Explanation:

The formula for gibbsite is Al2O3.xH2O, where x represents the number of water molecules (H2O) present in the compound.

To determine the value of x, we need to analyze the chemical composition of gibbsite.

Chemical composition:
- The compound consists of Al2O3, which represents two aluminum atoms (Al) and three oxygen atoms (O).
- The compound also contains x number of water molecules (H2O), where x is the value we are trying to determine.

Analysis:
- Aluminum oxide (Al2O3) has a molar mass of 101.96 g/mol. This means that two aluminum atoms and three oxygen atoms together weigh 101.96 grams.
- Water (H2O) has a molar mass of 18.02 g/mol. This means that one water molecule weighs 18.02 grams.
- To determine the value of x, we need to find the ratio of the molar mass of water to the molar mass of gibbsite.

Calculation:
- The molar mass of gibbsite is the sum of the molar masses of Al2O3 and xH2O.
- The molar mass of gibbsite is given by: 2(Al) + 3(O) + x(H2O)
- The molar mass of water is given by: x(H2O) * (18.02 g/mol)
- Equating the molar masses of gibbsite and water, we get: 2(Al) + 3(O) + x(H2O) = x(H2O) * (18.02 g/mol)

Solving the equation:
- Rearranging the equation, we get: 2(Al) + 3(O) = x(H2O) * (18.02 g/mol) - x(H2O)
- Simplifying further, we get: 2(Al) + 3(O) = x(H2O)(18.02 g/mol - 1)
- Simplifying the right side of the equation, we get: 2(Al) + 3(O) = x(H2O)(17.02 g/mol)

Final calculation:
- The molar mass of gibbsite is 101.96 g/mol, which is the sum of the molar masses of Al2O3 and xH2O.
- The molar mass of water is 18.02 g/mol.
- From the equation 2(Al) + 3(O) = x(H2O)(17.02 g/mol), we can substitute the values to solve for x.
- 2(Al) + 3(O) = x(H2O)(17.02 g/mol)
- 2(27) + 3(16) = x(18.02)
- 54 + 48 = 18.02x
- 102 = 18.02x
- x = 102/18.02
- x ≈ 5.66

Since x represents the number of water molecules, it cannot be a fraction or decimal. Therefore, we round the value of x to the nearest whole number, which is 6.

However, the question asks for an integer value from 0