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Chapter 12: Problem 37

Some vapor pressure data for Freon- \(12, \mathrm{CCl}_{2} \mathrm{F}_{2}\), once a common refrigerant, are \(-12.2^{\circ} \mathrm{C}, 2.0 \mathrm{atm} ; 16.1^{\circ} \mathrm{C}\) 5.0 atm; \(42.4^{\circ} \mathrm{C}, 10.0\) atm; \(74.0^{\circ} \mathrm{C}, 20.0\) atm. Also, \(\mathrm{bp}=-29.8^{\circ} \mathrm{C}, \quad T_{\mathrm{c}}=111.5^{\circ} \mathrm{C}, \quad P_{\mathrm{c}}=39.6 \mathrm{atm} .\) Use these data to plot the vapor pressure curve of Freon-12 What approximate pressure would be required in the compressor of a refrigeration system to convert Freon- 12 vapor to liquid at \(25.0^{\circ} \mathrm{C}\) ?

Short Answer

Expert verified
The exact pressure required to convert Freon-12 vapor to liquid at 25 degrees Celsius would be obtained from the intersection of the line and the curve in step 3. The precise value is subject to the accuracy of the interpolation on the vapor pressure curve.

Step by step solution

01

Plot the given data points

Using the given data, create a table that aligns given temperatures with their respective pressures. Convert the temperatures from Celsius to Kelvin by adding 273 to each temperature. Afterward, plot these data points on a graph where the x-axis represents temperature and the y-axis represents pressure.
02

Draw the Vapor Pressure Curve

Interpolate the data points by connecting them using smooth curves. Label it as a vapor pressure curve for Freon-12. Ensure the curves match with the general behavior of a vapor pressure curve. The curve should be increasing and be exponential in nature. This is because as temperature increases pressure, too, increases in a similar fashion.
03

Interpolate the pressure at 25 degrees Celsius

Locate the point on the x-axis that corresponds to the temperature 25 degrees Celsius (or 298 Kelvin using the conversion in step 1). Extend a line from this point to the corresponding point on the vapor pressure curve. The intersection of the line and the curve will give a corresponding point on the pressure axis. This will be the required pressure to convert Freon-12 vapor to liquid at 25.0 degrees Celsius.

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Key Concepts

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

Freon-12
Freon-12, chemically known as dichlorodifluoromethane or CCl\(_2\)F\(_2\), was widely used as a refrigerant. Refrigerants like Freon-12 are substances used in cooling mechanisms. They transition from a liquid to a gas and absorb heat during the process, making them useful in refrigeration systems.
Freon-12 gained popularity because of its stability and nonflammability, however, it was later identified as a powerful ozone-depleting substance. Despite its phased-out use due to environmental concerns, understanding Freon-12's properties, like its vapor pressure data, remains essential in educational contexts.
  • Stable and effective in heat absorption
  • Chemically known as CCl\(_2\)F\(_2\)
  • Contributes to ozone layer depletion
Refrigeration System
A refrigeration system is a process that extracts heat from an area to keep it cooler. The heart of such a system involves a refrigerant like Freon-12, which relocates heat. Understanding the phase change properties, like vapor pressure, of refrigerants at various temperatures is key to designing these systems efficiently.
In the cycle, the compressor plays a crucial role. It raises the pressure of the refrigerant vapor, making it easier to liquefy by removing heat in a condenser. This condensation allows the refrigerant to expel stored heat and return to the evaporator where it can absorb heat once again.
  • Involves compressing refrigerant vapor
  • Heat is expelled as refrigerant condenses
  • Cycle repeats to maintain a cool environment
Phase Diagram
A phase diagram shows which states (solid, liquid, gas) a substance will be under different pressure and temperature conditions. For Freon-12, examining its phase diagram through plotting its vapor pressure helps us predict how it behaves under typical refrigeration conditions.
This plotting involves graphing data points of temperature against pressure to see a vapor pressure curve. Such diagrams help in understanding conditions under which Freon-12 will condense or vaporize, vital for refrigeration system design.
  • Shows state changes under varied conditions
  • Plots properties like temperature and pressure
  • Useful for designing systems efficiently
Temperature Conversion
Temperature conversion is vital in scientific calculations, often needed between Celsius, Kelvin, and Fahrenheit. Here, temperature data of Freon-12 is given in degrees Celsius, but for accurate scientific graphing, converting to Kelvin is standard practice.
The conversion from Celsius to Kelvin involves adding 273 to the Celsius temperature (e.g., -12.2°C becomes 260.8 K). This straightforward method maintains the integrity of scientific data across different measurements, ensuring accuracy in plotting pressures on a phase diagram.
  • Converting Celsius to Kelvin is common
  • Ensures consistency in scientific data
  • Maintains accuracy in plotting and calculations

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Most popular questions from this chapter

In an ionic crystal lattice each cation will be attracted by anions next to it and repulsed by cations near it. Consequently the coulomb potential leading to the lattice energy depends on the type of crystal. To get the total lattice energy you must sum all of the electrostatic interactions on a given ion. The general form of the electrostatic potential is $$V=\frac{Q_{1} Q_{2} e^{2}}{d_{12}}$$ where \(Q_{1}\) and \(Q_{2}\) are the charges on ions 1 and \(2, d_{12}\) is the distance between them in the crystal lattice. and \(e\) is the charge on the electron. (a) Consider the linear "crystal" shown below. The distance between the centers of adjacent spheres is \(R .\) Assume that the blue sphere and the green spheres are cations and that the red spheres are anions. Show that the total electrostatic energy is $$V=-\frac{Q^{2} e^{2}}{d} \times \ln 2$$ (b) In general, the electrostatic potential in a crystal can be written as $$V=-k_{M} \frac{Q^{2} e^{2}}{R}$$ where \(k_{M}\) is a geometric constant, called the Madelung constant, for a particular crystal system under consideration. Now consider the NaCl crystal structure and let \(R\) be the distance between the centers of sodium and chloride ions. Show that by considering three layers of nearest neighbors to a central chloride ion, \(k_{M}\) is given by $$k_{M}=\left(6-\frac{12}{\sqrt{2}}+\frac{8}{\sqrt{3}}-\frac{6}{\sqrt{4}} \cdots\right)$$ (c) Carry out the same calculation for the CsCl structure. Are the Madelung constants the same?

A supplier of cylinder gases warns customers to determine how much gas remains in a cylinder by weighing the cylinder and comparing this mass to the original mass of the full cylinder. In particular, the customer is told not to try to estimate the mass of gas available from the measured gas pressure. Explain the basis of this warning. Are there cases where a measurement of the gas pressure can be used as a measure of the remaining available gas? If so, what are they?

You decide to cool a can of soda pop quickly in the freezer compartment of a refrigerator. When you take out the can, the soda pop is still liquid; but when you open the can, the soda pop immediately freezes. Explain why this happens.

A crystalline solid contains three types of ions, \(\mathrm{Na}^{+}, \mathrm{O}^{2-},\) and \(\mathrm{Cl}^{-}\). The solid is made up of cubic unit cells that have \(\mathrm{O}^{2-}\) ions at each corner, \(\mathrm{Na}^{+}\) ions at the center of each face, and \(\mathrm{Cl}^{-}\) ions at the center of the cells. What is the chemical formula of the compound? What are the coordination numbers for the \(\mathrm{O}^{2-}\) and \(\mathrm{Cl}^{-}\) ions? If the length of one edge of the unit cell is \(a,\) what is the shortest distance from the center of a \(\mathrm{Na}^{+}\) ion to the center of an \(\mathrm{O}^{2-}\) ion? Similarly, what is the shortest distance from the center of a \(\mathrm{Cl}^{-}\) ion to the center of an \(\mathrm{O}^{2-}\) ion?

The enthalpy of vaporization of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{l}),\) is \(33.9 \mathrm{kJmol}^{-1}\) at \(298 \mathrm{K}\). How many liters of \(\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{g})\) measured at \(298 \mathrm{K}\) and \(95.1 \mathrm{mmHg}\), are formed when \(1.54 \mathrm{kJ}\) of heat is absorbed by \(\mathrm{C}_{6} \mathrm{H}_{6}(1)\) at a constant f 298 K?
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