Refer to the phase diagram for sulfur. (The vertical axis is...

Refer to the phase diagram for sulfur. (The vertical axis is on a logarithmic scale.) Sulfur has two solid forms, monoclinic and rhombic. Which physical states should be present at equilibrium under the following conditions? (a) $10^{-1}$ atm and $110^{\circ} \mathrm{C}$; (b) $10^{-5}$ atm and $80^{\circ} \mathrm{C}$; (c) $5 \times 103 \mathrm{~atm}$ and $160^{\circ} \mathrm{C}$; (d) $10^{-1}$ atm and $80^{\circ} \mathrm{C}$; (e) $10^{-5}$ atm and $140^{\circ} \mathrm{C}$; (f) 1 atm and $140^{\circ} \mathrm{C} .$

Refer to the phase diagram for sulfur. (The vertical axis is on a logarithmic scale.) Sulfur has two solid forms, monoclinic and rhombic.
Which physical states should be present at equilibrium under the following conditions? (a) $10^{-1}$ atm and $110^{\circ} \mathrm{C}$;
(b) $10^{-5}$ atm and $80^{\circ} \mathrm{C}$;
(c) $5 \times 103 \mathrm{~atm}$ and $160^{\circ} \mathrm{C}$;
(d) $10^{-1}$ atm and $80^{\circ} \mathrm{C}$;
(e) $10^{-5}$ atm and $140^{\circ} \mathrm{C}$; (f) 1 atm and $140^{\circ} \mathrm{C} .$

Key Concepts

Phase Diagram

A phase diagram is a graphical representation that shows the conditions of temperature and pressure under which different phases of a substance are stable. It maps out the regions where distinct phases such as solid, liquid, and gas exist, as well as the boundaries where phase changes occur.

Phase Equilibrium

Phase equilibrium refers to the state in which different phases of a substance coexist without any net change in their proportions. At equilibrium, the chemical potentials of each phase are equal, meaning that the system is stable and does not spontaneously shift from one phase to another.

Polymorphism

Polymorphism is the ability of a substance to exist in more than one crystalline form, each with distinct physical properties. In the context of phase diagrams, polymorphism is important because different solid structures can be stable under different temperature and pressure conditions.

Triple Point

The triple point is the unique set of conditions where three phases of a substance (typically solid, liquid, and gas) coexist in thermodynamic equilibrium. It is an essential concept in phase diagrams as it represents the intersection of multiple phase boundaries.

Logarithmic Scale

A logarithmic scale is used in graphing when a wide range of values is involved, allowing each order of magnitude to be represented equally. In phase diagrams, a logarithmic pressure axis can help illustrate the behavior of a substance over several orders of magnitude, making it easier to identify phase boundaries and transitions.

Transcript

00:01 So in this question, we're referring to this phase diagram.

00:03 So far has two forms, and we just want to know what physical state is present under the positive addition.

00:08 So for the first one, we have 10 to the negative one atmospheres of the pressure and 110 degrees celsius.

00:13 So we'll locate 10 to the negative one on the y -axis, and then we have 110 here.

00:19 So this is right in between these two.

00:21 So let's move over, and we can see we landed right in the monoclinic area.

00:26 So that means that it's monoclinic.

00:29 So let's do the next one.

00:31 The next one, let's locate the pressure.

00:33 So it's right here, 10 to the negative 5, and then we have 80 degrees celsius.

00:38 So there's 80 degrees celsius, 10 to negative 5.

00:40 We ended up in rhombic, so it will be bromic.

00:45 Now if we go to c, we have 5 times 10 to the 3 atmospheres and 160 degrees.

01:03 So let's go to 10 to the 3.

01:07 So that's all the way up there.

01:09 So we are doing five times 10 to the three.

01:13 So this is one times 10 to the three.

01:16 So five times 10 to the three would be a little bit higher, but it's still in the range over there.

01:22 So we can just do an approximation...

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