Chemistry

Gas Compressibility Factor

Compare a measured gas state with ideal-gas behavior.

Z = \frac{P V}{n R T}

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Source & review

Difficulty

Intermediate

Read time

4 min

Prerequisites

Algebra, logarithms, and molar quantities

Review statusNeeds review

Source

OpenStax, Chemistry 2e, §9.6

Adapted from Teng-Jui Lin’s CHEM 145 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.

Definition

Understanding the core concept

The compressibility factor measures how a gas state departs from PV = nRT. An ideal gas has Z = 1; values below or above one indicate a smaller or larger PV product at the same amount and temperature.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$Z$	Compressibility factor	$1$
$P$	Absolute gas pressure	$Pa$
$V$	Gas volume	$m^{3}$
$n$	Amount of gas	$mol$
$R$	Molar gas constant	$J mo l^{- 1} K^{- 1}$
$T$	Absolute gas temperature	$K$

Real-World Applications

Where this formula is used in practice

Real-gas checks

Quantify departure from the ideal-gas equation.

Measured gas states

Compare experimental PV data with nRT.

Worked Example

Step-by-step calculation with real numbers

Problem

A gas sample has measured pressure 100000 Pa, volume 0.0240 m³, amount 1.00 mol, and temperature 300 K. Calculate Z using the listed gas constant.

Given

P = 100000 Pa

V = 0.0240 m^{3}

n = 1.00 mol

T = 300 K

R = 8.314462618 J mo l^{- 1} K^{- 1}

Solution

Z = \frac{P V}{n R T}

Z = \frac{( 100000 ) ( 0.0240 )}{( 1.00 ) ( 8.314462618 ) ( 300 )}

Z \approx 0.9622

Final Answer

Z \approx 0.9622

Formula Guide

Info

DifficultyIntermediate

Read Time4 min

PrerequisitesAlgebra, logarithms, and molar quantities

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

OpenStax, Chemistry 2e, §9.6

Adapted from Teng-Jui Lin’s CHEM 145 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.

Assumptions

• Use positive absolute pressure, volume, amount, and kelvin temperature for a single gas phase.
• Use a gas constant consistent with the pressure and volume units.

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