Question

The temperature at which real gases obey the ideal gas laws over a wide range of pressure is called (1) Critical temperature (2) Boyle's temperature (3) Inversion temperature (4) Reduced temperature

Short answer

Option (2) Boyle's temperature.

Step-by-step solution

Identify the Concept

Determine which gas law or concept is relevant to the problem. Here it is about the temperature at which real gases obey the ideal gas laws over a wide range of pressure.

Recall Definitions

Critical Temperature: The temperature above which a gas cannot be liquefied, no matter how much pressure is applied.Boyle's Temperature: The temperature at which a real gas obeys Boyle's law over a wide range of pressure (ideal gas behavior).Inversion Temperature: The temperature at which the Joule-Thomson coefficient changes sign.Reduced Temperature: The ratio of the actual temperature of a gas to its critical temperature.

Match Correct Definition

Identify the definition that matches 'the temperature at which real gases obey the ideal gas laws over a wide range of pressure'. This matches the definition of Boyle's Temperature.

Key concepts

ideal gas law

The Ideal Gas Law is a fundamental principle in chemistry and physics that describes the behavior of ideal gases. It is represented by the equation: \[ PV = nRT \] Where:

• P = Pressure of the gas
• V = Volume of the gas
• n = Number of moles of the gas
• R = Ideal gas constant
• T = Temperature in Kelvin

This law assumes that gas particles do not interact with each other and that the volume of the gas particles themselves is negligible. It works well for most gases at high temperatures and low pressures. However, real gases deviate from this ideal behavior under certain conditions, such as high pressure and low temperature.

real gases

Real gases differ from ideal gases because they have interactions between molecules and a finite volume. Under certain conditions, these deviations become significant.

Several factors cause real gases to deviate from ideal behavior:

• Molecular Attractions: At high pressures, gas molecules are closer together, and intermolecular forces, such as Van der Waals forces, become significant.
• Volume of Gas Molecules: At very high pressures, the actual volume occupied by gas molecules can no longer be neglected.
• Temperature: At low temperatures, gas molecules have less kinetic energy, and intermolecular attractions become more significant, causing deviations from ideal gas behavior.

To account for these deviations, the Van der Waals equation can be used:\[ \bigg(P + \frac{a}{V^2}\bigg)(V - b) = nRT \] Where a and b are constants that differ for each gas and account for intermolecular attractions and the finite size of molecules respectively.

pressure

Pressure is the force exerted by gas molecules as they collide with the walls of their container. It is a measure of how frequently and forcefully gas particles hit the container walls.

There are different units to measure pressure, including:

• Atmospheres (atm)
• Pascal (Pa)
• Millimeters of mercury (mmHg)
• Torr

Pressure plays a crucial role in understanding gas behavior, especially when studying real gases. For instance, at high pressures, the volume of a gas decreases and intermolecular forces become significant, causing deviations from ideal gas behavior.

Boyle's Temperature is particularly important here, as it is the temperature at which a real gas behaves like an ideal gas over a wide range of pressures. At this temperature, the gas follows Boyle's Law, which states that for a given amount of gas at constant temperature, the volume is inversely proportional to the pressure:\[ PV = \text{{constant}} \]