The aluminium sulphate hydrate contains 8.10 percent Al by mass. Calculate x, that is, the number of water molecules associated with each unit

Al2(SO4)3 = 342 grams / mol

H2O = 18 grams / mol
so
342 +18 x grams / mol total
Al = 27 so Al2 = 54 grams /mol
so
.081 = 54 / (342+18x)
answer is x times Avagadro's number

Damon has given you the correct answer strictly from a math viewpoint. I must say it is much simpler as a math problem than a chemistry problem; however, let me give you the chemical view. Remember either method should give the same/correct answer. Solving the math equation Damon gave gives x = 18. Here is the chemical approach.

Take a 100 grams sample of Al(SO4)3.xH2O. It will contain 8.1 g Al. How many mols is that? mols Al = g/atomic mass = 8.1/27 = 0.3.
Convert that to mols Al2(SO4)3.xH2O. That will be
0.3 mols Al x (1 mol Al2(SO4)3.xH2O/2 mols Al) = 0.15
Convert that to grams Al2(SO4)3. That is 0.15 x molar mass Al2(SO4)3 = 0.15 x 342 = 51.3 g. The sample weighed 100 g and this weighs 51.3 so 100-51.3 = 48.7 g H2O.
mols Al2(SO4)3 = 51.3/342 = 0.15 (but we already knew that from above)
mols H2O = 48.7/18 = 2.70. Now find the ratio. The easy way to do that is to divide both numbers by the smaller of the two. So,
mols Al(SO4)3 = 0.15/0.15 = 1.0
mols H2O = 2.70/18 = 18.0 and that makes the formula Al2(SO4)3.18H2O.
I must say the math way puts the chemistry way, at least in terms of simplicity and ease of working the problem, to shame.

To calculate the number of water molecules associated with each unit of aluminum sulfate hydrate, we need to determine the molar mass of aluminum sulfate and water, and then compare the mass of water to the mass of the entire hydrate.

The molar mass of aluminum sulfate (Al2(SO4)3) can be calculated as follows:
- The atomic mass of aluminum (Al) is 26.98 g/mol.
- The atomic mass of sulfur (S) is 32.07 g/mol.
- The atomic mass of oxygen (O) is 16.00 g/mol.
Therefore, the molar mass of aluminum sulfate is:
Molar mass of Al2(SO4)3 = (2 * 26.98 g/mol) + (3 * 32.07 g/mol) + (12 * 16.00 g/mol) = 342.15 g/mol.

Next, we calculate the mass of aluminum in one mole of aluminum sulfate:
Mass of Al in one mole of Al2(SO4)3 = (2 * 26.98 g/mol) = 53.96 g/mol.

Given that the aluminum sulfate hydrate contains 8.10% Al by mass, we can set up the equation:
Mass of Al in hydrate = (8.10/100) * mass of hydrate.

Let's assume the mass of the hydrate is 100g (to make calculations easier).

Mass of Al in hydrate = (8.10/100) * 100g = 8.10g.

Converting this mass of aluminum to moles:
Moles of Al in hydrate = (8.10g) / (53.96 g/mol) = 0.150 mol.

Finally, we need to determine the number of moles of water associated with each unit of aluminum:
Since each mole of aluminum sulfate corresponds to 6 moles of water, we can calculate the number of water molecules (x) as follows:
0.150 mol Al x (6 mol H2O / 1 mol Al) = 0.900 mol H2O.

Therefore, the number of water molecules associated with each unit of aluminum sulfate hydrate (x) is equal to 0.900.

To calculate the number of water molecules (x) associated with each unit of aluminum sulfate hydrate, we need to use the information given about the percent of aluminum in the compound.

The molecular formula of aluminum sulfate hydrate is Al2(SO4)3 · xH2O.

In this compound, there are 2 aluminum atoms (Al), 3 sulfate ions (SO4), and x number of water molecules (H2O).

Given that the compound contains 8.10 percent Al by mass, we can calculate the number of moles of aluminum.

First, assume we have 100 grams of the compound. Then, the mass of aluminum would be 8.10 grams (8.10 percent of 100 grams).

Next, we need to convert the mass of aluminum into moles. To do this, we divide the mass of aluminum by its molar mass. The molar mass of aluminum is 26.98 g/mol.

Number of moles of aluminum (n) = Mass of aluminum (m) / Molar mass of aluminum (M)
n = 8.10 g / 26.98 g/mol

Now, we need to find the moles of water associated with each mole of aluminum. According to the chemical formula, for every 2 moles of aluminum, there are x moles of water. Thus, we can set up the following ratio:

(2 moles of Al) / (n moles of H2O) = (2 / n)

Given that we are solving for x, we can set up another ratio:

(2 / n) = (x / 1)

Simplifying the equation above will give us the value of x:

(2 / n) = (x / 1)
2 = (x / n)
x = 2n

Therefore, the number of water molecules associated with each unit of aluminum sulfate hydrate is 2 times the number of moles of aluminum (n).