Problem 97 - Chemistry The Molecular Science

Question

The chlorofluorocarbon \(\mathrm{CCl}_{2} \mathrm{~F}_{2}\) was once used in air conditioners as the heat transfer fluid. Its normal boiling point is \(-30^{\circ} \mathrm{C}\), and its vaporization enthalpy is \(165 \mathrm{~J} \mathrm{~g}^{-1}\). The gas and the liquid have specific heat capacities of \(0.61 \mathrm{~J} \mathrm{~g}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) and \(0.97 \mathrm{~J} \mathrm{~g}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) respectively. Calculate the heat energy transfer when \(10.0 \mathrm{~g} \mathrm{CCl}_{2} \mathrm{~F}_{2}\) is cooled from \(40^{\circ} \mathrm{C}\) to \(-40^{\circ} \mathrm{C}\).

Step-by-Step Solution

Answer

The heat energy transfer is \(-2174 \text{ J}\).

Step 1: Calculating Heat to Cool Gas to Boiling Point

First, we need to cool the gas from its initial temperature of \(40^\circ C\) to its boiling point at \(-30^\circ C\). We use the formula for heat transfer \( q = mc\Delta T \), where \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.\[q_1 = (10.0 \text{ g})(0.61 \text{ J} \; \text{g}^{-1}\; ^\circ \text{C}^{-1})(-30 - 40)^\circ C = -427 \text{ J}\]

Step 2: Calculating Heat for Phase Change at Boiling Point

Next, we calculate the heat energy required to convert \( CCl_2 F_2 \) from gas to liquid at \(-30^\circ C\). This involves a phase change, so we use the enthalpy of vaporization (which is the same for condensation):\[q_2 = (10.0 \text{ g})(165 \text{ J} \; g^{-1}) = -1650 \text{ J}\]The negative sign indicates that heat is released during condensation.

Step 3: Calculating Heat to Cool Liquid to Final Temperature

Now, cool the liquid from the boiling point \(-30^\circ C\) to \(-40^\circ C\) using the formula for heat transfer:\[q_3 = (10.0 \text{ g})(0.97 \text{ J} \; \text{g}^{-1} \; ^\circ \text{C}^{-1})(-40 - (-30))^\circ C = -97 \text{ J}\]

Step 4: Adding Up Heat Transfers

Add the heat changes from each step to find the total heat energy transfer for the entire process:\[q_{\text{total}} = q_1 + q_2 + q_3 = -427 \text{ J} - 1650 \text{ J} - 97 \text{ J} = -2174 \text{ J}\]

Step 5: Conclusion

The total heat energy transfer when \( 10.0 \text{ g} \) of \( CCl_2 F_2 \) is cooled from \( 40^\circ C \) to \(-40^\circ C\) is \(-2174 \text{ J}\).

Key Concepts

Heat Transfer

Heat transfer is essential in understanding how energy moves from one substance to another. In this problem, we are dealing with the Chlorofluorocarbon (CFC) \((CCl_2 F_2)\), which was historically used in air conditioning systems. The process described involves removing heat from the CFC, cooling it down through different stages.
To calculate heat transfer, we use the equation: \[ q = mc\Delta T \] where:

• \(q\) represents the heat energy transferred,
• \(m\) is the mass of the substance,
• \(c\) is the specific heat capacity, and
• \(\Delta T\) is the change in temperature.

Each stage of the cooling process requires us to calculate the heat transferred as the CFC changes temperatures. This provides insights into how much energy is required to lower the temperature of a substance across different phases. It highlights the idea that heat is either absorbed or released, depending on the direction of the temperature change.

Phase Change

A phase change occurs when a substance changes from one state of matter to another, such as from gas to liquid. This involves breaking or forming intermolecular bonds rather than changing a substance’s temperature. In this problem, the CFC has to go through a phase change from gas to liquid.When a phase change takes place at the substance's boiling or melting point, it involves what we call latent heat. The latent heat of vaporization (or condensation when going from gas to liquid) describes the energy required per unit mass to change the substance's phase without altering its temperature. For \(CCl_2 F_2\), the latent heat is given as \165 \, ext{J} \, ext{g}^{-1}\. This means each gram of the compound releases 165 joules of energy during condensation. This energy removal at the boiling point represents a crucial step in the cooling process.Understanding phase changes helps us grasp how energy dynamics differ when substances transition between distinct phases compared to simple heating or cooling.

Specific Heat Capacity

Specific heat capacity represents the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius. It’s a material-specific property and varies with physical state (solid, liquid, gas). In this exercise, \(CCl_2 F_2\) has different specific heat capacities in its gaseous and liquid forms.

• For the gaseous form of \(CCl_2 F_2\), the specific heat capacity is given as \0.61 \, ext{J} \, ext{g}^{-1} \, ^ ext{°C}^{-1}\. This indicates how much energy is needed to decrease the temperature of the gas by a certain amount.
• For the liquid form, the specific heat capacity is \0.97 \, ext{J} \, ext{g}^{-1} \, ^ ext{°C}^{-1}\, which means it takes slightly more energy to change the temperature of the liquid compared to the gas.

The specific heat capacity helps us quantify how a given mass of \(CCl_2 F_2\) will respond to the absorption or release of heat. It is an essential factor in calculating the total energy change when altering the temperature of the substance in different phases. This information provides a clearer picture of the substance's thermal properties and its efficiency in heat transfer applications.