Impurities Effect on the Melting Point

## Melting Point Diagrams

The typical behavior of an impure solid containing two components is summarized by the general phase diagram in Figure 6.7a. The furthest left side of the graph represents a sample that is pure compound "A," while the furthest right side of the graph represents a sample of pure compound "B." The lines mark the solid-liquid transition temperature (melting points). The melting point decreases the further the composition is from purity, toward the middle of the graph. In many mixtures, the minimum melting temperature for a mixture occurs at a certain composition of components, and is called the eutectic point (Figure 6.7a). Some systems do not have any eutectic points and some have multiple eutectic points.

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Figure 6.7: a) Generic phase diagram of a two-component system (A+B), b) Same diagram with additional markings.

An impure solid is typically heterogeneous on the microscopic level, with pure regions of each component distributed through the bulk solid much like granite. When an impure solid is warmed, microscopic melting first occurs in a pure region by the component with the lower melting point (compound A in Figure 6.7a). This microscopic melting is not visible to the eye.

The preliminary melting of compound A in Figure 6.7a forms tiny pools of liquid that begin to dissolve compound B from the bulk solid. As compound B is dissolved into the melt (causing it to become more impure), the freezing point of this mixture is depressed. Compound B will continue to dissolve in the melt, until it reaches the eutectic composition (point a in Figure 6.7b), and the system will continue to melt at this composition until the entirety of the minor component (the impurity) is dissolved. Once the minor component is completely dissolved, further melting continues of the bulk component. This increases the purity of the melt, so the melting temperature increases somewhat. The system follows the melting line in Figure 6.7b either to the left or right of the eutectic temperature (depending on which side of the eutectic point is started), adjusting its melting temperature as the bulk component increases its concentration in the melt. This continues until the entire sample is melted.

Although microscopic melting begins at the eutectic temperature, the first value of the melting range (when a droplet of liquid is seen with the eye) is not necessarily recorded at this temperature. A droplet of liquid is not seen until approximately $$10$$-$$20\%$$ of the sample has melted. Depending on the quantity of impurity, the system may have progressed far from the eutectic temperature (perhaps to point b in Figure 6.7b) before liquid becomes visible to the eye. The final value of the melting range is at the highest the melting point of the pure solid, but is often lower, reflecting the depressed melting point of the bulk solid. For example, a solid that is $$20\%$$ compound A and $$80\%$$ compound B would have a final melting temperature of point c in Figure 6.7b. The recorded melting range for this system would be at the maximum between temperatures a and c, but if the first droplet is seen at point b, the recorded melting range would be between temperatures b and c.

### Melting Point Depression (Lowering the M. P.)

Melting of a pure solid occurs at a higher temperature than melting of an impure solid, a concept called melting point depression (or freezing point depression). The melting point is the temperature where the solid and liquid phases are in equilibrium with each other, and the change in free energy $$\left( \Delta G^\text{o} \right)$$ for the process (solid $$\rightleftharpoons$$ liquid) is zero. $$\Delta G^\text{o}$$ is dependent on both the changes in enthalpy $$\left( \Delta H^\text{o} \right)$$ and entropy $$\left( \Delta S^\text{o} \right)$$ during the process (see versions of the Gibbs free energy equation in Figure 6.8b), but the changes in enthalpy are similar when melting a pure and impure solid as similar intermolecular forces are broken. Melting point depression is the result of different changes in entropy when melting a pure and impure solid.

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As solids are restricted in atomic motion, there is little difference in entropy between a pure and impure solid. However, there is a more significant difference in entropy between a pure and impure liquid, and an impure liquid has greater disorder and greater entropy. Melting of an impure solid into an impure liquid therefore has a larger change in entropy than melting a pure solid into a pure liquid (Figure 6.8a). A larger change in entropy corresponds to a lower melting temperature. This can be rationalized either mathematically or conceptually. A mathematical description is in Figure 6.8b: as $$\Delta S^\text{o}$$ is the denominator in the final equation, a larger $$\Delta S^\text{o}$$ corresponds to a smaller $$T_\text{melting}$$. A conceptual approach is to consider that melting occurs when the enthalpy $$\left( \Delta H^\text{o} \right)$$ and entropy components $$\left( T \Delta S^\text{o} \right)$$ are equal in magnitude (when $$\Delta G^\text{o} = 0$$). A larger $$\Delta S^\text{o}$$ means that a smaller temperature will be required to "match" the enthalpy component.