Concept:
China clay, scientifically known as Kaolin, is a primary clay mineral. Understanding its chemical formula is fundamental to calculating glaze and clay body recipes in ceramics.
Step 1:
Kaolin is a hydrated aluminum silicate. This means its molecular structure is composed of alumina ($Al_{2}O_{3}$), silica ($SiO_{2}$), and chemically bound water ($H_{2}O$).
Step 2:
In a theoretically pure sample of kaolinite, the molar ratio of these components is exactly 1 part alumina to 2 parts silica to 2 parts water.
Step 3:
Combining these parts yields the standard theoretical formula for China clay:
\[
Al_{2}O_{3} \cdot 2SiO_{2} \cdot 2H_{2}O
\]
Step 4:
Options (1), (3), and (4) contain incorrect molecular proportions and non-existent stable chemical combinations for clay minerals (such as $H_{3}O$ in a solid crystal lattice or $Al_{3}O_{2}$).
Step 5:
Matching our derived formula with the given choices, the correct answer is Option 2.
\[
\boxed{\text{(2) } Al_{2}O_{3} \cdot 2SiO_{2} \cdot 2H_{2}O}
\]