/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 46 Carbon disulfide, \(\mathrm{CS}_... [FREE SOLUTION] | 91影视

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Chapter 11: Problem 46

Carbon disulfide, \(\mathrm{CS}_{2}\), is a volatile, flammable liquid. It has a vapor pressure of \(400.0 \mathrm{mmHg}\) at \(28.0^{\circ} \mathrm{C}\) and \(760.0\) \(\mathrm{mmHg}\) at \(46.5^{\circ} \mathrm{C}\). What is the heat of vaporization of this substance?

Short Answer

Expert verified
The heat of vaporization is approximately 29.18 kJ/mol.

Step by step solution

01

Understanding Clausius-Clapeyron Equation

The Clausius-Clapeyron equation relates the vapor pressure of a substance with its temperature and heat of vaporization, \(\Delta H_{vap}\). The equation is given by:\[\ln \left(\frac{P_2}{P_1}\right) = \frac{\Delta H_{vap}}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)\]where \(P_1\) and \(P_2\) are the vapor pressures at temperatures \(T_1\) and \(T_2\), respectively, and \(R\) is the ideal gas constant, \(8.314\, \text{J/mol路K}\).
02

Convert Temperatures to Kelvin

We need to convert the given temperatures from Celsius to Kelvin. Remember, \(K = ^{\circ}C + 273.15\).- For \(28.0^{\circ}C\):\[ T_1 = 28.0 + 273.15 = 301.15\, \text{K} \]- For \(46.5^{\circ}C\):\[ T_2 = 46.5 + 273.15 = 319.65\, \text{K} \]
03

Substitute Values into Clausius-Clapeyron Equation

Substitute the known values into the Clausius-Clapeyron equation:\[\ln \left(\frac{760.0}{400.0}\right) = \frac{\Delta H_{vap}}{8.314} \left(\frac{1}{301.15} - \frac{1}{319.65}\right)\]
04

Solve for Heat of Vaporization

Calculate \(\ln \left(\frac{760.0}{400.0}\right)\) and then solve for \(\Delta H_{vap}\):- Find the natural log:\[\ln \left(\frac{760.0}{400.0}\right) = \ln (1.9) \approx 0.6419\]- Calculate the temperature difference in reciprocals:\[\frac{1}{301.15} - \frac{1}{319.65} \approx 0.05448 - 0.05265 = 0.00183\, \text{K}^{-1}\]- Substitute these into the equation:\[0.6419 = \frac{\Delta H_{vap}}{8.314} \times 0.00183\]- Solve for \(\Delta H_{vap}\):\[\Delta H_{vap} = \frac{0.6419 \times 8.314}{0.00183} \approx 29178.5\, \text{J/mol} \approx 29.18\, \text{kJ/mol}\]
05

Final Step: Conclusion

The heat of vaporization of carbon disulfide is approximately \(29.18\, \text{kJ/mol}\).

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Key Concepts

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

Clausius-Clapeyron Equation
The Clausius-Clapeyron equation plays a crucial role in understanding the relationship between vapor pressure, temperature, and the heat of vaporization of a substance. This equation is essential for predicting how the vapor pressure of a liquid changes as its temperature changes.

The equation is expressed as:
  • \( \ln \left(\frac{P_2}{P_1}\right) = \frac{\Delta H_{\text{vap}}}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right) \)
Here:
  • \(P_1\) and \(P_2\) are the vapor pressures at the absolute temperatures \(T_1\) and \(T_2\), respectively.
  • \( \Delta H_{\text{vap}} \) is the heat of vaporization.
  • \( R \) is the ideal gas constant.
The main point of this equation is to calculate the heat of vaporization by comparing how vapor pressure changes with temperature. This can help in various applications, from understanding weather patterns to designing chemical processes.
Vapor Pressure
Vapor pressure is a fundamental concept in physical chemistry. It is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature.

This means that:
  • When a liquid is in a closed container, molecules evaporate into the space above.
  • Over time, a balance is reached where the number of molecules leaving the liquid equals those returning, creating equilibrium.
  • The pressure exerted by these vapor molecules is the vapor pressure.
Vapor pressure depends heavily on temperature. As temperature increases, vapor pressure rises due to the higher energy molecules that escape more easily into the vapor phase. This property is what the Clausius-Clapeyron equation exploits to relate changes in temperature to vapor pressure changes. In this exercise, the vapor pressure increases from 400 mmHg to 760 mmHg as the temperature rises from 28掳C to 46.5掳C.
Ideal Gas Constant
The ideal gas constant, denoted as \( R \), is a crucial part of many equations in chemistry and physics. It acts as a bridge between different physical properties and is an inherent part in the Clausius-Clapeyron equation.

The value of \( R \) is:
  • 8.314 J/mol路K
This constant helps link energy scales to temperature scales in equations dealing with gases and vapor.
In context:
  • When using the Clausius-Clapeyron equation, \( R \) helps quantify the relationship between temperature, pressure, and the heat involved in phase changes.
  • The unit J/mol路K represents that it relates energy in joules to the amount of substance in moles at a particular temperature in Kelvin.
Understanding \( R \) is vital for not only solving thermodynamics problems but also for interpreting how substance phases and states interact at molecular levels.

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Most popular questions from this chapter

A quantity of ice at \(0.0^{\circ} \mathrm{C}\) was added to \(33.6 \mathrm{~g}\) of water at \(21.0^{\circ} \mathrm{C}\) to give water at \(0.0^{\circ} \mathrm{C}\). How much ice was added? The heat of fusion of water is \(6.01 \mathrm{~kJ} / \mathrm{mol}\) and the specific heat is \(4.18 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\)

Acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}\), forms stable pairs of molecules held together by two hydrogen bonds. Such molecules - themselves formed by the association of two simpler molecules-are called dimers. The vapor over liquid acetic acid consists of a mixture of monomers (single acetic acid molecules) and dimers. At \(100.6^{\circ} \mathrm{C}\) the total pressure of vapor over liquid acetic acid is \(436 \mathrm{mmHg}\). If the vapor consists of \(0.630\) mole fraction of the dimer, what are the masses of monomer and dimer in \(1.000 \mathrm{~L}\) of the vapor? What is the density of the vapor?

How many atoms are there in a body-centered cubic unit cell of an atomic crystal in which all atoms are at lattice points?

Describe the face-centered cubic unit cell.

a. Draw Lewis structures of each of the following compounds: \(\mathrm{LiH}, \mathrm{NH}_{3}, \mathrm{CH}_{4}, \mathrm{CO}_{2}\) b. Which of these has the highest boiling point? Why? c. Which of these has the lowest boiling point? Why? d. Which of these has the next-to-highest boiling point? Why?
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