Problem 77 - Chemistry: An Atoms-Focused Approach

Question

Chlorofluorocarbons (CFCs) are no longer used as refrigerants because they catalyze the decomposition of stratospheric ozone. Trichlorofluoromethane (CC1 \(_{3} \mathrm{F}\) ) boils at \(23.8^{\circ} \mathrm{C}\) and its molar heat of vaporization is \(24.8 \mathrm{kJ} / \mathrm{mol}\) What is the molar entropy of vaporization of \(\mathrm{CCl}_{3} \mathrm{F}(\ell) ?\)

Step-by-Step Solution

Answer

Answer: The molar entropy of vaporization of CCl\(_3\)F(ℓ) is approximately 83.43 J/(mol×K).

Step 1: Convert the boiling point to Kelvin

Given that the boiling point of CCl\(_3\)F is \(23.8^{\circ} \mathrm{C}\), we need to convert this temperature to Kelvin(K) as it is the SI unit of temperature. To do this conversion, we use the following equation: \(Temperature_{(K)} = Temperature_{(°C)} +273.15.\) So, the boiling point in Kelvin is: \(23.8^{\circ} \mathrm{C} + 273.15 = 296.95\mathrm K\)

Step 2: Use the Clapeyron equation

Now we will use the Clapeyron equation to find the molar entropy of vaporization of CCl\(_3\)F(ℓ). The equation is as follows: \(\Delta{S}_{vaporization} = \frac{\Delta{H}_{vaporization}}{Temperature}\) Where, \(\Delta{S}_{vaporization}\) is the molar entropy of vaporization, \(\Delta{H}_{vaporization}\) is the molar heat of vaporization, and \(Temperature\) is the boiling point in Kelvin.

Step 3: Plug in the given values and find the molar entropy of vaporization

We are given the molar heat of vaporization as \(24.8 \mathrm{kJ/mol}\) or \(24800\mathrm{J/mol}\), and we found the boiling point in Kelvin as \(296.95\mathrm K\). Now, we can plug in these values into the Clapeyron equation: \(\Delta{S}_{vaporization} = \frac{24800\mathrm{J/mol}}{296.95\mathrm K}\) \(\Delta{S}_{vaporization} \approx 83.43 \mathrm{J/(mol \times K)}\) So, the molar entropy of vaporization of CCl\(_3\)F(ℓ) is approximately 83.43 J/(mol×K).

Key Concepts

Chlorofluorocarbons and Their Environmental Impact

Chlorofluorocarbons (CFCs), like trichlorofluoromethane (CCl\(_3\)F), have been widely used in the past, primarily as refrigerants and in aerosol propellants. These compounds are organic molecules containing carbon, chlorine, and fluorine atoms. Although they are chemically stable and non-flammable, making them excellent for industrial applications, CFCs have a significant downside.

When released into the atmosphere, CFCs gradually rise into the stratosphere, where they catalyze the breakdown of ozone. The stratospheric ozone layer is crucial as it absorbs the majority of the sun's harmful ultraviolet radiation. This decomposition reduces the ozone layer's effectiveness, leading to environmental issues such as increased UV exposure, which can cause skin cancer and cataracts, and affect ecosystems and wildlife.

Due to these detrimental effects, the use of CFCs has been largely phased out under international agreements like the Montreal Protocol. Current research focuses on finding alternatives that do not harm the ozone layer, such as hydrofluorocarbons (HFCs) which contain no chlorine atoms, thereby reducing the potential for ozone depletion.

Understanding the Clapeyron Equation

The Clapeyron equation is a fundamental principle used in thermodynamics to relate different properties of a system undergoing phase transformations, such as the transition from liquid to vapor. This equation is especially useful in calculating the molar entropy of vaporization, which is a measure of the disorder or randomness added to a system when a liquid turns into a gas.

The Clapeyron equation is given by:

• \[ \Delta{S}_{vaporization} = \frac{\Delta{H}_{vaporization}}{Temperature} \]

This formula shows the relationship between the molar heat of vaporization \( \Delta{H}_{vaporization} \), which is the energy needed to vaporize one mole of a substance, and the temperature in Kelvin at which this phase change occurs.

The outcome, \( \Delta{S}_{vaporization} \), represents the molar entropy change during vaporization, indicating how much more disordered the gaseous state is compared to the liquid state. Calculations use this equation to determine important thermodynamic properties in systems including engineering applications and natural phenomena.

Conversion to Kelvin in Thermodynamic Calculations

In thermodynamics, temperature is a critical variable. However, precise scientific calculations often require the temperature to be in Kelvin, the SI unit of temperature. This unit starts from absolute zero, where all molecular motion theoretically ceases, making it convenient for formulas that involve energy and entropy, like the Clapeyron equation.

To convert temperature from Celsius to Kelvin, a straightforward formula is used:

• \[ Temperature_{(K)} = Temperature_{(°C)} + 273.15 \]

This conversion is essential because many equations, including the Clapeyron equation, rely on absolute temperatures to ensure accuracy and consistency in calculations. By converting to Kelvin, it’s possible to maintain uniformity across scientific research and practical applications, leading to more reliable results.

Understanding this conversion is foundational for students and professionals working in chemistry, physics, and engineering fields. It exemplifies the importance of standard units in scientific methodologies to ensure clear communication and comparison of data across studies and languages.