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 274.53 g of \(\mathrm{CCl}_{2}\mathrm{F}_{2}\) must evaporate to freeze the 200 g of water initially at 15°C.

Step-by-step solution

Calculate the energy needed to decrease the temperature of water

First, let's calculate the amount of energy required to bring the water's temperature down from 15°C to 0°C. We'll use the formula: Energy (Q) = mass (m) × specific heat capacity (c) × temperature change (ΔT) Given: Mass (m) = 200 g Specific heat capacity (c) = 4.18 J/g·K Initial temperature (T₁) = 15°C Final temperature (T₂) = 0°C Temperature change (ΔT) = T₂ - T₁ = 0°C - 15°C = -15°C Now, using the formula: Q = m × c × ΔT Q = 200 g × 4.18 J/g·K × (-15 K) Q = -12540 J Since energy is being released, we will take the absolute value of Q as the required energy. So, Q = 12540 J.

Calculate the energy needed to freeze water at 0°C

Now, let's calculate the amount of energy required to freeze the 200 g of water at 0°C. We'll use the formula: Energy (Q) = mass (m) × heat of fusion (L) Given: Mass (m) = 200 g Heat of fusion (L) = 334 J/g Using the formula: Q = m × L Q = 200 g × 334 J/g Q = 66800 J

Calculate the total energy needed

To determine the total energy required, we add the energy from step 1 and step 2: Total energy = Energy to decrease temperature + Energy to freeze water Total energy = 12540 J + 66800 J Total energy = 79340 J

Find the mass of the CFC needed

Now, we need to find the mass of the \(\mathrm{CCl}_{2}\mathrm{~F}_{2}\) that needs to evaporate to provide this total energy. We'll use the formula: Energy (Q) = mass (m) × heat of vaporization (L) Given: Total energy (Q) = 79340 J Heat of vaporization (L) = 289 J/g Rearrange the formula to solve for mass (m): m = Q / L Substitute the values and solve: m = 79340 J / 289 J/g m ≈ 274.53 g So, approximately 274.53 g of \(\mathrm{CCl}_{2}\mathrm{~F}_{2}\) must evaporate to freeze the 200 g of water initially at 15°C.

Key concepts

Heat of Vaporization

Heat of vaporization is the amount of energy required to convert a substance from its liquid phase to its gaseous phase without changing its temperature. It's a critical concept in thermodynamics and has practical implications in various industries, including refrigeration, where substances like chlorofluorocarbons (CFCs) are used.

Understanding the heat of vaporization helps us calculate the energy needed for phase transitions, which can be particularly important when designing systems that rely on heat exchange. For example, when a substance like CFC evaporates, it absorbs energy from its surroundings, resulting in a cooling effect. This property made CFCs popular as refrigerants before their environmental impact was fully understood.

Specific Heat Capacity

Specific heat capacity is a measure of the amount of heat needed to raise the temperature of one gram of a substance by one degree Celsius. It reflects how much energy a substance can store, making it a fundamental concept in studying and predicting temperature changes within chemical systems like the environment or industrial processes.

In our exercise, specific heat capacity allows us to calculate the energy required to change the temperature of water before its phase transition to ice. This value can vary widely among different substances, which is why water, with a relatively high specific heat capacity, is invaluable for moderating Earth's climate by absorbing and releasing heat slowly.

Heat of Fusion

The heat of fusion is the energy needed to change a substance from solid to liquid, or vice versa, at a constant temperature, typically the substance's melting or freezing point. It is an intrinsic property that is key to understanding phase changes.

This concept is applied in calculating the amount of energy needed to freeze water in the given problem. The heat of fusion of water is relatively high—334 J/g—indicating the strong hydrogen bonds that need to be overcome to change water's phase. This property has environmental implications, too, since the melting and freezing of ice masses affect sea levels and climate patterns.

Thermodynamics in Chemistry

Thermodynamics is the branch of physical science that deals with the relations between heat and other forms of energy. In chemistry, it helps explain how energy is transferred in chemical reactions and physical changes of state, providing insights into reaction spontaneity, equilibrium, and efficiency.

Our exercise incorporates thermodynamics principles to understand how energy is exchanged during the cooling and freezing of water and how the energy needed for these processes can be supplied by the vaporization of CFCs. Applying thermodynamics can help us design more energy-efficient systems and understand environmental processes.

Environmental Chemistry

Environmental chemistry focuses on the chemical processes occurring in the environment and the effects of human activities on these processes. One aspect looks at compounds like CFCs and their impact. While useful as refrigerants due to their heat of vaporization properties, CFCs deplete the ozone layer and contribute to greenhouse gas accumulation.

This field helps us assess the risks and benefits of chemicals, leading to better regulations and alternatives that minimize environmental harm, such as replacing CFCs with less-harmful substances. Understanding environmental chemistry is vital for developing strategies to protect our planet's air, water, and soil from pollution.