In physical chemistry, which of the following is an example of an extensive property of matter (a property that depends on the amount of substance)?

Introduction / Context:
This question tests your understanding of the difference between intensive and extensive properties in physical chemistry. An extensive property depends on the amount of matter present, while an intensive property does not change when you change the size of the sample. Recognising which properties are extensive helps in thermodynamics, material science, and practical laboratory work, because it tells you which variables scale with the size of the system and which do not. The question asks you to identify one example of an extensive property from a list of commonly discussed physical properties.

Given Data / Assumptions:
- The properties listed are volume, density, temperature, and pressure.
- You must select which of these is extensive, meaning it depends on the amount of substance.
- It is assumed that you know basic definitions of these properties and how they behave when the sample size changes.
- Only one option is intended to be correct as a purely extensive property in this list.

Concept / Approach:
Extensive properties, such as mass, volume, and total energy, scale with the size or quantity of material. If you double the amount of substance, these properties typically double. Intensive properties, such as density, temperature, and pressure, do not depend on the total amount of material. For example, the density of water remains the same whether you have one litre or ten litres, provided temperature and pressure are constant. In the list given, volume clearly increases as you have more of the substance, while density, temperature, and pressure remain characteristic of the material or system regardless of the total amount. Therefore, volume is the correct example of an extensive property.

Step-by-Step Solution:
Step 1: Recall that extensive properties change when the quantity of matter changes, while intensive properties remain the same. Step 2: Consider volume: if you have one litre of water and add another litre, the total volume becomes two litres. This shows that volume depends on the amount and is an extensive property. Step 3: Consider density, defined as mass per unit volume. For a given substance at fixed temperature and pressure, density does not change when you simply take a larger or smaller sample, so density is intensive. Step 4: Temperature measures the average kinetic energy of particles and remains the same if you combine two samples at the same temperature, meaning it is intensive. Step 5: Pressure is a measure of force per unit area and, for a uniform system, does not double just because you double the amount of gas while keeping conditions appropriate; it is intensive. Step 6: Conclude that among the listed properties, volume is the example of an extensive property.

Verification / Alternative check:
You can verify this classification by imagining cutting a sample in half. If you start with a block of material and cut it into two equal pieces, each piece will have half the mass and half the volume. This confirms that mass and volume depend on the amount of substance and are extensive. However, the density of each piece, its temperature (if no heat is added or removed), and the internal pressure (for a gas in a container with the same conditions) remain unchanged, showing that these are intensive properties. Most textbooks list volume explicitly as an extensive property alongside mass and total energy, confirming the answer.

Why Other Options Are Wrong:
Density is an intensive property because it remains the same for a homogeneous substance, regardless of sample size. Temperature is intensive because it does not depend on how much substance you have; mixing two equal samples at the same temperature yields a combined sample at the same temperature. Pressure is also intensive, as it characterises the state of a fluid or gas and does not simply double because you double the amount of substance while maintaining suitable conditions. Therefore, options B, C, and D do not represent extensive properties in this context.

Common Pitfalls:
A common mistake is to think that any property must be extensive because it seems to change during experiments, or to confuse density with mass, leading students to treat density as extensive. Another error is to forget that intensive properties often define the state of a system, such as temperature and pressure, and are independent of system size. To avoid these pitfalls, remember a simple test: imagine combining two identical samples. If the property doubles, it is extensive; if it stays the same, it is intensive. Applying this test quickly shows that volume is extensive while density, temperature, and pressure are intensive.

Final Answer:
An example of an extensive property of matter from the list is volume.