Question

Read the assertion and reason carefully to mark the correct option out of the option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the reason. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. (e) If assertion is false but reason is true. Assertion: The molecules of $0^{\circ }\mathrm{C}$ ice and $0^{\circ }\mathrm{C}$ water will have same potential energy. Reason: Potential energy depends only on temperature of the system. (A) a (B) $b$ (C) $\mathrm{c}$ (D) d (E) e

Short answer

The short answer is: Option (D) is correct, as both the assertion and reason are false. The assertion is false because the potential energy of molecules in ice and liquid water at $0^{\circ }\mathrm{C}$ is not the same, and the given reason is false as the potential energy depends on factors other than just temperature.

Step-by-step solution

Understand the assertion

The given assertion states that "The molecules of $0^{\circ }\mathrm{C}$ ice and $0^{\circ }\mathrm{C}$ water will have the same potential energy." We need to determine if this assertion is true or false.

Understand the reason

The given reason is that "Potential energy depends only on the temperature of the system." We need to determine if this reason is true or false and if it provides the correct explanation for the assertion.

Evaluate the assertion

The assertion is false. Although the ice and water might have the same temperature, the potential energy of their molecules is not the same. In ice, the water molecules are held together in a rigid lattice structure, and a certain amount of energy is required to break these bonds and change the state from solid to liquid. This implies that the potential energy of the molecules in ice is higher than that of liquid water at the same temperature.

Evaluate the reason

The given reason is also false. Though temperature is directly related to the kinetic energy of the molecules in a system, potential energy is a result of the interaction between molecules in the given substance. Factors responsible for varying potential energy can include state of matter, presence of strong/weak intermolecular forces, and other factors not correlated to temperature.

Choose the correct option

Since the assertion is false and the reason is also false, the correct option is (D): "If the assertion and reason both are false."

Key concepts

Potential Energy

Potential energy is an important concept in understanding how molecules interact with each other. It refers to the energy that is stored within a system due to its position or configuration. In the context of molecules, potential energy is primarily influenced by the interactions between molecules, such as the forces holding them in place in a solid structure. The potential energy can be higher or lower depending on the arrangement of the molecules:

• In solids, molecules are closely packed in a fixed structure, which often means higher potential energy due to the strong intermolecular forces keeping them in place.
• In liquids and gases, molecules have more freedom to move, typically resulting in lower potential energy compared to solids at the same temperature.

This difference in potential energy is why materials change states, such as when ice (solid) melts into water (liquid). In this process, energy is required to break the rigid lattice of the ice, indicating higher potential energy before melting.

Temperature and Phase Transition

Understanding how temperature affects phase transitions helps explain the movement and behavior of molecules as they change state. Temperature is a measure of the average kinetic energy of the molecules within a system. When the temperature changes, it can lead to a phase transition, such as:

• Melting, where a solid becomes a liquid.
• Freezing, which is the reverse process.
• Vaporization, where a liquid turns into a gas.
• Condensation, where gas changes back into a liquid.

During a phase transition, the temperature of a substance remains constant until the entire material has changed state. This constancy occurs because energy is used to alter the potential energy of the molecules, rather than the kinetic energy, highlighting the intricate balance between kinetic and potential energy in these processes.

Intermolecular Forces

Intermolecular forces are the forces that act between molecules, playing a crucial role in determining the physical properties of substances, such as their state at a given temperature. These include forces such as:

• Van der Waals forces, which are weak and act between different molecules.
• Hydrogen bonds, which are stronger and occur when hydrogen is attracted to electronegative atoms like oxygen.
• Dipole-dipole interactions, which occur between polar molecules.

The strength of these intermolecular forces largely determines the state (solid, liquid, or gas) of a substance at a particular temperature. For instance, ice is solid at 0°C due to hydrogen bonds holding the water molecules in a structured, rigid lattice. Breaking these intermolecular forces requires energy, highlighting the relationship between potential energy and intermolecular forces.

State of Matter

The state of matter of a substance—be it solid, liquid, or gas—depends significantly on temperature and pressure, as well as the strength of intermolecular forces. In solids, molecules are tightly packed in a fixed arrangement, while in liquids, they are loosely arranged, allowing them to flow freely over one another. In gases, molecules are far apart and move independently:

• Solids have the highest potential energy and associated intermolecular forces for a given temperature compared to liquids and gases.
• Liquids have enough energy to overcome some intermolecular forces, allowing them to flow but not expand significantly.
• Gases exhibit minimal intermolecular interactions, enabling expansion to fill available space.

Understanding the state of matter is essential when evaluating molecular potential energy and the effects of temperature changes.

Kinetic vs Potential Energy

Kinetic and potential energy are two forms of energy that, when combined, describe the total energy of a system. Kinetic energy is energy of motion, and it increases with temperature as molecule movement intensifies. Potential energy, however, is stored energy derived from molecular interactions:

• Kinetic energy depends directly on temperature—higher temperatures correspond to increased kinetic energy.
• Potential energy is more affected by molecular arrangement and interactions, such as the formation or breaking of bonds.

In systems with phase changes, such as melting ice, the kinetic energy remains stable while potential energy changes significantly. This distinction underpins why the assertion in the exercise is false; even at the same temperature, different states (ice vs. water) involve varied potential energies due to different molecular structures and interactions.