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 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 total heat required to convert 35.0 grams of $C_{2}C{l}_3{F}_3$ from a liquid at 10.00 °C to a gas at 105.00 °C can be found by calculating the heat required for three separate processes: heating the liquid, vaporizing the liquid, and heating the gas. Using the given information, we calculate the heat required for each step: 1. Heating the liquid: $q_1=35.0g\times 0.91\frac{J}{g-K}\times 37.6K$ 2. Vaporizing the liquid: $q_2=n\times 27490\frac{J}{mol}$, where $n=\frac{35.0g}{187.39g/mol}$ 3. Heating the gas: $q_3=35.0g\times 0.67\frac{J}{g-K}\times 57.4K$ Finally, the total heat required is the sum of these three values: $q_{\text{total}}=q_1+q_2+q_3$.

Step-by-step solution

Calculate the heat required to heat the liquid

First, we need to find the heat required to heat the liquid from 10 °C to its boiling point of 47.6 °C. We use the formula: $q=m\times c\times \mathrm{\Delta }T$ Where: - $q$ is the heat (in J), - $m$ is the mass (in g), - $c$ is the specific heat capacity (in J/g-K), and - $\mathrm{\Delta }T$ is the change in temperature (in K or °C, as this is the difference between temperatures). In this case, the specific heat capacity of the liquid is 0.91 J/g-K, the mass is 35.0 g, and the change in temperature is 47.6 °C - 10 °C = 37.6 °C. So, the heat required for heating the liquid is: $q_1=35.0g\times 0.91\frac{J}{g-K}\times 37.6K$

Calculate the heat required for vaporization

Next, we need to find the heat required to vaporize the liquid at its boiling point. We use the formula: $q=n\times \mathrm{\Delta }H$ Where: - $q$ is the heat (in J), - $n$ is the number of moles, and - $\mathrm{\Delta }H$ is the heat of vaporization (in J/mol). First, we need to calculate the number of moles in 35.0 g of the compound. The molar mass of ${\mathrm{C}}_2{\mathrm{Cl}}_3{\mathrm{F}}_3$ is $2\times 12.01+3\times 35.45+3\times 18.998=187.39g/mol$. Then, we can calculate the number of moles as $n=\frac{35.0g}{187.39g/mol}$. Now, we know the heat of vaporization is 27.49 kJ/mol, which we need to convert to J/mol: 27.49 kJ/mol × 1000 J/kJ = 27490 J/mol. So, the heat required for vaporization is: $q_2=n\times 27490\frac{J}{mol}$

Calculate the heat required to heat the gas

Finally, we need to find the heat required to heat the gas from its boiling point of 47.6 °C to the final temperature of 105 °C. We can use the same formula as in step 1: $q=m\times c\times \mathrm{\Delta }T$ In this case, the specific heat capacity of the gas is 0.67 J/g-K, the mass is 35.0 g, and the change in temperature is 105 °C - 47.6 °C = 57.4 °C. So, the heat required for heating the gas is: $q_3=35.0g\times 0.67\frac{J}{g-K}\times 57.4K$

Calculate the total heat required

Now that we have calculated the heat for each process, we can add them all together to find the total heat required: $q_{\text{total}}=q_1+q_2+q_3$ First, calculate each heat value using the formulas given in the previous steps, then add those values together to get the total heat required.

Key concepts

Specific Heat Capacity

Specific heat capacity is a property of substances that indicates how much heat energy is needed to raise the temperature of one gram of the substance by one degree Celsius (or one Kelvin). It’s symbolized by the letter ‘c’ in the formula for heat energy:

$q=m\times c\times \mathrm{\Delta }T$
where 'q' represents the heat energy in joules (J), 'm' is the mass of the substance in grams (g), 'c' is the specific heat capacity (J/g-K), and $\mathrm{\Delta }T$ is the change in temperature.
Different substances have varying specific heat capacities, which means that they require different amounts of energy to change their temperatures. For example, water has a high specific heat capacity, which explains why it takes a longer time to boil compared to other liquids. When solving problems, knowing the specific heat capacity is crucial for calculating the energy involved in heating or cooling the substance.

Enthalpy Change

Enthalpy change, often symbolized as $\mathrm{\Delta }H$, refers to the total heat content in a system and its change during a process at constant pressure. It is an essential concept in thermochemistry and thermodynamics, related to the energy involved in making and breaking chemical bonds. Enthalpy change can manifest in different forms such as heat of vaporization, which is the energy required for a substance to change from liquid to gas.
The heat of vaporization is a type of enthalpy change and represents the amount of energy needed to vaporize one mole of a substance at its boiling point, while the pressure remains constant. As it is intrinsic to the substance, this value is critical when calculating the heat required for phase changes, especially when dealing with substances transitioning from liquid to gas or vice versa.

Energy Required for Phase Change

To understand the energy required for phase change, it's essential to distinguish between two main types of thermal energy changes: temperature change within a phase and phase transitions like melting or boiling. The energy required for phase change doesn't increase the temperature of the substance; instead, it breaks the intermolecular bonds to change the physical state. When a substance reaches a phase transition temperature, such as the boiling point, any added heat is used to convert the substance from one phase to another, not to raise its temperature.
To calculate the heat absorbed or released during a phase transition, we use the formula:
$q=n\times \mathrm{\Delta }H$
where $q$ is the heat required, $n$ is the moles of substance, and $\mathrm{\Delta }H$ represents the enthalpy change for the phase transition (e.g., heat of vaporization or heat of fusion). By determining the number of moles involved and the specific enthalpy change, we can calculate the exact energy required for the substance to undergo the phase transition, which is a fundamental step in thermochemistry calculations.

Thermochemistry Calculations

Thermochemistry calculations involve several steps and considerations to determine the heat involved in chemical reactions and physical changes. The basic principles include careful accounting for mass, temperature change, and phase transitions, as well as the specific properties of the materials involved, such as specific heat capacity and enthalpy of vaporization.
To perform these calculations, multiple formulas can be used and often need to be combined for a complete understanding of the thermal environment. For example, in practical scenarios such as the provided exercise, you may need to use one formula to calculate the heat needed to raise the temperature to the boiling point, another for the phase change from liquid to gas, and a third for the final heating of the vapor. Each step requires careful consideration of the unique properties of the substance, and the sum of the energies from each step reveals the total energy involved in the entire process. Thermochemistry calculations are critical for predicting outcomes in various fields, including environmental science, engineering, and materials science.