Problem 44 - Chemistry The Central Science In Si Units

Question

CHClFz is a type of hydrochlorofluorocarbon (HCFC) that has a comparatively lower damaging effect on the ozone layer. It is used as a replacement for chlorofluorocarbons (CFCs). The heat of vaporization is \(233.95 \mathrm{~kJ} / \mathrm{g}\). What mass of this substance must evaporate to freeze \(15 \mathrm{~g}\) of water ini. tially at \(15^{\circ} \mathrm{C} ?\) (The heat of fusion of water is \(334 \mathrm{~J} / \mathrm{g}\); the specific heat of water is \(4.18 \mathrm{~J} / \mathrm{g} \cdot \mathrm{K} .\) )

Step-by-Step Solution

Answer

Approximately 0.0254 grams of CHClFz must evaporate.

Step 1: Calculate the Energy Required to Freeze Water

Firstly, we need to drop the temperature of the water from \(15^{\circ}C\) to \(0^{\circ}C\), and then freeze it. We calculate the energy needed for these two processes starting with cooling the water:\[Q_1 = m \cdot c \cdot \Delta T = 15 \, \text{g} \times 4.18 \, \text{J/g}^\circ\text{C} \times (0 - 15) ^\circ\text{C}\]This results in:\[Q_1 = -15 \, \text{g} \times 4.18 \, \text{J/g}^\circ\text{C} \times 15 ^\circ\text{C} = -942.3 \, \text{J}\]Next, calculate the heat required to freeze the water:\[Q_2 = m \cdot \Delta H_f = 15 \, \text{g} \times 334 \, \text{J/g} = 5010 \, \text{J}\]Total energy \(Q_{\text{total}}\) required is:\[Q_{\text{total}} = |Q_1| + Q_2 = 942.3 \, \text{J} + 5010 \, \text{J} = 5952.3 \, \text{J}\]

Step 2: Convert Total Energy to kJ

Convert the total energy required from joules to kilojoules since the heat of vaporization is given in \(233.95 \, \text{kJ/g}\). \[Q_{\text{total}} = \frac{5952.3 \, \text{J}}{1000} = 5.9523 \, \text{kJ}\]

Step 3: Calculate Mass of CHClFz Required to Evaporate

To find the mass of CHClFz that must evaporate to provide the required energy, we'll use the heat of vaporization:\[Q = m_\text{CHClFz} \cdot \Delta H_\text{vap}\]Solving for the mass \(m_\text{CHClFz}\):\[m_\text{CHClFz} = \frac{Q}{\Delta H_\text{vap}} = \frac{5.9523 \, \text{kJ}}{233.95 \, \text{kJ/g}} \approx 0.0254 \, \text{g}\]

Key Concepts

Enthalpy

Understanding enthalpy is key in exploring many chemical processes, especially those involving energy changes in phase transitions and reactions. Enthalpy is the total heat content of a system, represented as \( H \). It reveals how much heat energy is needed or released during a chemical process.

When a substance changes phase — for example, from a liquid to gas (vaporization) or from liquid to solid (freezing) — energy is either absorbed or released. The enthalpy change, or \( \Delta H \), measures this energy. For instance, during vaporization, a substance absorbs a set amount of energy per unit mass called the "heat of vaporization," while freezing releases energy, termed the "heat of fusion."

In our exercise, we calculate these energy changes to understand the transition from water to ice and how much energy is required for this transformation.

Specific Heat Capacity

The specific heat capacity of a substance is the amount of heat needed to raise the temperature of one gram of the substance by one degree Celsius. For water, this value is \( 4.18 \, \text{J/g} \cdot \text{K} \). This measure is crucial for understanding how substances absorb or release heat.

When you heat or cool water, you calculate the energy change using the equation:

• \( Q = m \cdot c \cdot \Delta T \)

This formula illustrates how the amount of energy \( Q \) needed is proportional to the mass \( m \) of the water, its specific heat \( c \), and the temperature change \( \Delta T \).

In the exercise given, this concept is applied in the first step to determine how much heat energy is needed to cool water from \( 15^{\circ}\)C to \( 0^{\circ}\)C.

Phase Transitions

Phase transitions refer to the changes between different states of matter, such as solid, liquid, and gas. These transitions occur through processes like melting, freezing, vaporization, condensation, sublimation, and deposition.

Each of these changes involves an energy transfer in the form of heat. This is because energy is required to overcome the forces holding molecules together in a given phase, leading to a change in state:

• Freezing: liquid to solid, releasing heat (exothermic).
• Vaporization: liquid to gas, absorbing heat (endothermic).
• Fusion: solid to liquid, absorbing heat (endothermic).

In our exercise, we focus on freezing and vaporization. Freezing releases energy that must be counteracted by the energy absorbed during the vaporization of CHClFz.

Understanding these processes helps predict how substances behave under different thermal conditions, underscoring the crucial role of heat transfer.

Calculations Involving Hydrocarbons

When performing calculations with hydrocarbons, such as CHClFz, the key is to understand both their chemical properties and how they interact with energy changes.

Hydrocarbons are compounds made primarily of hydrogen and carbon. In this exercise, CHClFz acts as a working fluid whereby its heat of vaporization is exploited. By evaporating CHClFz, energy is absorbed. This energy can be used to cause phase transitions in other substances, such as freezing water.

• Calculate total energy needed for a process.
• Convert energy into compatible units to compare with other substances.
• Consider energy transfer in the context of the hydrocarbon's physical properties.

In the solution, the mass of CHClFz that must evaporate to freeze water is determined by aligning its vaporization energy with the energy requirements of the water's phase change. This detailed understanding highlights the central role of hydrocarbons in energy transfer applications.