Understanding Boyle's Law

Boyle’s law is a fundamental gas law that describes the relationship between the pressure and volume of a fixed amount of gas at a constant temperature. It's a key concept in chemistry and physics when studying the behavior of gases.

The Relationship between Volume and Pressure according to Boyle’s Law

According to Boyle’s law, for a fixed mass of gas kept at a constant temperature, the volume of the gas is inversely proportional to its pressure. This means if you increase the pressure on the gas, its volume will decrease, and if you decrease the pressure, its volume will increase, assuming the temperature and the amount of gas remain unchanged.

Mathematically, Boyle's Law can be expressed as:

$$V \propto \frac{1}{P} \quad (\text{at constant temperature and fixed mass})$$

Where:

• \(V\) represents the volume of the gas.
• \(P\) represents the pressure of the gas.
• \(\propto\) means “is proportional to”.

This relationship also implies that the product of the pressure and volume is approximately constant for a fixed amount of gas at constant temperature:

$$P \times V = \text{Constant}$$

For comparing the same gas under two different sets of pressure and volume conditions (at the same constant temperature and fixed mass), Boyle's Law can be written as:

$$P_1 V_1 = P_2 V_2$$

Where \(P_1\) and \(V_1\) are the initial pressure and volume, and \(P_2\) and \(V_2\) are the final pressure and volume.

Analyzing the Options based on Boyle's Law

Let's look at the given options in the context of Boyle's Law:

• directly proportional to its pressure: This means as pressure increases, volume increases. This contradicts the principle of Boyle's Law.
• inversely proportional to its pressure: This means as pressure increases, volume decreases, and vice versa. This is exactly what Boyle's Law states for a fixed mass of gas at constant temperature.
• the square root of its pressure: This suggests a different mathematical relationship (\(V \propto \sqrt{P}\) or \(V \propto \frac{1}{\sqrt{P}}\)) which is not described by Boyle's Law.
• none of these: Since the second option correctly describes Boyle's Law, this option is incorrect.

Therefore, according to Boyle’s law, the volume of a fixed mass of a gas, at constant temperature, is inversely proportional to its pressure.