mol% TiO2 is mixed with 99.9 mol% Al2O3 and reacted to form a non-stoichiometric homogeneous solid solution.

(a) Write 3 defect reactions:
- All TiO2 atoms go into regular sites.
- All anions go into regular sites.
- All cations go into regular sites.

(b) Addition of TiO2 to Al2O3 generates defects. Calculate the net variation of mass for each of the reactions in (a) in relation to perfect Al2O3 by considering the result of the defect reaction, e.g., Ti substituting for Al (gain of mass mTi – mAl =....). Which reaction generates the highest net gain of mass?

(c) For each defect reaction, write the chemical formula of the solid solution.

The question involves defect chemistry, specifically the inclusion of TiO2 into Al2O3 to form a non-stoichiometric solid solution. Defect reactions would involve Ti4+ replacing Al3+, which results in an increase in mass because Ti is heavier than Al. The general chemical formula for the solid solution could be written as (Al2-xTix)O3, where x represents the fraction of Al replaced by Ti.

Explanation:

The student has posed a question related to the formation of a non-stoichiometric homogeneous solid solution when mol% TiO2 is mixed with 99.9 mol% Al2O3 (alumina).

Defect Reactions

Since specific defect reactions are not provided in the question, a generic explanation would be necessary:

Ti4+ replacing Al3+ would lead to vacancies or the need for additional cations to compensate for the charge difference.

O2- going into regular sites does not change if we're assuming all anions occupy regular sites.

Al3+ going into regular sites is expected and would be unaltered if only Ti is replacing Al.

Net Variation of Mass

To calculate net variation of mass for each reaction, we consider the mass difference between Ti and Al cations:

Gain of mass = mTi - mAl

The atomic mass of Ti is approximately 47.867 g/mol, and that of Al is approximately 26.982 g/mol. Thus, a substitution defect where Ti replaces Al would lead to an increase in mass due to the heavier Ti atoms. As more Ti is added, the mass gain would increase, making this the defect with the highest net gain of mass.

Chemical Formula of the Solid Solution

Chemical formulas for the solid solutions in each defect scenario would depend on the specific amounts and types of defects, but as Ti replaces Al in the lattice, the general form could be written as (Al2-xTix)O3, where x represents the fraction of Al replaced by Ti.