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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 a negative slope in the solid-liquid equilibrium line. This is because the density of solid gallium is lower than the density of the liquid phase, which is not commonly observed in materials. Hence, as the temperature increases at constant pressure, solid gallium transforms to higher-density liquid gallium.

Step by step solution

01

Recall Common Density Relationships in Phase Diagrams

In most materials, the solid phase has a higher density than the liquid phase. This is because, in the solid state, particles are more closely packed together. However, in this case, the solid phase of gallium has a lower density compared to the liquid phase just above its melting point. This is an unusual behavior in phase diagrams.
02

Observe How Density Relationships Affect Phase Diagrams

In the phase diagram of most materials, the solid-liquid equilibrium line has a positive slope because the solid phase is denser than the liquid phase. However, in the case of gallium, since the solid has a lower density than the liquid phase, the solid-liquid equilibrium line will likely have a negative slope. This negative slope indicates that as temperature increases at constant pressure, solid gallium transforms to liquid gallium, which has a higher density.
03

Identify the Unusual Feature in Gallium's Phase Diagram

Based on the information given, the unusual feature we would expect to find in the phase diagram of gallium is a negative slope in the solid-liquid equilibrium line. This is because the solid phase of gallium has a lower density than the liquid phase, which is not commonly observed in materials. So, the solid-liquid equilibrium line will show solid gallium transforming to higher-density liquid gallium with increasing temperature at a constant pressure.

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Most popular questions from this chapter

You are high up in the mountains and boil water to make some tea. However, when you drink your tea, it is not as hot as it should be. You try again and again, but the water is just not hot enough to make a hot cup of tea. Which is the best explanation for this result? (a) High in the mountains, it is probably very dry, and so the water is rapidly evaporating from your cup and cooling it. (b) High in the mountains, it is probably very windy, and so the water is rapidly evaporating from your cup and cooling it. (c) High in the mountains, the air pressure is significantly less than 1 atm, so the boiling point of water is much lower than at sea level. (d) High in the mountains, the air pressure is significantly less than 1 atm, so the boiling point of water is much higher than at sea level.

Name the phase transition in each of the following situations and indicate whether it is exothermic or endothermic: (a) When ice is heated, it turns to water. (b) Wet clothes dry on a warm summer day. (c) Frost appears on a window on a cold winter day. (d) Droplets of water appear on a cold glass of lemonade.

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 greater than dispersion forces.( \(\mathbf{d}\) ) All other factors being the same, dispersion forces between linear molecules are greater than those between molecules whose shapes are nearly spherical. (e) The larger the atom, the more polarizable it is.

Liquid butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\) is stored in cylinders to be used as a fuel. The normal boiling point of butane is listed as \(-0.5^{\circ} \mathrm{C}\) . (a) Suppose the tank is standing in the sun and reaches a temperature of \(35^{\circ} \mathrm{C}\) . Would you expect the pressure in the tank to be greater or less than atmospheric pressure? How does the pressure within the tank depend on how much liquid butane is in it? (b) Suppose the valve to the tank is opened and a few liters of butane are allowed to escape rapidly. What do you expect would happen to the temperature of the remaining liquid butane in the tank? Explain. (c) How much heat must be added to vaporize 250 \(\mathrm{g}\) of butane if its heat of vaporization is 21.3 \(\mathrm{kJ} / \mathrm{mol}\) ? What volume does this much butane occupy at 755 torr and \(35^{\circ} \mathrm{C} ?\)

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 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 \(78^{\circ} \mathrm{C} ?(\mathbf{b})\) How much heat is required to convert the same amount of ethanol at \(-155^{\circ} \mathrm{C}\) to the vapor phase at \(78^{\circ} \mathrm{C} ?\)
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