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Step-by-Step Explanation
Step 1: Overview of Group 13 Oxides
Group 13 elements include Boron (B), Aluminium (Al), Gallium (Ga), Indium (In), and Thallium (Tl). Their oxides exhibit varying acidic, amphoteric, or basic properties depending on the metallic or non-metallic character of the element. As we move down the group, the metallic character increases and, correspondingly, so does the basicity of their oxides.
Step 2: Acidic Nature of Boron Trioxide (Statement I)
Boron is the least metallic in the group. Its oxide, $B_{2}O_{3}$, is composed of a non-metal (boron) bonded with oxygen. Non-metal oxides tend to be acidic in nature. Thus, $B_{2}O_{3}$ readily reacts with bases to form salts, confirming its acidic behavior. This supports Statement (I).
Step 3: Amphoteric Nature of Aluminium and Gallium Oxides (Statement II)
As we move from Boron to Aluminium and Gallium, the elements become more metallic than Boron but still retain partial non-metallic characteristics. Consequently, the oxides of Aluminium ($Al_{2}O_{3}$) and Gallium ($Ga_{2}O_{3}$) can react with both acids and bases, displaying amphoteric properties. This property is typical of metals in the βborderlineβ region between non-metals and true metals. Hence, $Al_{2}O_{3}$ and $Ga_{2}O_{3}$ are amphoteric oxides, validating Statement (II).
Step 4: Basic Nature of Indium and Thallium Oxides (Statement III)
Indium and Thallium are more metallic than Aluminium and Gallium. As metallic character increases, the oxides tend to become more basic. Therefore, $In_{2}O_{3}$ and $Tl_{2}O$ are predominantly basic oxides because they react readily with acids to form salts, but not as readily with bases as the amphoteric oxides do. This confirms Statement (III).
Step 5: Conclusion
All three statements (I), (II), and (III) accurately describe the acidic, amphoteric, and basic nature of Group 13 oxides moving from Boron down to Thallium. Hence, the correct answer includes all three statements.