Question

The fluorocarbon compound \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{~F}_{3}\) has a normal boiling point of \(47.6^{\circ} \mathrm{C}\). The specific heats of \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{~F}_{3}(l)\) and \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{~F}_{3}(g)\) are \(0.91 \mathrm{~J} / \mathrm{g}-\mathrm{K}\) and \(0.67 \mathrm{~J} / \mathrm{g}-\mathrm{K},\) respectively. The heat of vaporization for the compound is \(27.49 \mathrm{~kJ} / \mathrm{mol} .\) Calculate the heat required to convert \(35.0 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{~F}_{3}\) from a liquid at \(10.00^{\circ} \mathrm{C}\) to a gas at \(105.00^{\circ} \mathrm{C}\).

Short answer

The heat required to convert \(35.0 \mathrm{g}\) of \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{F}_{3}\) from a liquid at \(10.00^{\circ} \mathrm{C}\) to a gas at \(105.00^{\circ} \mathrm{C}\) is approximately \(7702.89 \mathrm{J}\).

Step-by-step solution

Heat the liquid from initial temperature to boiling point

To calculate the heat required to heat the liquid from its initial temperature to boiling point, we will use the formula: \(q = mc\Delta T\), where \(q\) is the heat, \(m\) is the mass, \(c\) is the specific heat, and \(\Delta T\) is the change in temperature. Given data: \(m = 35.0 \mathrm{g}\), \(c = 0.91 \mathrm{ J / gK} \), \(\Delta T = T_\mathrm{final} - T_\mathrm{initial} = T_\mathrm{boil} - T_\mathrm{initial} = 47.6^{\circ}\mathrm{C} - 10.00^{\circ}\mathrm{C} = 37.6^{\circ}\mathrm{C}\), We can now calculate the heat required: \(q_1 = (35.0 \mathrm{g}) (0.91 \mathrm{ J / gK}) (37.6\mathrm{K}) = 1209.71 \mathrm{J}\).

Vaporize the liquid at its boiling point

To calculate the heat required to vaporize the liquid, we will use the formula: \(q = n \Delta H_\mathrm{vap}\), where \(n\) is the number of moles, and \(\Delta H_\mathrm{vap}\) is the heat of vaporization. Given data: \(\Delta H_\mathrm{vap} = 27.49 \mathrm{ kJ/mol} \), First, we need to calculate the molar mass of \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{F}_{3}\): Molar mass = (2 × 12.01) + (3 × 35.45) + (3 × 19.00) = 24.02 + 106.35 + 57.00 = 187.37 \(\mathrm{g/mol}\). Now we calculate the number of moles: \(n = \frac{m}{M} = \frac{35.0\mathrm{g}}{187.37\mathrm{g/mol}} = 0.1869\mathrm{mol}\), Finally, we can calculate the heat required to vaporize the liquid: \(q_2 = (0.1869\mathrm{mol}) (27.49 \times 10^3 \mathrm{J/mol}) = 5139.97\mathrm{J}\).

Heat the gas from boiling point to the final temperature

To calculate the heat required to heat the gas from its boiling point to the final temperature, we will use the formula: \(q = mc\Delta T\), where \(q\) is the heat, \(m\) is the mass, \(c\) is the specific heat, and \(\Delta T\) is the change in temperature. Given data: \(m = 35.0 \mathrm{g}\), \(c = 0.67 \mathrm{ J / gK} \), \(\Delta T = T_\mathrm{final} - T_\mathrm{initial} = T_\mathrm{final} - T_\mathrm{boil} = 105.00^{\circ}\mathrm{C} - 47.6^{\circ}\mathrm{C} = 57.4^{\circ}\mathrm{C}\), We can now calculate the heat required: \(q_3 = (35.0 \mathrm{g}) (0.67 \mathrm{ J / gK}) (57.4\mathrm{K}) = 1352.21 \mathrm{J}\).

Calculate the total heat required

To find the total heat required to convert the compound from liquid at \(10.00^{\circ} \mathrm{C}\) to gas at \(105.00^{\circ} \mathrm{C}\), we just add the heat from the previous steps: Total heat (\(q_\mathrm{total}\)) = \(q_1 + q_2 + q_3 = 1209.71\mathrm{J} + 5139.97\mathrm{J} + 1352.21\mathrm{J} = 7702.89\mathrm{J}\). Therefore, the heat required to convert \(35.0 \mathrm{g}\) of \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{F}_{3}\) from a liquid at \(10.00^{\circ} \mathrm{C}\) to a gas at \(105.00^{\circ} \mathrm{C}\) is approximately \(7702.89 \mathrm{J}\).

Key concepts

Heat of Vaporization

The heat of vaporization is a key concept in thermochemistry. It refers to the amount of heat required to convert a given quantity of a liquid into a gas at its boiling point, without a change in temperature.
This value is usually expressed in terms of energy per mole, such as kilojoules per mole (kJ/mol). For the compound \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{F}_{3}\) considered in the exercise, the heat of vaporization is \(27.49\, \mathrm{kJ/mol}\).
In our calculations, we use this to determine the energy needed to change the liquid to its gaseous state. It's crucial to first find out the number of moles of the substance we have. Once we have that, we multiply by the heat of vaporization to find the total energy absorbed during the phase change from liquid to gas.

• The heat of vaporization is specific to each substance, so different substances will require different amounts of energy for vaporization.
• This concept is applicable to various scientific fields, from industrial processes to meteorology.
• It's essential in understanding phenomena like boiling and condensation.

Specific Heat Capacity

Specific heat capacity is a property that describes how much energy is required to change the temperature of 1 gram of a substance by 1 Kelvin (or 1 degree Celsius).
In this exercise, we calculate the energy needed to heat \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{F}_{3}\) in both liquid and gaseous forms. Specifically,\(0.91\, \mathrm{J/g-K}\) for the liquid and \(0.67\, \mathrm{J/g-K}\) for the gas.

• The specific heat capacity allows us to understand how different states (liquid vs. gas) of the same substance require different amounts of energy for the same temperature change.
• In practice, lower specific heat capacities mean less energy is needed to change the temperature.

When performing calculations, we use the formula \(q = mc\Delta T\), where \(m\) represents mass, \(c\) the specific heat capacity, and \(\Delta T\) the change in temperature. This formula is used multiple times in phase change calculations to assess the heat involved in warming substances to their boiling points or cooling them to their freezing points.

Phase Change Calculations

Phase change calculations are an important aspect of thermochemistry, as they allow us to understand the amount of energy required for a substance to change from one state of matter to another, like from liquid to gas.
These calculations are carried out by considering both warming the substance to reach the boiling point and the energy required during the phase change itself.
In the exercise's context, calculating the energy needed involves multiple steps:

• First, calculating the energy required to raise the temperature of the liquid to its boiling point using the specific heat of the liquid.
• Second, determining the energy needed for the actual phase change using the heat of vaporization and the amount in moles.
• Finally, we need to calculate any additional energy required to heat the substance in its gaseous state to the desired temperature using the specific heat of the gas.

This systematic approach ensures all energy changes are accounted for. Correctly setting up these problems requires attention to detail, including correct units and vigilance in following each step.