Question 7.4: The melting points of the pure compounds A and B are 120 and...
The melting points of the pure compounds A and B are 120 and 150 K, respectively. The two substances undergo a chemical reaction to form a solid compound AB:
A(l) + B(l) \xrightleftharpoons[]{} AB(s).
The melting point of the compound AB is 140 K. The system has two eutectic points at atmospheric pressure: one at the mole fraction 0.25 of component A (110 K) and another at 0.80 (90 K). Sketch the phase diagram of this system, and another diagram of the cooling curves at the three mole fraction values 0.25, 0.50, and 0.75 of A. Mark the temperatures given in the text and assign phases. Explain the shapes of the cooling curves.
The sketch of the phase diagram according to the data given looks like
the one below.
Stable phases are liquid (shaded upper area), pure solid B (left edge below 150 K), pure solid A (right edge below 120 K), and the solid compound AB (vertical line at x_{A} = 0.5, below 140 K). Eutectical lines at 90 K and 110 K are marked dashed.
Cooling curves at the given three mole fractions are sketched below.
At x _{A} = 0.25, there is a eutectic point. Thus, the liquid cools down until the eutectic temperature of 110 K, where it solidifies. The cooling rate slightly decreases with decreasing melt temperature until 110 K, but the temperature remains constant at this value during solidification. Once the entire system becomes a solid eutectic microcrystalline mixture, cooling down is continued again with a decreasing cooling rate.
At x _{A} = 0.5, there is a reaction forming the compound AB at solidification.
Thus, the liquid cools down until the solidification temperature of the compound at 140 K, where it solidifies, while the temperature remains constant. When the entire system becomes the solid compound AB, cooling down is continued again with a decreasing cooling rate.
At x _{A} = 0.75, the liquid begins to solidify at approximately 107 K (as it can be read from the phase diagram); thus, the cooling rate is abruptly slowed down due to the release of the heat of freezing. (The breakpoint is marked by an arrow. The solid formed is the compound AB). During this freezeout, the concentration continuously changes toward the eutectic concentration of x _{A} = 0.8, where the eutectic microcrystals are formed at the constant temperature 90 K, again without cooling.
As soon as the remaining liquid mixture becomes a solid eutectic microcrystalline mixture, cooling down is continued again with a decreasing cooling rate.
Note that this cooling behavior makes it possible to experimentally determine the phase diagram from cooling curves. A congruent freezing (where the composition of the solid formed is identical to the composition of the liquid) is always accompanied by a horizontal (constant temperature) portion of the cooling curve, while an abrupt change of the slope of the cooling curve (but with continuing cooldown) indicates the onset of formation of a solid phase when composition changes continuously. By determining the constant temperatures and the breakpoint temperatures at different mixture concentrations, we can construct the phase diagram.
