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Chapter 11: Problem 51

(a) What is the significance of the critical point in a phase diagram? (b) Why does the line that separates the gas and liquid phases end at the critical point?

Short Answer

Expert verified
(a) The significance of the critical point in a phase diagram is that it marks the end of the gas-liquid phase boundary and the beginning of the supercritical region, where distinct gas and liquid phases no longer exist. Above the critical point, the substance can no longer be condensed into a liquid, regardless of the applied pressure. The critical point plays an essential role in understanding and predicting a substance's phase behavior under various conditions. (b) The line that separates the gas and liquid phases ends at the critical point because, beyond this point, the densities of the liquid and gas phases become equal, making them indistinguishable. In the supercritical region, the substance demonstrates properties of both gas and liquid states, making it difficult to classify the substance as either a gas or liquid.

Step by step solution

01

(Understanding phase diagrams)

Phase diagrams are graphical representations of the state of matter (solid, liquid, or gas) of a substance as a function of temperature and pressure. They are used to show the conditions under which a substance will change from one state to another (phase transitions). A typical phase diagram presents three primary lines 鈥� the vaporization line (separating gas and liquid), the melting line (separating solid and liquid), and the sublimation line (separating solid and gas).
02

(The critical point in a phase diagram)

In a phase diagram, the critical point is a unique state where the substance's liquid and gas phases can no longer be distinguished as separate phases. Above the critical temperature (Tc) and critical pressure (Pc), the substance behaves as a supercritical fluid, with properties blending liquid and gas phases. At the critical point, the densities of the liquid and gas become equal, and their physical properties merge. (a) The significance of the critical point in a phase diagram:
03

(Importance of the critical point)

The critical point has several crucial implications in the study of a substance's phase behavior: 1. The critical point marks the end of the gas-liquid phase boundary and the beginning of the supercritical region, where distinct gas and liquid phases no longer exist. 2. Above the critical point, the substance can no longer be condensed into a liquid, no matter how much pressure is applied 鈥� it can only be compressed, similar to a gas. 3. The critical point plays an essential role in understanding and predicting a substance's phase behavior under various conditions. For example, it is crucial for designing chemical processes, such as high-pressure and high-temperature reactions involving supercritical fluids. (b) Why does the line that separates the gas and liquid phases end at the critical point?
04

(Relation between gas and liquid phase boundary and critical point)

As mentioned earlier, the critical point is the unique state where the liquid and gas phases can no longer be differentiated. Below the critical temperature and pressure, the substance's properties change significantly when it undergoes a phase transition from liquid to gas or vice versa. The line that separates the gas and liquid phases represents these phase transitions. At the critical point, the densities of liquid and gas become equal, making them indistinguishable. Therefore, the phase boundary ends at the critical point because beyond this point, the substance no longer exhibits distinct gas and liquid phases. In the supercritical region, the substance demonstrates properties of both gas and liquid states, making it difficult to classify the substance as either a gas or liquid.

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Most popular questions from this chapter

Butane and 2 -methylpropane, whose space-filling models are shown, are both nonpolar and have the same molecular formula, yet butane has the higher boiling point \(\left(-0.5^{\circ} \mathrm{C}\right.\) compared to \(\left.-11.7{ }^{\circ} \mathrm{C}\right)\). Explain.

Which type (or types) of crystalline solid is characterized by each of the following: (a) high mobility of electrons throughout the solid; (b) softness, relatively low melting point; (c) high melting point and poor electrical conductivity; (d) network of covalent bonds; (e) charged particles throughout the solid.

Refer to Figure \(11.27(\mathrm{~b})\), and describe the phase changes (and the temperatures at which they occur) when \(\mathrm{CO}_{2}\) is heated from \(-80{ }^{\circ} \mathrm{C}\) to \(-20{ }^{\circ} \mathrm{C}\) at \((\mathrm{a})\) a constant pressure of \(3 \mathrm{~atm}\), (b) a constant pressure of \(6 \mathrm{~atm}\).

The critical temperatures (K) and pressures (atm) of a series of halogenated methanes are as follows: $$ \begin{array}{lllll} \hline \text { Compound } & \mathrm{CCl}_{3} \mathrm{~F} & \mathrm{CCl}_{2} \mathrm{~F}_{2} & \mathrm{CClF}_{3} & \mathrm{CF}_{4} \\ \hline \text { Critical Temperature } & 471 & 385 & 302 & 227 \\ \text { Critical Pressure } & 43.5 & 40.6 & 38.2 & 37.0 \\ \hline \end{array} $$ (a) List the intermolecular forces that occur for each compound. (b) Predict the order of increasing intermolecular attraction, from least to most, for this series of compounds. (c) Predict the critical temperature and pressure for \(\mathrm{CCl}_{4}\) based on the trends in this table. Look up the experimentally determined critical temperatures and pressures for \(\mathrm{CCl}_{4}\), using a source such as the \(\mathrm{CRC}\) Handbook of Chemistry and Physics, and suggest a reason for any discrepancies.

Indicate the type of crystal (molecular, metallic, covalent-network, or ionic) each of the following would form upon solidification: (a) \(\mathrm{CaCO}_{3},(\mathrm{~b}) \mathrm{Pt}\), (c) \(\mathrm{ZrO}_{2}\) (melting point, \(2677^{\circ} \mathrm{C}\) ), (d) table sugar \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\), (e) benzene, (f) \(I_{2}\).
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