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Chapter 11: Problem 64

At \(25^{\circ} \mathrm{C}\) gallium is a solid with a density of \(5.91 \mathrm{~g} / \mathrm{cm}^{3}\). Its melting point, \(29.8{ }^{\circ} \mathrm{C},\) is low enough that you can melt it by holding it in your hand. The density of liquid gallium just above the melting point is \(6.1 \mathrm{~g} / \mathrm{cm}^{3} .\) Based on this information, what unusual feature would you expect to find in the phase diagram of gallium?

Short Answer

Expert verified
The unusual feature in the phase diagram of gallium is that it has a negative slope between the solid and liquid phases, as its liquid state has a higher density (\(6.1 \thinspace g/cm^3\)) than the solid state (\(5.91 \thinspace g/cm^3\)). This behavior implies that upon melting, gallium contracts rather than expands, which is uncommon among most substances.

Step by step solution

01

Compare Density of Solid and Liquid Gallium

Compare the density of solid gallium (5.91 g/cm鲁) and liquid gallium (6.1 g/cm鲁). We will notice that the density of liquid gallium is larger than the density of solid gallium.
02

Analyze the Unusual Feature

In most substances, the density of a solid state is greater than the liquid state. However, gallium is an exception to this rule as its liquid state has a higher density than the solid state. This implies that upon melting, gallium will contract rather than expand. This unusual behavior will be reflected in its phase diagram as a negative slope between the solid and liquid phases.

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Key Concepts

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

Density
Density is a significant property of substances that determines how much mass is contained in a given volume. This property can alter under different conditions of temperature and pressure.
For most materials, solids are denser than their liquid forms. This means they have more mass packed into each cubic centimeter. When a solid melts into a liquid, it usually expands and occupies more volume, resulting in a lower density.
This is why ice floats on water, because water expands when it freezes, making the ice less dense than the liquid water.
  • Density in solid gallium: 5.91 g/cm鲁
  • Density in liquid gallium: 6.1 g/cm鲁
Gallium, however, defies this usual behavior, with a liquid density higher than its solid density. This peculiar property makes gallium contract upon melting, instead of expanding.
Gallium
Gallium is a fascinating element primarily because of its unique properties. It is a soft, silvery metal that can melt in your hand because of its low melting point, just under 30掳C. It belongs to Group 13 in the periodic table, often associated with elements like aluminum.
Pieces of gallium can transform from solid to liquid when held, highlighting its unusual behavior. Unlike most metals, once gallium is liquid, it is denser than when it's solid. This trait shows that its molecules pack more tightly in the liquid form, which is not typical for metals under these conditions. Scientists capitalize on such properties to use gallium in electronics and material sciences.
  • Melting Point: 29.8掳C
  • Solid Density: 5.91 g/cm鲁
  • Liquid Density: 6.1 g/cm鲁
Gallium鈥檚 unusual density behavior can be encountered in its phase diagram, which challenges typical expectations.
Solid and liquid phases
In chemistry, understanding the transitions between solid and liquid phases is crucial. These transitions are represented in phase diagrams, which map the conditions of temperature and pressure under which the phases of a substance exist.
Substances typically expand upon melting, with solid densities higher than liquid densities. For gallium, the contrary is true. This makes its phase diagram unique, featuring a negative slope between the solid and liquid phases. In a phase diagram, the slope indicates how a substance behaves when transitioning between phases.
For gallium, because the liquid is denser, the line indicating solid to liquid transition on the diagram slopes downwards. This reflects the contraction in volume as gallium melts 鈥� an unusual behavior that sets it apart from most substances. Such a phase transition also hints at interesting applications, especially in fields where density changes are critical.

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Most popular questions from this chapter

The fact that water on Earth can readily be found in all three states (solid, liquid, and gas) is in part a consequence of the fact that the triple point of water \(\left(T=0.01^{\circ} \mathrm{C}, P=0.006 \mathrm{~atm}\right)\) falls within a range of temperatures and pressures found on Earth. Saturn's largest moon Titan has a considerable amount of methane in its atmosphere. The conditions on the surface of Titan are estimated to be \(P=1.6\) atm and \(T=-178^{\circ} \mathrm{C}\). As seen from the phase diagram of methane (Figure 11.30 ), these conditions are not far from the triple point of methane, raising the tantalizing possibility that solid, liquid, and gaseous methane can be found on Titan. (a) What state would you expect to find methane in on the surface of Titan? (b) On moving upward through the atmosphere the pressure will decrease. If we assume that the temperature does not change, what phase change would you expect to see as we move away from the surface?

Ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) melts at \(-114{ }^{\circ} \mathrm{C}\) and boils at \(78{ }^{\circ} \mathrm{C}\). The enthalpy of fusion of ethanol is \(5.02 \mathrm{~kJ} / \mathrm{mol},\) and its enthalpy of vaporization is \(38.56 \mathrm{~kJ} / \mathrm{mol}\). The specific heats of solid and liquid ethanol are \(0.97 \mathrm{~J} / \mathrm{g}-\mathrm{K}\) and \(2.3 \mathrm{~J} / \mathrm{g}-\mathrm{K},\) respectively. (a) How much heat is required to convert \(42.0 \mathrm{~g}\) of ethanol at \(35^{\circ} \mathrm{C}\) to the vapor phase at \(78{ }^{\circ} \mathrm{C} ?\) (b) How much heat is required to convert the same amount of ethanol at \(-155^{\circ} \mathrm{C}\) to the vapor phase at \(78^{\circ} \mathrm{C}\) ?

Do you expect the viscosity of glycerol, \(\mathrm{C}_{3} \mathrm{H}_{5}(\mathrm{OH})_{3},\) to be larger or smaller than that of 1 -propanol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\) ? Explain. [Section 11.3\(]\)

Rationalize the difference in boiling points in each pair: (a) \(\mathrm{HF}\left(20^{\circ} \mathrm{C}\right)\) and \(\mathrm{HCl}\left(-85^{\circ} \mathrm{C}\right),(\mathbf{b}) \mathrm{CHCl}_{3}\left(61{ }^{\circ} \mathrm{C}\right)\) and \(\mathrm{CHBr}_{3}\) \(\left(150^{\circ} \mathrm{C}\right),(\mathrm{c}) \mathrm{Br}_{2}\left(59^{\circ} \mathrm{C}\right)\) and \(\mathrm{ICl}\left(97^{\circ} \mathrm{C}\right)\)

True or false: (a) For molecules with similar molecular weights, the dispersion forces become stronger as the molecules become more polarizable. (b) For the noble gases the dispersion forces decrease while the boiling points increase as you go down the column in the periodic table. (c) In terms of the total attractive forces for a given substance dipole- dipole interactions, when present, are always larger than dispersion forces. (d) All other factors being the same, dispersion forces between linear molecules are greater than dispersion forces between molecules whose shapes are nearly spherical.
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