Question

State the following gas laws in words and also in the form of an equation: Boyle's law, Charles's law, Avogadro's law. In each case, indicate the conditions under which the law is applicable, and give the units for each quantity in the equation.

Short answer

Boyle's Law: \( P \times V = \text{constant} \); Charles's Law: \( \frac{V}{T} = \text{constant} \); Avogadro's Law: \( \frac{V}{n} = \text{constant} \).

Step-by-step solution

Boyle's Law Description

Boyle's Law states that the pressure of a given amount of gas is inversely proportional to its volume, provided the temperature remains constant. It is applicable under isothermal (constant temperature) conditions. The relationship can be expressed as: \[ P \times V = \text{constant} \]Where:- \( P \) is the pressure of the gas (units: Pascals, Pa)- \( V \) is the volume of the gas (units: cubic meters, m³).

Charles's Law Description

Charles's Law states that the volume of a given mass of gas is directly proportional to its absolute temperature, provided the pressure remains constant. This law applies under isobaric (constant pressure) conditions. It can be written as:\[ \frac{V}{T} = \text{constant} \]Where:- \( V \) is the volume of the gas (units: cubic meters, m³)- \( T \) is the temperature of the gas in Kelvin (units: Kelvin, K).

Avogadro's Law Description

Avogadro's Law states that equal volumes of all gases at the same temperature and pressure contain an equal number of molecules. This law holds true under conditions of constant temperature and pressure. The equation is:\[ \frac{V}{n} = \text{constant} \]Where:- \( V \) is the volume of the gas (units: cubic meters, m³)- \( n \) is the amount of substance of the gas (units: moles, mol).

Key concepts

Boyle's Law

Boyle's Law is one of the fundamental principles governing the behavior of gases. It describes how the pressure of a gas decreases when its volume increases, as long as the temperature remains constant. It is important to remember that this law operates under **isothermal conditions**, meaning that the temperature is held steady throughout any changes in pressure or volume.
In equation form, Boyle's Law is expressed as \( P \times V = \text{constant} \). Here:

• \( P \) represents the pressure of the gas, measured in Pascals (Pa).
• \( V \) symbolizes the volume, measured in cubic meters (m³).

This inverse relationship means that if you increase the volume of a gas, the pressure decreases, and vice versa. This concept is crucial in understanding behaviors such as the compression of gases in syringes or scuba tanks.

Charles's Law

Charles's Law provides insight into how gases expand when heated. It states that the volume of a gas increases with an increase in temperature, provided that the pressure remains unchanged. Consequently, Charles's Law applies under **isobaric conditions**, where pressure is constant throughout the process.
The mathematical expression of Charles's Law is \( \frac{V}{T} = \text{constant} \). In this formula:

• \( V \) denotes the volume of the gas, in cubic meters (m³).
• \( T \) is the absolute temperature, measured in Kelvin (K).

This direct proportionality indicates that as the temperature goes up, so does the volume. It's a practical concept for understanding how hot air balloons rise when the air inside them is heated.

Avogadro's Law

Named after Amedeo Avogadro, Avogadro's Law emphasizes the connection between the volume of a gas and the number of molecules it contains. Specifically, it states that equal volumes of all gases at the same temperature and pressure will have the same number of molecules. This remains true under fixed conditions of constant temperature and pressure.
The equation for Avogadro's Law is \( \frac{V}{n} = \text{constant} \). Here:

• \( V \) represents the volume, in cubic meters (m³).
• \( n \) is the number of moles, a unit measuring the amount of substance.

Avogadro's Law is foundational in chemical sciences as it provides a direct relationship between the volume a gas occupies and the number of particles it contains. This helps in calculating the molar volume or determining how a chemical reaction involving gases evolves.

Isothermal Conditions

The term **isothermal** is used in thermodynamics to describe a process where the temperature remains constant. This is a key condition for applying Boyle's Law. In an isothermal process, even though heat exchange might occur with the surroundings, the overall temperature of the system doesn't change.
When conditions are isothermal, the internal energy of an ideal gas doesn't increase because temperature isn't altered. Therefore, all work done on or by the gas is at the expense of energy, not stored as a change in internal temperature. This is crucial in understanding how gases behave in real-world applications, such as in engines or refrigeration cycles.

Isobaric Conditions

**Isobaric conditions** are those where the pressure within a system remains steady. This is the setting in which Charles's Law can be observed. When a gas undergoes an isobaric process, its volume and temperature can change, but the pressure remains constant.
This type of process is commonly seen in natural phenomena and engineering systems, such as when a pot of water is heated on a stove. As the water heats and the steam expands, the pressure in the pot won't change markedly if it remains open to the atmosphere.
Isobaric conditions are particularly important in understanding phase changes like vaporization and condensation, where volume and temperature can shift dramatically while the pressure remains unaltered.