When kaolinite clay [Al2(Si2O5)(OH)4] is heated to a sufficiently high temperature, chemi- cal water is driven off. (a) Under these circumstances, what is the com- position of the remaining product (in weight per- cent Al2O3)? (b) What are the liquidus and solidus tempera- tures of this material?

The molar mass of a substance is the weight of 1 mole of that substance, typically expressed in grams per mole (g/mol). It's calculated by adding up the atomic masses of all atoms in a molecule, based on the values found in the periodic table.

For kaolinite clay, which has the formula Al2(Si2O5)(OH)4, the molar mass is the sum of the molar masses of aluminum (Al), silicon (Si), oxygen (O), and hydrogen (H). The calculation goes as follows:
For Kaolinite Clay (Al2(Si2O5)(OH)4):\[\text{Molar mass} = 2*(26.98) + 2*(28.09) + 9*(16.00) + 8*(1.01) = 258.16 \text{ g/mol}\]
Understanding the molar mass is critical because it helps in determining the proportions of each element within a compound and is the foundation for further calculations, such as determining the weight percentage of elements in a compound.

When analyzing the composition of a compound like kaolinite clay, weight percentage gives us an understanding of the relative mass of each component as compared to the total mass. It’s pivotal in material science when we want to know how much of each substance is present after a reaction or a process like thermal decomposition.

In this context, after kaolinite is heated and the water is driven off, we would calculate the weight percentage of aluminum oxide (Al2O3) in the residue as follows:
\[\text{Weight percentage of Al2O3} = \left( \frac{\text{Mass of Al2O3}}{\text{Mass of Al2O3} + \text{Mass of remaining kaolinite}} \right) * 100\]
The resulting number represents the proportion of Al2O3 in the remaining product, which in this case is about 35.4%. This calculation informs us of the purity of the material post-reaction, which is crucial for various applications where specific material characteristics are required.

In material science, the liquidus and solidus temperatures are important parameters that describe the temperatures at which a substance transitions from solid to liquid (melting) and vice versa. The liquidus temperature is the lowest temperature at which the whole material becomes a liquid, while the solidus temperature is the highest temperature at which the material is completely solid.

For aluminum oxide (Al2O3), a critical component of kaolinite clay after thermal decomposition, these temperatures are particularly high due to Al2O3's strong ionic bonds and crystalline structure. According to phase diagrams and scientific literature:
- Liquidus temperature of Al2O3 ≈ 2054°C
- Solidus temperature of Al2O3 ≈ 2072°C

Knowing these temperatures is vital, especially during processes involving high heat, such as metal smelting and ceramic production, where controlling the state of materials is crucial to the quality of the final products.