A You are given the following data for ethanol, C2 H5 OH. Normal melting point -117^∘ C Normal b

A You are given the following data for ethanol, C2 H5 OH....

A You are given the following data for ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$. Normal melting point $-117^{\circ} \mathrm{C}$ Normal boiling point $78.0^{\circ} \mathrm{C}$ Critical temperature $243^{\circ} \mathrm{C}$ Critical pressure $63.0 \mathrm{~atm}$ Assume that the triple point is slightly lower in temperature than the melting point and that the vapor pressure at the triple point is about $10^{-5}$ torr. (a) Sketch a phase diagram for ethanol. (b) Ethanol at 1 atm and $140 .{ }^{\circ} \mathrm{C}$ is compressed to $70 .$ atm. Are two phases present at any time during this process? (c) Ethanol at 1 atm and $270 .{ }^{\circ} \mathrm{C}$ is compressed to 70 . atm. Are two phases present at any time during this process?

A You are given the following data for ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$.
Normal melting point $-117^{\circ} \mathrm{C}$
Normal boiling point $78.0^{\circ} \mathrm{C}$
Critical temperature $243^{\circ} \mathrm{C}$
Critical pressure $63.0 \mathrm{~atm}$
Assume that the triple point is slightly lower in temperature than the melting point and that the vapor pressure at the triple point is about $10^{-5}$ torr. (a) Sketch a phase diagram for ethanol. (b) Ethanol at 1 atm and $140 .{ }^{\circ} \mathrm{C}$ is compressed to $70 .$ atm. Are two phases present at any time during this process? (c) Ethanol at 1 atm and $270 .{ }^{\circ} \mathrm{C}$ is compressed to 70 . atm. Are two phases present at any time during this process?

Key Concepts

Phase Diagram

A phase diagram is a graphical representation that shows the equilibrium conditions between different phases of a substance (solid, liquid, and gas) as a function of temperature and pressure. It highlights the boundaries at which phase transitions occur and allows one to predict the state of a substance under different conditions.

Triple Point

The triple point is the unique set of conditions (a specific temperature and pressure) at which all three phases of a substance coexist in equilibrium. This concept is important in determining the full phase behavior of a substance and serves as a reference point in constructing phase diagrams.

Critical Point

The critical point marks the end of the liquid-gas phase boundary on a phase diagram. Beyond this point, the distinction between liquid and gas phases vanishes, and the substance exists as a supercritical fluid. It is characterized by a critical temperature and critical pressure.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid (or sometimes solid) phase at a given temperature. It plays a crucial role in phase transitions, particularly in determining the boiling point where the vapor pressure equals the external pressure.

Phase Equilibrium

Phase equilibrium refers to the state in which different phases of a substance coexist without any net change in their amounts over time. This equilibrium is determined by the balance of thermodynamic variables like temperature and pressure, and is depicted on a phase diagram.

Isothermal Compression

Isothermal compression involves changing the pressure of a substance while maintaining a constant temperature. Understanding how a substance moves through its phase diagram during compression is essential for predicting whether phase transitions will occur, such as moving into or out of a two-phase region.

Transcript

00:01 In this question, we are going to sketch the phase diagram for ethanol.

00:07 So let's define what we are given.

00:10 So we have a normal melting point and boiling point.

00:13 So this is the melting point and boiling point at one atmosphere of pressure.

00:20 The critical temperature and critical pressure gives us the critical point.

00:25 The critical point is a point at which the substance is between two phases, liquid, and gas.

00:40 The triple point is the point at which all three phases coexist with one another at the same time.

00:49 So let's do our sketch.

00:51 We're going to do two axes.

00:53 On the y -axis, we have pressure in atmospheres.

00:56 On the excesses, we have temperature and degrees celsius.

01:02 So our phase diagram generally is going to look like a y that is going sideways and the curve between the liquid and gas phases generally does curve a little bit more.

01:15 Than it's all in liquid, but it depends on the substance and as long as you kind of show a little bit of a curve.

01:24 That should be fine.

01:27 So i just want to get the general sketch down.

01:36 But now we're going to label the parts that we're given.

01:41 So first of all, at one atmosphere of pressure, we're going to draw a line over to where we have the line that indicates the face.

01:56 Change between solid and liquid.

01:59 And then we're going to draw a line down to temperature, the x -axis.

02:03 And then we're going to label that as the melting point, because that is the normal melting point, where it goes from the solid to a liquid.

02:10 So then again, going back to one atmosphere of pressure, we are going to be drawing another line to the line between the liquid and the gas phase.

02:23 We're going to label the place where crosses the x -axis as the boiling point because that's where it's turning from the liquid to the gas so that's all at one atmosphere because it's the normal melting point and boiling point and as you know stp has standard pressure as one atmosphere so it would make sense okay so now let's label the critical point so the critical point is basically the point right where the line between the liquid and the gas phase ends in the point.

03:05 So that's where the liquid and gas coexist simultaneously.

03:10 So we're just going to label, we're going to find a critical pressure, 63 atmospheres on the y -axis, draw a line over.

03:20 And when we hit the line between liquid and gas, we're just going to draw a line down to the x -axis, to the critical temperature, 245 degrees celsius.

03:29 And then we're just going to put a point.

03:31 There that is going to be our critical point we just label it cp that's critical point so now we're going to try to label the triple point so the triple point is pretty low we're given the triple point in tor so we're going to just convert it to atmosphere so we have it in the same units so one atmosphere is equal to 760 tor so divide that by 760 and we get the pressure in atmospheres...

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