The distinction between intensive vs extensive properties is fundamental in general chemistry because it clarifies whether a measured quantity changes when the amount of matter changes.
Core idea: An intensive property is independent of system size, while an extensive property depends on the amount of substance and typically scales with it.
1) Definitions
Intensive properties do not depend on the quantity of matter present. If the system is split into smaller pieces, the intensive property of each piece (under the same conditions) remains the same.
Extensive properties depend on the amount of matter. When two identical subsystems are combined, extensive properties add.
2) A practical identification test (scaling and additivity)
Consider two identical samples of the same substance at the same temperature and pressure, labeled A and B. Let the combined system be A + B.
- If a quantity doubles when going from A to A + B (and is additive), it is extensive.
- If a quantity stays unchanged when going from A to A + B, it is intensive.
Additivity criterion: For an extensive property \(X\), identical subsystems satisfy \(X_{A+B} = X_A + X_B\). For an intensive property \(y\), the combined system has \(y_{A+B} = y_A = y_B\) (when equilibrium conditions match).
3) Common examples in general chemistry
| Type | Typical examples | How it behaves when doubling the sample |
|---|---|---|
| Extensive | mass \(m\), volume \(V\), moles \(n\), internal energy \(U\), enthalpy \(H\), entropy \(S\), total charge | increases proportionally; for identical samples often \(X_{A+B} = 2X_A\) |
| Intensive | temperature \(T\), pressure \(P\), density \(\rho\), concentration \(c\), boiling point, melting point | unchanged; for identical samples \(y_{A+B} = y_A\) |
4) Derived properties: why ratios of extensive properties become intensive
Many important intensive quantities are formed by dividing one extensive property by another. Density is the standard example:
\[ \rho = \frac{m}{V} \]
If the amount of material doubles, both \(m\) and \(V\) double, so the ratio stays constant:
\[ \rho' = \frac{2m}{2V} = \frac{m}{V} = \rho \]
The same logic applies to concentration \(c = \frac{n}{V}\) and molar quantities such as molar volume \(\frac{V}{n}\) and molar enthalpy \(\frac{H}{n}\).
5) Useful classification checklist
- Ask “Does it depend on how much?” If yes, it is likely extensive.
- Try the combination test: Combine two identical samples and check whether the value adds or stays the same.
- Look for ratios: If it is a ratio of two extensive properties, it is typically intensive.
One-line summary: Extensive properties scale with the size of the system and are additive, whereas intensive properties characterize the system’s state without depending on the amount of matter.