Question

Compounds like \(\mathrm{CCl}_{2} \mathrm{~F}_{2}\) are known as chlorofluorocarbons, or CFCs. These compounds were once widely used as refrigerants but are now being replaced by compounds that are believed to be less harmful to the environment. The heat of vaporization of \(\mathrm{CCl}_{2} \mathrm{~F}_{2}\) is \(289 \mathrm{~J} / \mathrm{g}\). What mass of this substance must evaporate to freeze \(200 \mathrm{~g}\) 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 \(4.18 \mathrm{~J} / \mathrm{g}-\mathrm{K}\).)

Short answer

Approximately 187.75 grams of CCl2F2 must evaporate to freeze 200 grams of water initially at 15ºC.

Step-by-step solution

Calculate the heat to cool the water to 0ºC

We can use the specific heat formula to find the heat required to cool the water to 0ºC: Q = mcΔT where Q is the heat, m is the mass of the water (200g), c is the specific heat of the water (4.18 J/g-K), and ΔT is the temperature change (0ºC - 15ºC). Q = (200 g)(4.18 J/g-K)(-15 K) Q = -12540 J

Calculate the heat to freeze the water at 0ºC

We can use the heat of fusion formula to find the heat required to freeze the water at 0ºC: Q = mLf where m is the mass of the water (200g) and Lf is the heat of fusion for water (334 J/g). Q = (200 g)(334 J/g) Q = 66800 J

Sum the heat required in both steps

Now, we sum the heat required to cool the water and the heat required to freeze it: Total heat (Q_total) = Q1 + Q2 = -12540 J + 66800 J = 54260 J

Calculate the mass of CCl2F2 that must evaporate to absorb the total heat

Finally, we can find the mass of CCl2F2 that must evaporate by using the heat of vaporization formula: Q = mLv where m is the mass of the CCl2F2 we need to find, and Lv is the heat of vaporization for CCl2F2 (289 J/g). 54260 J = m(289 J/g) To find the mass of CCl2F2, we can rearrange the equation and solve for m: m = 54260 J / 289 J/g m ≈ 187.75 g So, approximately 187.75 grams of CCl2F2 must evaporate to freeze 200 grams of water initially at 15ºC.

Key concepts

Chlorofluorocarbons

Chlorofluorocarbons, or CFCs, are a group of organic compounds that contain carbon, chlorine, and fluorine atoms. These compounds are notably used in refrigeration, air conditioning, and as propellants in aerosol sprays in the past. However, CFCs have been found to contribute significantly to ozone layer depletion, a crucial component of the Earth's atmosphere that protects living organisms from harmful ultraviolet radiation.
Environmental concerns have led to regulations phasing out the use of CFCs. Alternatives, such as hydrochlorofluorocarbons (HCFCs) and hydrofluorocarbons (HFCs), which are less ozone-depleting, are now replacing CFCs.
Understanding the environmental impact of these compounds is essential for making responsible choices in chemical manufacturing and usage. Initiatives and international agreements, like the Montreal Protocol, have been instrumental in addressing the harmful effects of CFCs on the ozone layer.

Heat of Vaporization

When a substance changes from liquid to gas, it absorbs a precise amount of heat energy without changing its temperature. This energy is called the heat of vaporization. It is crucial in processes where energy transfers during phase changes, like in refrigeration cycles.
For chlorofluorocarbon \(\text{CCl}_2\text{F}_2\), the heat of vaporization is given as 289 J/g. This means that every gram of this substance requires 289 joules of energy to convert from liquid to gas at its boiling point.
For practical applications, knowing the heat of vaporization helps in calculating the energy required for processes involving evaporation. For example, in the exercise, it helps determine how much \(\text{CCl}_2\text{F}_2\) must evaporate to absorb enough heat to freeze water.

Heat of Fusion

The heat of fusion is the amount of energy necessary to change a substance from solid to liquid at its melting point. For ice, specifically, it indicates the energy required to melt ice into water at 0°C.
In this problem, the heat of fusion for water is given as 334 J/g. It tells us that 334 joules are needed for each gram of ice to melt. Similarly, when freezing water, the same amount of energy must be released.
Understanding the heat of fusion is important for calculating the energy involved in phase transitions. In our example, it ensures accurate calculations of how much energy is required to freeze 200 grams of water starting at 15ºC. This calculation is necessary to determine how much \(\text{CCl}_2\text{F}_2\) needs to evaporate.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius or Kelvin. It is a property unique to each material and is crucial in thermodynamic calculations.
The specific heat capacity of water is 4.18 J/g-K, indicating that raising one gram of water by 1ºC requires 4.18 joules of energy. This property is essential in understanding how materials react to heat changes.
In this exercise, the specific heat capacity helps calculate the energy removed from water as it cools from 15ºC to 0ºC. Understanding this concept allows for accurate determination of total energy involved in cooling and freezing processes, key for deciding how much \(\text{CCl}_2\text{F}_2\) must evaporate to facilitate these changes.