Physical Chemistry week 7 Wednesday February 20, 2013 page 1
Consider a two dimensional diagram with temperature on the vertical axis and mole fraction of
substance A on the horizontal axis. This graph has a curve that starts on the bottom near the left side,
comes up to a maximum, then goes back down to the bottom near the right side. Underneath this curve
there are two phases. Above this curve there is one phase. At the very top of the curve is the maximum
temperature to have two phases. This is called the upper critical temperature. For any point D under
the curve, the lever rule applies: (nA+nB)(l1)=(nA+nB)(l2).
Consider a two dimensional diagram with temperature on the vertical axis and mole fraction of
substance A on the horizontal axis. A curve starts at the left side near the top and comes down, then
goes most of the way across before coming up to touch the right side near the top. This is for a solution
of H2O and (C2H5)3N. The bottom of the curve is the lower critical temperature. Above the curve there
are two phases. Below the curve there is one phase, due to hydrogen bonding in this case. The lower
critical temperature is about 0°C in this case.
Consider a two dimensional diagram with temperature on the vertical axis and mole fraction on the
horizontal axis. This is for nicotine and water. Nicotine is alkaloid. In the middle of the graph is a
completely enclosed curve, roughly shaped like a circle. Inside the curve there are two phases. Outside
the curve there is one phase. The top of the curve is the upper critical temperature. The bottom of the
curve is the lower critical temperature. The upper critical temperature is due to the entropy effect:
TΔS > ΔH.
Two component solid-liquid equilibrium
Let A and B be miscible in all proportions in the liquid phase and completely immiscible in the solid
phase.
Consider a two dimensional graph with temperature on the vertical axis and mole fraction of A on the
horizontal axis. Pressure is constant. Just above the bottom is a horizontal line from side to side. Below
this curve there is pure solid A and pure solid B. On this curve is point E. Coming up from E is a curve up
and left all the way to the left side to point TB*. TB* is the melting point of pure B. This curve is the
freezing point depression of B due to the addition of A. Below this curve is a liquid solution and solid B.
The lever rule applies here. Also from point E is a curve up and right all the way to the right side to
point TA*. TA* is the melting point of pure A. This curve is the freezing point depression of pure A due to
the addition of B. Below this curve is a liquid solution and solid A. The lever rule applies here. Above
the two curves that come up from E there is liquid solution. Start in the liquid solution part above the
left curve at a point we’ll call R. Come down to the curve and call that point F. The tie line goes all the
way to the left, so pure B freezes out at this point. Come down below this curve but above the
horizontal line to a point we’ll call H. The lever rule shows that pure B is still coming out here. Go all the
way down to the horizontal line to a point we’ll call K. At point K there are three phases: solid A, solid B,
and liquid solution. Here, the phase rule gives f=c-p+2=2-3+1 but P is constant so f=0. E is the eutectic
point. Eutectic means easily melted. This is the minimum melting point.
Solid solutions
Substance A and substance B mix and form a solid solution at the molecular (atomic) level.
1. Similar chemical properties
2. Similar crystal structure
3. Appropriate radius ratio
I complete miscibility
II partial miscibility
III complete immiscibility
Interstitial solid solution
Have one type of atom in nice neat rows and columns. Have another type of atom in between those
atoms. The first type of atom is Fe. The second type of atom is C. This is called steel.
Substitutional solid solution
Have nice near rows and columns of atoms. Any atom can be one element or the other with no
necessary pattern. One type is Ni. The other type is Cu. For Ni, r=0.125nm. For Cu, R=0.128nm.
A “nickel” coin is 25% Ni by weight and 75% copper by weight. This solution is harder than either pure
metal and more resistant to corrosion that either pure metal.
Liquid phase miscibility and solid phase miscibility
Consider a two dimensional diagram with temperature on the vertical axis and mole fraction of nickel on
the horizontal axis. This is for copper and nickel. There is a point on the left side and a higher point on
the right side. Two curves go from the left point to the right point, one higher than the other. Above
the higher curve is a liquid solution. Below the bottom curve is a solid solution. Between the two curves
is both liquid solution and solid solution. Start at any arbitrary point above the top curve and come
down. The first solid to come out is an alloy richer is nickel since nickel has the higher melting point of
the two. The top curve is called the freezing curve. The bottom curve is called the melting curve. At
the melting curve the solid solution that comes out will have the same composition as the original liquid
solution. Normally adding impurity causes freezing point depression but in this case starting at the left
with pure copper and adding nickel, the nickel causes freezing point elevation instead. Likewise, if the
solvent is more volatile, adding impurity will cause boiling point depression instead of elevation.
Consider a two dimensional graph with temperature on the vertical axis and mole fraction of gold on the
horizontal axis. This is for copper and gold. At the left side is a point at 1083°C. At the right side is a
point at 1063°C. In the graph is a point near the middle. From this point two curves go up and left to
that left point with one above the other and two curve goes up and right to that right point with one
above the other. Below all the curves is solid solution. Above all the curves is liquid solution, also called
melt. Between the two left curves is solid solution and liquid solution. Between the two right curves is
solid solution and liquid solution. This type of curve has a minimum melting mixture, which is nonideal.
Consider a two dimensional diagram with temperature on the vertical axis and mole fraction on the
horizontal axis. This is for optical isomers of carvoxime with d (dextro) at the left and l (levo) on the
right. Near the top middle is a point. Coming down and left from that are two curves that meet at the
left side. Coming down and right from that are two curves that meat at the right side. Below all these
curves is solid solution. Above all these curves is melt. Between each pair of curves is solid solution and
liquid solution.
Liquid phase miscibility and solid phase partial miscibility
Consider a two dimensional diagram with temperature on the vertical axis and mole fraction of copper
on the horizontal axis. This is for silver and copper. Near the middle left is a point. From this left point
a straight line comes down and left to the origin. From that left point is a straight line that goes up and
left to the left side near the top. Near the middle right is a point. From this right point a straight line
goes down and right to the bottom right corner. From this same right point a straight line goes up and
right to the right side near the top. A straight line connects the left point to the right point. There is
also a point on this line near the middle. From here a straight line goes up and left to the same point
that came from the first left point. Also from this middle point, a straight line goes up and right to the
same point that came from the right point. Above all the curves is liquid solution. Below all the curves
is α + β. At the middle left is α. At the middle right is β. Left of center and below the top curve is liquid
solution + α. Right of center and below the top curve is liquid solution and β.
Continued on Friday