage vessels. The chart is also reversible: if you know Z and T_r, you can read off P_r and find the actual pressure at that condition.
The law of corresponding states has limits. Polar molecules (water, ammonia) and molecules with complex shapes deviate noticeably from the universal chart. The acentric factor ω, introduced by Pitzer, is a third parameter that corrects for non-spherical molecular shape: Z = Z⁰(T_r, P_r) + ωZ¹(T_r, P_r), where Z⁰ is the simple two-parameter correlation and Z¹ is a shape correction. With the acentric factor, the Pitzer correlations achieve accuracy within a few percent for most engineering applications, making the compressibility factor approach the workhorse of industrial gas calculations.