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Homework 9 Solutions - Physical Chemistry I | CHEM 3410, Assignments of Physical Chemistry

Material Type: Assignment; Professor: Richard; Class: PHYSICAL CHEMISTRY I; Subject: Chemistry; University: The Richard Stockton College of New Jersey; Term: Fall 2008;

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The Richard Stockton College of New Jersey
Chemistry Program, School of Natural Sciences and Mathematics
PO Box 195, Pomoma, NJ
CHEM 3410: Physical Chemistry I Fall 2008
Homework 9— Solutions
1. (a) Point A represents the melting point of pure Ge. Point B is the melting point of pure Si.
(b) At point C you would observe the solid solution (a single-phase mixture of Ge and Si solid).
At Point D you would have two phases: a liquid Ge–Si solutions and a solid Ge–Si solution.
At point E there would be a single liquid solution phase.
(c) Line F is the liquidus curve. Upon cooling it represents the temperature where solid will begin
to form out of the liquid.
(d) The cooling curve for line H is shown below. The first solid b egins to form at point A while
the last liquid solidifies at point B.
(e) Along line I, pure Si liquid is being cooled. For a single component system, there is a unique
melting point where you would observe a thermal arrest. The temperature would not continue
to decrease until all the liquid had solidified. A schematic of this is shown in the figure below.
(f) The free energy curves for the two phases must be drawn in a manner that clearly indicates
which phase(s) is stable.
The solid solution phase is stable for all compositions at 900C . The free energy curve for
the solid must be below the liquid for all compositions.
At 1200C , there are 3 regions of phase stability: liquid is stable from 0 to 18 wt% Si,
there is a two-phase equilibrium of solid + liquid between 18 wt% and 43 wt% Si, and the
solid solution is the stable phase at compositions above 43 wt% Si. The two phase region is
highlighted with a heavy common tangent line. This line indicates that the chemical potential
of Si in the solid is equal to that of Si in the solid in the two phase region (along the common
tangent). It also means the chemical potential of Ge in the solid equals the chemical potential
of Ge in the liquid in this composition range.
The liquid solution phase is stable for all compositions at 1450C . The free energy curve for
the liquid must be below the solid for all compositions.
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The Richard Stockton College of New Jersey

Chemistry Program, School of Natural Sciences and Mathematics PO Box 195, Pomoma, NJ

CHEM 3410: Physical Chemistry I — Fall 2008

Homework 9— Solutions

  1. (a) Point A represents the melting point of pure Ge. Point B is the melting point of pure Si.

(b) At point C you would observe the solid solution (a single-phase mixture of Ge and Si solid). At Point D you would have two phases: a liquid Ge–Si solutions and a solid Ge–Si solution. At point E there would be a single liquid solution phase. (c) Line F is the liquidus curve. Upon cooling it represents the temperature where solid will begin to form out of the liquid. (d) The cooling curve for line H is shown below. The first solid begins to form at point A while the last liquid solidifies at point B.

(e) Along line I, pure Si liquid is being cooled. For a single component system, there is a unique melting point where you would observe a thermal arrest. The temperature would not continue to decrease until all the liquid had solidified. A schematic of this is shown in the figure below.

(f) The free energy curves for the two phases must be drawn in a manner that clearly indicates which phase(s) is stable. The solid solution phase is stable for all compositions at 900◦C. The free energy curve for the solid must be below the liquid for all compositions. At 1200◦C , there are 3 regions of phase stability: liquid is stable from 0 to 18 wt% Si, there is a two-phase equilibrium of solid + liquid between 18 wt% and 43 wt% Si, and the solid solution is the stable phase at compositions above 43 wt% Si. The two phase region is highlighted with a heavy common tangent line. This line indicates that the chemical potential of Si in the solid is equal to that of Si in the solid in the two phase region (along the common tangent). It also means the chemical potential of Ge in the solid equals the chemical potential of Ge in the liquid in this composition range. The liquid solution phase is stable for all compositions at 1450◦C. The free energy curve for the liquid must be below the solid for all compositions.

  1. (a) Point A is the melting point of pure Ge. Point B is the melting point of pure Sb.

(b) Point C would be pure Ge, point D would be a two-phase mixture of Ge and Sb, and point E would be a single-phase liquid solutions of Ge and Sb. (c) Line F is the eutectic temperature where you would find all three phases in equilibrium. (d) Along line H you would expects to see a change of slope when you encounter the liquidus at around 800◦C. There would be a thermal arrest (plateau) at 592◦C corresponding to the eutectic temperature.

(e) Along line I, you would only observe a single thermal arrest (plateau) at the eutectic temper- ature. At this temperature the liquid transforms directly into the two solid phases (Ge and