Question

A real gas will approach the behaviour of ideal gas at (a) low temperature and low pressure (b) low temperature and high pressure (c) high temperature and high pressure (d) high temperature and low temperature

Short answer

The correct statement is (d) High temperature and low pressure.

Step-by-step solution

Understand Real and Ideal Gases

Real gases are those gases which do not exactly follow the Ideal Gas Law (PV=nRT), while an ideal gas strictly adheres to this law. Real gases deviate from the ideal gas law because of the molecular interactions and the volume occupied by gas molecules.

Analyze The Options

We have to choose the condition under which a real gas behaves like an ideal gas. We do this by eliminating the conditions that cause deviations. Low temperature and high pressure cause more deviations to ideal behavior. Hence, the viable options are those that involve high temperature and low pressure. This leaves us with (c) and (d).

Choose the Correct Statement

From step 2, we know that high temperature (which increases the kinetic energy and thus reduces the effect of intermolecular forces) and low pressure (since it increases the volume and reduces the chances of intermolecular collisions) causes a real gas to behave more like an ideal gas. Hence, the statement (d) High temperature and low pressure is the correct.

Key concepts

Real Gas

A real gas is a gas that does not behave exactly like the model of an ideal gas, especially under certain conditions such as low temperature or high pressure. In a real gas, there are interactions between molecules that affect their motion and spacing. This is because molecules occupy space, and they exert forces on one another.

Under normal conditions, these molecular interactions can make the behavior of real gases different from the hypothetical ideal gases. If we compress or cool down a gas, these interactions become more pronounced compared to when the gas is at a high temperature or low pressure.

• Real gases deviate more at low temperatures when the molecules move slower and intermolecular forces are stronger.
• At high pressures, the volume occupied by gas molecules becomes significant compared to the empty space, thus further altering their behavior.

Ideal Gas Law

The Ideal Gas Law is a mathematical relationship that explains how ideal gases behave under different conditions of temperature, pressure, and volume. It is expressed by the equation \(PV = nRT\), where \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles of the gas, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.

This law assumes that gas particles:

• have no volume, meaning they are point-sized,
• and do not interact with each other, implying no intermolecular forces.

Under these ideal conditions, the gas will behave predictably. However, we must remember that no real gas perfectly fits this model, although many gases approximate ideal behavior under typical conditions of high temperature and low pressure.

Molecular Interactions

Molecular interactions are forces that act between gas particles and can influence their behavior and properties. These interactions are not considered in the ideal gas model but are significant in real gases.

These forces include:

• Van der Waals forces, which are weak attractions between atoms and molecules, and
• ionic or covalent bonds, which are stronger and more specific forces encountered in polar gases.

When gases are cooled to low temperatures, these interactions become more prominent as the molecules lose kinetic energy and move closer together. Similarly, at high pressures, the volume occupied by gas molecules relative to their intermolecular space becomes more considerable, leading to increased interactions.

In terms of practical applications, recognizing and accounting for these forces are it crucial in fields like chemistry and engineering, where accurate predictions of gas behavior are necessary.

Deviations from Ideal Behavior

Deviations from ideal behavior occur when real gases do not follow the Ideal Gas Law due to the presence of intermolecular forces and the finite size of gas particles. More significant deviations are seen under conditions such as low temperatures and high pressures.

High temperatures help mitigate deviations because:

• Increased kinetic energy lessens the impact of intermolecular forces, allowing the gas to behave more ideally.

On the other hand, high pressures force molecules closer, making their actual volume significant relative to the overall volume. Thus, the gas behaves less ideally.

Understanding these deviations helps in practical applications where precise gas behavior predictions are necessary, such as in chemical reactions and industrial processes. By adjusting conditions to high temperatures and low pressures, we can often make gases behave more ideally, simplifying calculations and predictions.