Understanding Gas Laws: Volume and Pressure Relationship

The question asks about the law that describes the inverse relationship between the volume and pressure of a gas. Several fundamental laws govern the behavior of gases under different conditions. Let's examine the options provided to identify the correct law.

Analyzing the Gas Laws

We are given four options, each representing a key gas law:

• Boyle's Law
• Charles's Law
• Gay-Lussac's Law
• Avogadro's Law

We need to determine which of these laws specifically states that the volume of a gas is inversely proportional to its pressure.

Boyle's Law Explained

Boyle's law, named after Robert Boyle, describes the relationship between the pressure and volume of a fixed amount of gas at constant temperature. It states that at a constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.

Mathematically, this relationship can be expressed as:

$$V \propto \frac{1}{P} \quad (\text{at constant } T \text{ and } n)$$

Where:

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

This inverse proportionality means that if the pressure of a gas increases, its volume decreases, and if the pressure decreases, its volume increases, assuming the temperature and the amount of gas remain unchanged. Another way to express Boyle's law is that the product of pressure and volume is constant for a fixed amount of gas at constant temperature:

$$PV = k$$

Where $k$ is a constant. For a gas undergoing a change from state 1 to state 2 at constant temperature and amount, Boyle's law can also be written as:

$$P_1V_1 = P_2V_2$$

Other Gas Laws

To further clarify, let's briefly look at what the other laws state:

• Charles's Law: Relates volume and temperature. It states that the volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature ($V \propto T$ at constant $P$ and $n$).
• Gay-Lussac's Law: Relates pressure and temperature. It states that the pressure of a fixed amount of gas at constant volume is directly proportional to its absolute temperature ($P \propto T$ at constant $V$ and $n$).
• Avogadro's Law: Relates volume and the amount of gas. It states that the volume of a gas at constant temperature and pressure is directly proportional to the number of moles of gas ($V \propto n$ at constant $T$ and $P$).

Comparing these laws, it is clear that Boyle's law is the one that describes the inverse proportionality between the volume and pressure of a gas.

Conclusion

Based on the definitions of the gas laws, Boyle's law is the one that explicitly states that the volume of a gas is inversely proportional to the pressure, assuming temperature and the amount of gas are kept constant.

Revision Table: Summary of Key Gas Laws

Additional Information on Ideal Gases

The laws discussed (Boyle's, Charles's, and Avogadro's) can be combined to form the Ideal Gas Law, which is a single equation relating pressure, volume, temperature, and the number of moles of an ideal gas:

$$PV = nRT$$

Where:

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

An ideal gas is a theoretical concept where gas particles are assumed to have no volume and no intermolecular forces. Real gases deviate from ideal behavior, especially at high pressures and low temperatures, but the ideal gas law provides a very useful model for understanding gas behavior under many common conditions.