Problem 40 - Chemistry and Chemical Reactivity

Question

If your air conditioner is more than several years old, it may use the chlorofluorocarbon \(\mathrm{CCl}_{2} \mathrm{F}_{2}\) as the heat transfer fluid. The normal boiling point of \(\mathrm{CCl}_{2} \mathrm{F}_{2}\) is \(-29.8^{\circ} \mathrm{C},\) and the enthalpy of vaporization is \(20.11 \mathrm{kJ} / \mathrm{mol} .\) The gas and the liquid have molar heat capacities of \(117.2 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K}\) and \(72.3 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K},\) respectively. How much energy is evolved as heat when \(20.0 \mathrm{g}\) of \(\mathrm{CCl}_{2} \mathrm{F}_{2}\) is cooled from \(+40^{\circ} \mathrm{C}\) to \(-40^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

1858.54 J of heat is evolved when cooling 20.0 g of CCl2F2 from +40°C to -40°C.

Step 1: Calculate the Moles of CCl2F2

To find the total energy evolved, we need to know how many moles of \(\mathrm{CCl}_{2}\mathrm{F}_{2}\) we're dealing with. The molar mass of \(\mathrm{CCl}_{2}\mathrm{F}_{2}\) is \(12.01 + 2 \times 35.45 + 2 \times 19.00 = 120.91 \ \mathrm{g/mol}\). For \(20.0 \ \mathrm{g} \) of \(\mathrm{CCl}_{2}\mathrm{F}_{2}\):\[n = \frac{20.0\ \mathrm{g}}{120.91\ \mathrm{g/mol}} = 0.1655\ \mathrm{mol}.\]

Step 2: Calculate Heat Released on Cooling Gas from 40°C to -29.8°C

The heat released when cooling the gas from \(40\degree\mathrm{C}\) to its boiling point at \(-29.8\degree\mathrm{C}\) is calculated using \(q = nC\Delta T\). The change in temperature, \(\Delta T\), is \(-29.8 - 40 = -69.8\degree\mathrm{C}\). The molar heat capacity \(C\) is \(117.2 \ \mathrm{J/mol \cdot K}\).\[q = 0.1655\ \, \mathrm{mol} \times 117.2\ \, \mathrm{J/mol \cdot K} \times ( -69.8\, \mathrm{K}) = -1349.33\ \mathrm{J}.\]

Step 3: Calculate Heat Released on Condensation

When \(\mathrm{CCl}_{2}\mathrm{F}_{2}\) condenses from gas to liquid at its boiling point, it releases energy equal to its enthalpy of vaporization. This is calculated as \(q = n\Delta H_\mathrm{vap}\), where \(\Delta H_\mathrm{vap} = 20.11\ \mathrm{kJ/mol}\).\[q = 0.1655\ \, \mathrm{mol} \times 20.11\ \, \mathrm{kJ/mol} = 3.33\ \mathrm{kJ} = 3330\ \mathrm{J}.\]

Step 4: Calculate Heat Released on Cooling Liquid from -29.8°C to -40°C

The liquid \(\mathrm{CCl}_{2}\mathrm{F}_{2}\) needs to be cooled further from \(-29.8 \degree\mathrm{C}\) to \(-40\degree\mathrm{C}\). Use \(q = nC\Delta T\), where \(C\) for liquid is \(72.3 \ \mathrm{J/mol \cdot K}\). \(\Delta T = -40 + 29.8 = -10.2\degree\mathrm{C}\).\[q = 0.1655\ \, \mathrm{mol} \times 72.3\, \mathrm{J/mol \cdot K} \times (-10.2\, \mathrm{K}) = -122.13\ \mathrm{J}.\]

Step 5: Total Heat Evolved

Sum the energy changes from each step to find the total heat evolved: \[q_\text{total} = (-1349.33 \ \mathrm{J}) + (3330 \ \mathrm{J}) + (-122.13 \ \mathrm{J}) = 1858.54\ \mathrm{J}.\] Therefore, approximately \(1858.54\ \mathrm{J}\) of energy is evolved as heat.

Key Concepts

Enthalpy of Vaporization

Enthalpy of Vaporization is a critical concept in thermodynamics. It refers to the amount of energy required to convert a liquid into vapor at its boiling point without changing its temperature. This energy is absorbed during vaporization and released during condensation.
For substances like chlorofluorocarbon (CCl₂F₂), which is used in older air conditioners, the enthalpy of vaporization is crucial in the phase change process. Knowing this value, which is 20.11 kJ/mol for CCl₂F₂, helps determine how much energy is involved during condensation or vaporization.
Understanding enthalpy of vaporization can aid in predicting energy requirements and efficiency of processes involving phase changes, particularly in heating and cooling systems.

Heat Capacity

Heat Capacity is an essential property of substances that describes how much heat a substance can hold. It is the amount of energy needed to change the temperature of one mole of a substance by one Kelvin.
In our exercise, both the gas and liquid forms of CCl₂F₂ have different heat capacities. The gas has a higher capacity ( 117.2 J/mol·K), meaning it requires more energy to change its temperature compared to the liquid ( 72.3 J/mol·K).
Understanding heat capacity is crucial when calculating the energy changes as a substance cools or heats during a phase change. It allows us to predict how substances will behave energetically when subjected to temperature changes.

Phase Change

A Phase Change is the process of transitioning between solid, liquid, and gas states. The most common phase changes are melting, freezing, vaporization, condensation, sublimation, and deposition.
In the scenario provided, CCl₂F₂ undergoes a phase change from gas to liquid at its boiling point of -29.8°C. During this phase change, energy is released as heat due to the enthalpy of vaporization.

• Vaporization: liquid to gas, requires energy
• Condensation: gas to liquid, releases energy

Recognizing these phase changes is key in understanding how energy is absorbed or released, which is directly related to the enthalpy changes during these transitions.

Energy Calculations

Energy Calculations involve determining the heat energy absorbed or released during chemical processes, such as phase changes and temperature alterations.
In the provided exercise, the energy evolved when 20.0 g of CCl₂F₂ is cooled involves several steps:

• Calculate moles of CCl₂F₂ using its molar mass.
• Compute heat released when cooling from one temperature to another based on heat capacity and temperature difference.
• Account for energy released during phase change (condensation).
• Add all energy changes to find total heat evolved.

These calculations show how much energy is involved in cooling CCl₂F₂ from a higher to a lower temperature, including both gaseous movement and phase change. Mastering these calculations equips one with the ability to assess energy efficiency in thermal systems.