Question

From the information on the temperature stability of white and gray tin given in this chapter, which form would you expect to have the more ordered structure (have the smaller positional probability)?

Short answer

Gray tin is consists of more ordered structure.

Step-by-step solution

Define positional probability

Positional probability is a sort of probability that is based on the number of spatial arrangements that result in a specific condition.

Allotropic modification of tin                      

White tin, grey tin, and brittle tin are the three allotropic variations of tin that are known.

Grey tin is the cubic phase of tin that is not stable at room temperature. It transforms into white tin, a more stable phase in which a Sn atom has six closest neighbours in a highly deformed octahedral array. When white tin is chilled to $13.2{}^{°}C$, it transforms into grey tin.

The phase change according to the temperature

The change of the phase :

$Sn\left(gray\right)\to Sn\left(white\right)$

In the temperature above $13.2{}^{°}C$,the $∆G$ will be negative.Because the change is spontaneous in that temperature.

$∆G$ will be positive when the temperature is below $13.2{}^{°}C$.

The equation for the free energy is $\Delta G=\Delta H-\text{T}\Delta S$.

This will be positive when $∆H$ and $T∆S$ are positive.

Because $∆S$ is positive, the grey tin has a lower positional probability and consequently a more ordered structure.

So, gray tin is consists of more ordered structure.