Problem 33 - General Chemistry

Question

A \(250-\mathrm{g}\) sample of water at \(20.0^{\circ} \mathrm{C}\) is placed in a freezer that is held at a constant temperature of \(-20.0^{\circ} \mathrm{C}\). Considering the water as the "system," answer the following questions: a. what is the sign of \(q_{\text {sys }}\) for the water after it is placed in the freezer? b. After a few hours, what will be the state of the water? c. How will the initial enthalpy for the water compare with the final enthalpy of the water after it has spent several hours in the freezer? d. What will the temperature of the water be after several hours in the freezer?

Step-by-Step Solution

Answer

a. Negative b. Solid (ice) c. Initial enthalpy is greater d. -20.0°C

Step 1: Determine the Sign of q_sys

The sign of \( q_{\text{sys}} \) represents the heat exchange for the system. When the water is placed in the freezer, it loses heat because it is being cooled. Therefore, \( q_{\text{sys}} \) is negative as the system is losing heat energy to the surroundings (the freezer).

Step 2: Predict the State of the Water

Initially, the water is in a liquid state at \( 20.0^{\circ}\, \mathrm{C} \). When placed in the freezer at \( -20.0^{\circ}\, \mathrm{C} \), it will eventually freeze. After a few hours, the water will solidify and become ice as it reaches temperatures below its freezing point.

Step 3: Compare Initial and Final Enthalpy

The initial enthalpy of the water is greater than its final enthalpy. As water cools and eventually freezes, it releases heat to the surroundings, causing a decrease in enthalpy due to phase change from liquid to solid.

Step 4: Determine Final Temperature of the Water

After several hours in the freezer maintained at \( -20.0^{\circ}\, \mathrm{C} \), the water temperature will equilibrate with the freezer's temperature, reaching \( -20.0^{\circ}\, \mathrm{C} \).

Key Concepts

Enthalpy Change

Enthalpy change is a crucial concept in thermodynamics that involves the amount of heat absorbed or released during a process, at constant pressure. When water is placed in a freezer, heat is lost from the system (the water), which means the enthalpy change (\( \Delta H \)) is negative.
Water starts at a higher energy state due to its higher temperature, and as it loses heat to the surroundings, its energy decreases. As a result, the initial enthalpy of liquid water is higher compared to the final enthalpy when the water becomes ice.

• A negative enthalpy change indicates that the process is exothermic, such as freezing or cooling.
• Enthalpy change is an important factor when considering state changes, where the system releases energy.

This concept helps us understand energy transformations in processes like freezing, where the system loses energy to the surroundings.

Phase Change

Phase change refers to the transition between different states of matter, such as solid, liquid, and gas. In this scenario, water undergoes a phase change from liquid to solid as it is cooled in a freezer.
Water begins as a liquid at 20°C and transitions to ice as its temperature drops towards -20°C. This change in state is accompanied by a release of latent heat, which is the energy necessary to change the phase without altering the temperature.

• During freezing, the energy is released to the environment, contributing to the overall temperature decrease.
• Phase changes are critical for understanding how substances behave under varying temperature and pressure conditions.

Understanding phase changes provides insight into natural processes such as water freezing and informs various applications in science and industry.

Heat Transfer

Heat transfer is the movement of thermal energy from one region or substance to another. It is a key concept in thermodynamics, especially when analyzing how substances change temperature or state.
In the exercise, heat transfer occurs primarily from the water to the surrounding air in the freezer. Since the freezer is at -20°C, which is much colder than the starting temperature of the water, heat flows out of the water to equilibrate the temperatures. This transfer continues until the water reaches the freezer's temperature.

• There are three main modes of heat transfer: conduction, convection, and radiation. However, conduction involves direct contact, which is most relevant here as the water and the air are in contact through the container.
• A lower temperature in the surroundings accelerates the heat loss from the water, driving the cooling process efficiently.

Heat transfer explains why the water's temperature drops and eventually equilibrates with the freezer, leading to the water's conversion from liquid to solid.