Understanding Gas Laws: Avogadro's Principle Explained

The question asks to identify a fundamental law in Physics that relates the volume of gases to the number of molecules they contain, under specific conditions of temperature and pressure.

Let's examine the statement carefully: "equal volume of all gases under the same conditions of temperature and pressure contain the equal number of molecules." This statement describes a direct relationship between the volume of a gas and the number of its constituent particles (molecules or atoms) when both temperature and pressure are kept constant.

Analyzing the Options

We need to determine which of the given laws corresponds to this description.

• Ohm's Law: Ohm's Law deals with electrical circuits, specifically the relationship between voltage, current, and resistance ($V = IR$). It has no relevance to the behavior of gases or the number of molecules.
• Charles's Law: Charles's Law describes the relationship between the volume and temperature of a fixed amount of gas at constant pressure. It states that the volume of a gas is directly proportional to its absolute temperature ($V \propto T$, when pressure and the number of moles are constant). While it involves volume and temperature, it does not relate volume directly to the number of molecules.
• Avogadro's Law: Avogadro's Law states that, at the same temperature and pressure, equal volumes of all gases contain the same number of molecules (or moles). Conversely, at the same temperature and pressure, the volume of a gas is directly proportional to the number of moles ($V \propto n$, when temperature and pressure are constant). This law perfectly matches the description provided in the question.
• Boyle's Law: Boyle's Law describes the relationship between the pressure and volume of a fixed amount of gas at constant temperature. It states that the pressure of a gas is inversely proportional to its volume ($P \propto 1/V$ or $PV = \text{constant}$, when temperature and the number of moles are constant). This law deals with pressure and volume but not directly with the number of molecules.

Based on the analysis, the law that fits the description is Avogadro's Law.

Avogadro's Law in Detail

Avogadro's law, named after Amedeo Avogadro, is a key gas law. It can be stated mathematically as:

$$V \propto n \quad \text{at constant } T \text{ and } P$$

where:

• $V$ is the volume of the gas.
• $n$ is the number of moles of the gas.
• $T$ is the absolute temperature.
• $P$ is the pressure.

This means if you double the number of moles of a gas (at constant temperature and pressure), the volume will also double. The law implies that the size of the individual gas molecules is insignificant compared to the average distance between them at typical temperatures and pressures, and that all gases behave similarly under these conditions regardless of their chemical identity.

A significant consequence of Avogadro's law is that at standard temperature and pressure (STP, $0^\circ C$ and $1 \text{ atm}$), one mole of any ideal gas occupies approximately $22.4 \text{ liters}$.

Summary of Gas Laws

Comparing the question's statement with the principles of these laws, it is clear that Avogadro's Law accurately describes the scenario where equal volumes of different gases, under the same conditions of temperature and pressure, contain the same number of molecules.

Revision Table: Key Gas Laws

Additional Information: The Ideal Gas Law

Boyle's Law, Charles's Law, and Avogadro's Law can be combined into a single comprehensive equation called the Ideal Gas Law:

$$PV = nRT$$

where:

• $P$ is the pressure of the gas.
• $V$ is the volume of the gas.
• $n$ is the number of moles of the gas.
• $R$ is the ideal gas constant.
• $T$ is the absolute temperature.

This law describes the behavior of an ideal gas, which is a theoretical gas composed of many randomly moving point particles that do not interact with each other except through elastic collisions. Real gases approximate ideal gas behavior at relatively low pressures and high temperatures.

Avogadro's number is defined as the number of constituent particles (atoms, molecules, ions, etc.) per mole of a substance, approximately $6.022 \times 10^{23} \text{ mol}^{-1}$. Avogadro's Law is fundamental to understanding the stoichiometry of chemical reactions involving gases.