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Chapter 12: Problem 138

The following data are given for \(\mathrm{CCl}_{4}\). Normal melting point, \(-23^{\circ} \mathrm{C} ;\) normal boiling point, \(77^{\circ} \mathrm{C} ;\) density of liquid \(1.59 \mathrm{g} / \mathrm{mL} ; \Delta H_{\text {fus }}=3.28 \mathrm{kJ} \mathrm{mol}^{-1} ;\) vapor pressure at \(25^{\circ} \mathrm{C}, 110\) Torr. (a) What phases-solid, liquid, and/or gas-are present if \(3.50 \mathrm{g} \mathrm{CCl}_{4}\) is placed in a closed \(8.21 \mathrm{L}\) container at \(25^{\circ} \mathrm{C} ?\) (b) How much heat is required to vaporize 2.00 L of \(\mathrm{CCl}_{4}(\mathrm{l})\) at its normal boiling point?

Short Answer

Expert verified
a) The CCl4 would be in the liquid phase. b) The heat required to vaporize the CCl4 would be 67.50 kJ.

Step by step solution

01

Determine phase(s) of CCl4

Given that the melting point of \(\mathrm{CCl}_{4}\) is \(-23^{\circ} \mathrm{C}\) and the boiling point is \(77^{\circ} \mathrm{C}\), if \(\mathrm{CCl}_{4}\) is placed in a closed \(8.21 \mathrm{L}\) container at \(25^{\circ} \mathrm{C}\), it would be in liquid state because \(25^{\circ} \mathrm{C}\) is between the melting and boiling points.
02

Calculate molar volume of CCl4

First, use the given density to convert the volume of CCl4 to be vaporized into mass. The density of \(\mathrm{CCl}_{4}\) is given as \(1.59 \mathrm{g}/\mathrm{mL}\). Therefore, \(2.00 \mathrm{L} = 2000 \mathrm{mL} = 2000 \mathrm{mL} \times 1.59 \mathrm{g}/\mathrm{mL} = 3180 \mathrm{g}\). Then, calculate the molar volume using the molar mass of CCl4 (154.5 g/mol): molar volume = \(3180 \mathrm{g} / 154.5 \mathrm{g/mol} = 20.58 \mathrm{mol}\)
03

Find the heat of vaporization

The heat of vaporization can be found by multiplying the number of moles by the heat of fusion (change in enthalpy during phase transition). The given heat of fusion of CCl4 is \(3.28 kJ/mol\). So, the heat of vaporization is \(20.58 \mathrm{mol} \times 3.28 \mathrm{kJ/mol} = 67.50 \mathrm{kJ}\)
04

Transfer heat to vaporize

The heat required to vaporize 2.00 L of liquid CCl4 at its normal boiling point is simply equal to the heat of vaporization, which has been calculated to be 67.50 kJ.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vaporization
Vaporization is a phase transition where a substance changes from its liquid state to its gaseous state. It is an essential concept in thermodynamics and occurs at the boiling point of the substance.
This process requires energy to overcome intermolecular forces between the liquid molecules. The required energy is called the heat of vaporization. This energy input does not change the temperature of the substance but transforms its state from liquid to gas.
There are two main types of vaporization:
  • Evaporation: Occurs at the surface of a liquid at any temperature below its boiling point.
  • Boiling: Takes place throughout the entire body of the liquid at a specific temperature called the boiling point.
For example, when \(\mathrm{CCl}_4\), with a normal boiling point of \(77^{\circ} \mathrm{C}\), is heated to this temperature, it converts from liquid to gas, requiring significant energy input to overcome its intermolecular forces.
Molar Volume
Molar volume is an essential concept in understanding the amount of space that one mole of a substance occupies. It is typically expressed in liters per mole (L/mol). For most liquids and solids, molar volume can be calculated by dividing the mass of the substance by its density and then by the molar mass of the substance.
This value gives insight into the structure and the packing of molecules in a particular phase. For example, knowing the density of \(\mathrm{CCl}_4\) (which is \(1.59 \text{g/mL}\)), you can calculate its molar volume by converting the volume of liquid to grams and then converting the grams to moles.
To find the molar volume of \(\mathrm{CCl}_4\), we used the formula:
  • Molar Volume = \(\frac{\text{Mass}}{\text{Molar Mass}}\)
For \(\mathrm{CCl}_4\), with a calculated mass of \(3180 \mathrm{g}\), this results in a molar volume:
  • \(3180 \mathrm{g} \div 154.5 \mathrm{g/mol} = 20.58 \mathrm{mol}\)
Heat of Fusion
The heat of fusion refers to the energy required to change a substance from solid to liquid at its melting point, without changing its temperature. It is a crucial measure of a substance's internal bonding strength.
For \(\mathrm{CCl}_4\), the heat of fusion is given as \(3.28\, \mathrm{kJ/mol}\). This value reflects the amount of energy required for each mole of carbon tetrachloride to transition from a solid to a liquid.
Though we focused on vaporization above for the boiling point calculation, the heat of fusion allows us to understand the enthalpy changes during melting:
  • Phase transition occurs at the melting point, which for \(\mathrm{CCl}_4\), is \(-23^{\circ} \mathrm{C}\).
  • It considers only the solid-to-liquid transformation, not the liquid-to-gas seen in vaporization.
Even though the exercise emphasized the energy for vaporization, understanding the heat of fusion gives a complete cycle of transitioning phases for any given substance.

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Most popular questions from this chapter

If the triple point pressure of a substance is greater than 1 atm, which two of the following conclusions are valid? (a) The solid and liquid states of the substance cannot coexist at equilibrium. (b) The melting point and boiling point of the substance are identical. (c) The liquid state of the substance cannot exist. (d) The liquid state cannot be maintained in a beaker open to air at 1 atm pressure. (e) The melting point of the solid must be greater than \(0^{\circ} \mathrm{C}\) (f) The gaseous state at 1 atm pressure cannot be condensed to the solid at the triple point temperature.

Argon, copper, sodium chloride, and carbon dioxide all crystallize in the fcc structure. How can this be when their physical properties are so different?

One handbook lists the sublimation pressure of solid benzene as a function of Kelvin temperature, \(T\), as \(\log \mathrm{P}(\mathrm{mmHg})=9.846-2309 / \mathrm{T} .\) Another hand- book lists the vapor pressure of liquid benzene as a function of Celsius temperature, \(t,\) as \(\log P(\mathrm{mmHg})=\) \(6.90565-1211.033 /(220.790+t) .\) Use these equations to estimate the normal melting point of benzene, and compare your result with the listed value of \(5.5^{\circ} \mathrm{C}\)

All solids contain defects or imperfections of structure or composition. Defects are important because they influence properties, such as mechanical strength. Two common types of defects are a missing ion in an otherwise perfect lattice, and the slipping of an ion from its normal site to a hole in the lattice. The holes discussed in this chapter are often called interstitial sites, since the holes are in fact interstices in the array of spheres. The two types of defects described here are called point de kcts because they occur within specific sites. In the 1930 s, two solidstate physicists, W. Schottky and J. Fraenkel, studied the two types of point defects: A Schottky defect corresponds to a missing ion in a lattice, while a Fraenkel defect corresponds to an ion that is displaced into an interstitial site. (a) An example of a Schottky defect is the absence of a \(\mathrm{Na}^{+}\) ion in the NaCl structure. The absence of a \(\mathrm{Na}^{+}\) ion means that a \(\mathrm{Cl}^{-}\) ion must also be absent to preserve electrical neutrality. If one NaCl unit is missing per unit cell, does the overall stoichiometry change, and what is the change in density? (b) An example of a Fraenkel defect is the movement of \(a \mathrm{Ag}^{+}\) ion to a tetrahedral interstitial site from its normal octahedral site in \(\mathrm{AgCl}\), which has a structure like \(\mathrm{NaCl}\). Does the overall stoichiometry of the compound change, and do you expect the density to change? (c) Titanium monoxide (TiO) has a sodium chloridelike structure. X-ray diffraction data show that the edge length of the unit cell is \(418 \mathrm{pm}\). The density of the crystal is \(4.92 \mathrm{g} / \mathrm{cm}^{3}\) Do the data indicate the presence of vacancies? If so, what type of vacancies?

A 7.53 I. sample of \(\mathrm{N}_{2}(\mathrm{g})\) at \(742 \mathrm{mmHg}\) and \(45.0^{\circ} \mathrm{C}\) is bubbled through \(\mathrm{CCl}_{4}(1)\) at \(45.0^{\circ} \mathrm{C} .\) Assuming the gas becomes saturated with \(\mathrm{CCl}_{4}(\mathrm{g}),\) what is the volume of the resulting gaseous mixture, if the total pressure remains at \(742 \mathrm{mm} \mathrm{Hg}\) and the temperature remains at \(45^{\circ} \mathrm{C} ?\) The vapor pressure of \(\mathrm{CCl}_{4}\) at \(45^{\circ} \mathrm{C}\) is \(261 \mathrm{mmHg}\)
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