You are given the following data for butane, C4 H10. Normal melting point -138^∘ C -150 0 Critic

You are given the following data for butane, C4 H10. Normal...

You are given the following data for butane, $\mathrm{C}_{4} \mathrm{H}_{10}$. Normal melting point $-138^{\circ} \mathrm{C}$ -150 0 Critical Normal mal be ical te temperature boiling point $x$ $0^{\circ} \mathrm{C}$ Critical 1 1 $152^{\circ} \mathrm{C}$ pressure $38 \mathrm{~atm}$ Assume that the triple point is slightly lower in temperature than the melting point and that the vapor pressure at the triple (a) Sketch a phase diagram for butane. point is $3 \times 10^{-5}$ torr. (b) Butane at $1 \mathrm{~atm}$ and $140^{\circ} \mathrm{C}$ is compressed to $40 \mathrm{~atm}$. Are two phases present at any time during this process? (c) Butane at $1 \mathrm{~atm}$ and $200^{\circ} \mathrm{C}$ is compressed to $40 \mathrm{~atm}$. Are two phases present at any time during this process?

You are given the following data for butane, $\mathrm{C}_{4} \mathrm{H}_{10}$.
Normal melting point $-138^{\circ} \mathrm{C}$ -150
0 Critical Normal mal be
ical te temperature boiling point $x$ $0^{\circ} \mathrm{C}$
Critical 1 1 $152^{\circ} \mathrm{C}$ pressure $38 \mathrm{~atm}$
Assume that the triple point is slightly lower in temperature than the melting point and that the vapor pressure at the triple
(a) Sketch a phase diagram for butane. point is $3 \times 10^{-5}$ torr.
(b) Butane at $1 \mathrm{~atm}$ and $140^{\circ} \mathrm{C}$ is compressed to $40 \mathrm{~atm}$. Are two phases present at any time during this process? (c) Butane at $1 \mathrm{~atm}$ and $200^{\circ} \mathrm{C}$ is compressed to $40 \mathrm{~atm}$. Are two phases present at any time during this process?

Key Concepts

Phase Equilibrium and Two-Phase Regions

Phase equilibrium occurs when multiple phases of a substance coexist without net change over time. Two-phase regions in a phase diagram, such as the liquid-vapor coexistence region, indicate where a substance simultaneously exists in two different phases. Understanding these regions is critical for analyzing processes like isothermal or isobaric compression, where the system may pass through conditions that allow for the coexistence of two phases.

Critical Point

The critical point marks the end of the liquid-vapor equilibrium curve on a phase diagram. Beyond this point, the distinction between the liquid and gas phases disappears, so the substance becomes a supercritical fluid. This concept is key to understanding the limitations of phase transitions and the behavior of fluids under high pressure and temperature.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its condensed phases (solid or liquid) at a given temperature. It is essential for determining the phase boundaries in a phase diagram, as it helps predict the temperature and pressure at which a substance will undergo phase changes.

Phase Diagram

A phase diagram represents the equilibrium phases of a substance as functions of temperature and pressure. It includes boundaries that separate regions of stability for different phases and can feature critical points, triple points, and lines of phase coexistence, all of which are crucial for understanding the conditions under which a substance will exist as a solid, liquid, or gas.

Triple Point

The triple point is the unique set of conditions (temperature and pressure) where all three phases of a substance—solid, liquid, and gas—can coexist in equilibrium. It provides a fundamental fixed point that is important for calibrating measurement devices and understanding phase transitions.

Transcript

00:01 So in this problem, we need to draw a phase diagram for butane given the information provided.

00:09 So in the phase diagram, we're basically going to draw a v -like shape, and the lines in this phase diagram are going to be separated in different phases, solid liquid and gas.

00:25 So let's define the different parts that we're given.

00:32 The normal boiling point is the temperature at which the substance changes from liquid to gas.

00:41 So that's where it passes this line at one atmosphere.

00:46 So if we go to one atmosphere on the axis, which is pressure, we draw a line to the line between the gas and liquid phase, and then we find that temperature is going to be the normal boiling point and that's 0 degrees celsius.

01:02 Then the normal melting point is just going to be the melting point at one atmosphere.

01:12 So we just draw the line to the line between someone.

01:21 Then we have the pressure at the triple point.

01:23 So the pressure of the triple point is given to us in tor.

01:27 And then we just need to divide us 760 to give us the pressure in atmospheres.

01:33 And we're told that the temperature at the triple point is slightly less than the melting point.

01:39 So that makes sense because you can see if we draw the line down, it's actually a little bit less than the normal melting.

01:50 Then we're told the critical pressure and temperature.

01:56 So what that is is these are the pressure and temperature at which the line between the liquid and gas phase ends.

02:11 So basically this line between liquid and gas phase will end at this point...

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