Problem 44 - Chemistry: The Central Science in SI Units, Global Edition

Question

\(\mathrm{CHClF}_{2}\) 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 initially 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 \(0.0254\mathrm{~g}\) of \(\mathrm{CHClF}_{2}\) must evaporate to freeze \(15\mathrm{~g}\) of water initially at \(15^{\circ}\mathrm{C}\).

Step 1: Calculate the energy required to cool down the water

To calculate the energy required to cool down the water, we will use the formula: \(Q = mc\Delta T,\) where \(Q\) is the energy required, \(m\) is the mass of the object, \(c\) is the specific heat of the object, and \(\Delta T\) is the change in temperature. In this case, the mass of water is \(15\mathrm{~g}\), the specific heat of water is \(4.18\mathrm{~J/g\cdot K}\), and the change in temperature is from \(15^{\circ}\mathrm{C}\) to \(0^{\circ}\mathrm{C}\), which is a change of \(-15\mathrm{~K}\). So, \(Q_1 = (15\mathrm{~g})(4.18\mathrm{~J/g\cdot K})(-15\mathrm{~K}) = -942.9\mathrm{~J}\). Since we are only interested in the amount of energy required, we will use the absolute value: \(Q_1=942.9\mathrm{~J}\).

Step 2: Calculate the energy required to freeze the water

To calculate the energy required to freeze the water, we will use the heat of fusion formula: \(Q = mL,\) where \(Q\) is the energy required, \(m\) is the mass of the object, and \(L\) is the heat of fusion of the object. In this case, the mass of water is \(15\mathrm{~g}\), and the heat of fusion of water is \(334\mathrm{~J/g}\). So, \(Q_2 = (15\mathrm{~g})(334\mathrm{~J/g}) = 5010\mathrm{~J}\).

Step 3: Find the total energy required

To find the total energy required, we will add the energies found in steps 1 and 2: \(Q_\mathrm{total} = Q_1 + Q_2 = 942.9\mathrm{~J} + 5010\mathrm{~J} = 5952.9\mathrm{~J}\).

Step 4: Calculate the mass of \(\mathrm{CHClF}_{2}\) needed

To calculate the mass of \(\mathrm{CHClF}_{2}\) needed to provide the required energy by evaporating, we will use the formula: \(m_\mathrm{CHClF_{2}} = \frac{Q_\mathrm{total}}{L_\mathrm{CHClF_{2}}}\), where \(m_\mathrm{CHClF_{2}}\) is the mass of \(\mathrm{CHClF}_{2}\) required, \(Q_\mathrm{total}\) is the total energy required, and \(L_\mathrm{CHClF_{2}}\) is the heat of vaporization of \(\mathrm{CHClF}_{2}\). The heat of vaporization of \(\mathrm{CHClF}_{2}\) is given as \(233.95\mathrm{~kJ/g}\), which is equal to \(233,950\mathrm{~J/g}\). So, \(m_\mathrm{CHClF_{2}} = \frac{5952.9\mathrm{~J}}{233,950\mathrm{~J/g}} = 0.0254\mathrm{~g}\). So, approximately \(0.0254\mathrm{~g}\) of \(\mathrm{CHClF}_{2}\) must evaporate to freeze \(15\mathrm{~g}\) of water initially at \(15^{\circ}\mathrm{C}\).

Key Concepts

Heat of Vaporization

When we talk about the heat of vaporization, we are referring to the amount of energy needed to turn a substance from a liquid into a gas. This energy must be absorbed by the substance in order to break the intermolecular forces that hold the molecules together in the liquid state.
For instance, in our exercise, \( \mathrm{CHClF}_{2} \) has a substantial heat of vaporization of \( 233.95 \, \mathrm{kJ} / \mathrm{g} \). It means that to vaporize even a small amount of this chemical, a large amount of energy input is needed because of the strong intermolecular forces present.
This property is critical in refrigeration and air conditioning, where these and similar substances are used. It facilitates the absorption of heat from the surrounding environment or items you wish to cool down.

• Heat of vaporization is vital for processes where heat transfer takes place through phase changes.
• It influences how much of a substance must evaporate to achieve a desired temperature change in another material, like water in this case.

Heat of Fusion

Heat of fusion refers to the amount of energy needed to change a substance from a solid to a liquid at its melting point. When ice melts into water, or, as in the exercise, water freezes into ice, the energy associated with the process is linked to the heat of fusion.
For water, the heat of fusion is \( 334 \, \mathrm{J/g} \), which means that for each gram of water that transitions phase at this temperature, 334 Joules of energy are required or released, depending on the direction of the phase change.
In our problem, the energy required to freeze the water is calculated using this property. This process is important in understanding how much energy a phase change will consume or release, affecting energy budgets in thermal management systems.

• Heat of fusion is crucial when calculating energy exchanges in processes involving melting or freezing.
• It shows how robust water's phase change properties are, needing significant energy compared to many other substances.

Specific Heat Capacity

Specific heat capacity is a measure of how much energy is needed to change the temperature of a unit mass of a substance by one degree Celsius. In this exercise, we see that the specific heat of water is \( 4.18 \, \mathrm{J/g \, \cdot \, K} \).
This tells us that water requires relatively high energy to change its temperature, making it an excellent solvent and temperature buffer in biochemical and environmental settings.
During the cooling of water from \( 15^{\circ} \mathrm{C} \) to \( 0^{\circ} \mathrm{C} \), understanding and applying the specific heat capacity helps us to calculate accurately how much total energy will be needed or given off during temperature changes.

• Specific heat capacity is a key thermal property that dictates how substances heat up or cool down.
• It has implications on climate, cooking, and any operations involving thermal energy transfer.

Hydrochlorofluorocarbons (HCFCs)

Hydrochlorofluorocarbons, or HCFCs, like \( \mathrm{CHClF}_{2} \), were developed as alternatives to the more harmful chlorofluorocarbons (CFCs). While HCFCs still pose some risk to the ozone layer, they are much less destructive compared to CFCs.
HCFCs have been largely used in refrigeration and air conditioning systems because of their effective thermal properties, such as a high heat of vaporization which makes them suitable for heat transfer processes.
Additionally, multiple international agreements, such as the Montreal Protocol, have been focusing on phasing them out due to their ozone-depleting nature. Their replacements include more environmentally friendly compounds.

• HCFCs helped transition industries from more detrimental CFCs to less harmful alternatives.
• The environmental impact is a significant consideration, with ongoing global efforts to find even safer refrigerants.