Problem 98 - Chemistry An Atoms First Approach

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)?

Step-by-Step Solution

Answer

Gray tin has a more ordered structure and smaller positional probability compared to white tin. This is because gray tin is stable at lower temperatures, where atoms or molecules have lower kinetic energy, leading to a more predictable and less variable arrangement.

Step 1: Understanding White and Gray Tin

White tin is a metallic form of tin with a tetragonal crystal structure, and it is stable at room temperature and above. On the other hand, gray tin is a non-metallic form of tin with a cubic crystal structure, and it is stable at lower temperatures below roughly 13.2℃. As the temperature changes, tin undergoes a phase transition between white and gray forms.

Step 2: Relationship Between Temperature Stability and Ordered Structure

The more ordered a structure is, the lower its positional probability. Positional probability refers to the number of ways atoms or molecules can be arranged in a given structure. A structure with a higher degree of order will have the most predictable and least variable arrangement of atoms, leading to a small positional probability. In contrast, a less ordered structure will have a greater positional probability because atoms or molecules can be arranged in a higher number of ways.

Step 3: Relating Temperature Stability to Ordered Structure

Generally, a more ordered structure will be stable at lower temperatures due to the lower kinetic energy of the atoms or molecules providing a smaller positional probability. At higher temperatures, where atoms or molecules have higher kinetic energy, a less ordered structure with larger positional probability may be more stable as it allows for more atomic or molecular movement and arrangements.

Step 4: Determining the More Ordered Structure

Considering the temperature stability information provided, we know that gray tin is stable at lower temperatures, while white tin is stable at room temperature and above. Based on the relationship between temperature stability and ordered structure, we can conclude that gray tin, which is stable at lower temperatures, has a more ordered structure and smaller positional probability compared to white tin. So, the gray tin form has a more ordered structure and smaller positional probability.