Question

Dichlorodifluoromethane, \(\mathrm{CCl}_{2} \mathrm{~F}_{2}\), one of the chlorofluorocarbon refrigerants responsible for destroying part of the Earth's ozone layer, has \(P_{\text {vap }}=40.0 \mathrm{~mm} \mathrm{Hg}\) at \(-81.6^{\circ} \mathrm{C}\) and \(P_{\mathrm{vap}}=400 \mathrm{~mm} \mathrm{Hg}\) at \(-43.9^{\circ} \mathrm{C}\). What is the normal boiling point of \(\mathrm{CCl}_{2} \mathrm{~F}_{2}\) in \({ }^{\circ} \mathrm{C}\) ?

Short answer

The normal boiling point is approximately -29.8°C.

Step-by-step solution

Understand the Problem

We need to find the normal boiling point of dichlorodifluoromethane, which is the temperature at which the vapor pressure of the liquid equals 1 atm (760 mm Hg).

Use the Clausius-Clapeyron Equation

The Clausius-Clapeyron equation relates the change in vapor pressure with temperature: \[ \ln \left(\frac{P_2}{P_1}\right) = \frac{\Delta H_{\text{vap}}}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right) \] where \(\Delta H_{\text{vap}}\) is the enthalpy of vaporization, \(R\) is the gas constant, and \(T_1\) and \(T_2\) are the absolute temperatures corresponding to \(P_1\) and \(P_2\).

Convert Celsius to Kelvin

Convert the given temperatures in Celsius to Kelvin: \(-81.6^\circ C = 191.55\ K\) and \(-43.9^\circ C = 229.25\ K\).

Calculate Enthalpy of Vaporization

Using the given data, take \(P_1 = 40\ mm\ Hg\), \(T_1 = 191.55\ K\), \(P_2 = 400\ mm\ Hg\), \(T_2 = 229.25\ K\), and solve the Clausius-Clapeyron equation for \(\Delta H_{\text{vap}}\).

Determine Normal Boiling Point

Use the value of \(\Delta H_{\text{vap}}\) to find the temperature \(T_\text{boil}\) when \(P = 760\ mm\ Hg\). This can be done by plugging \(P_1 = 40\ mm\ Hg\), \(T_1 = 191.55\ K\), and \(P_2 = 760\ mm\ Hg\) into the Clausius-Clapeyron equation and solving for \(T_2\).

Convert Result to Celsius

The normal boiling point calculated in Kelvin can be converted back to Celsius to get the final answer by subtracting 273.15 from the Kelvin temperature.

Key concepts

Vapor Pressure

Vapor pressure is an essential concept in understanding the behavior of liquids. It is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. When a liquid is placed in a closed container, molecules from the liquid phase escape into the vapor phase. As more molecules enter the vapor phase, some will return to the liquid phase, eventually reaching a state of dynamic equilibrium. At this point, the pressure exerted by the vapor is called the vapor pressure.

Vapor pressure increases with temperature. This is because a higher temperature provides more kinetic energy to liquid molecules, allowing them to escape into the vapor phase more readily.

• High vapor pressure indicates that a liquid evaporates easily.
• Low vapor pressure suggests that the liquid evaporates slowly.

Understanding vapor pressure is crucial in predicting how substances like dichlorodifluoromethane behave under different conditions, particularly when assessing its boiling point and other thermodynamic properties.

Boiling Point

The boiling point of a substance is the temperature at which its vapor pressure equals the external atmospheric pressure. For most practical purposes, this external pressure is one standard atmosphere (760 mm Hg). At this temperature, bubbles of vapor form within the liquid and rise to the surface, resulting in boiling.

Different substances have varying boiling points due to differences in intermolecular forces. A higher boiling point indicates stronger intermolecular forces that require more energy to overcome. Changes in atmospheric pressure affect the boiling point, with lower pressures leading to lower boiling points.

When calculating the normal boiling point of dichlorodifluoromethane, the requirement is to find the temperature where its vapor pressure is 760 mm Hg, ensuring the vapor pressure equals atmospheric pressure at sea level.

Enthalpy of Vaporization

The enthalpy of vaporization, \( \Delta H_{\text{vap}} \), is a significant property of a substance. It represents the amount of energy required to convert one mole of a liquid at its boiling point into vapor without a change in temperature. This process requires energy to overcome the intermolecular forces that hold the liquid molecules together.

The Clausius-Clapeyron equation is used to determine the enthalpy of vaporization by relating the change in vapor pressure with temperature changes. Understanding this concept helps in explaining why some substances require more energy to vaporize than others.

• High \( \Delta H_{\text{vap}} \) implies strong intermolecular forces.
• Low \( \Delta H_{\text{vap}} \) suggests weaker intermolecular forces.

In exercises involving the Clausius-Clapeyron equation, the enthalpy of vaporization is crucial for calculating changes in vapor pressure over different temperature ranges. This is particularly useful in determining the boiling point and other thermodynamic characteristics of refrigerants like dichlorodifluoromethane.