I don't understand how to find the formula of a hydrate. Here's one of the question. if you guide me through it I think I'll be able to do the rest of them. Thanks :)

When 100g of ZnSO4x�œH2O is heated, 43.86g of water is given off. Calculate the formula of the hydrate.

ZnSO4xH20 �¨ ZnSO4 + xH2O

No. of moles of H2O = mass �€ molar mass
= 43.86 �€ 18
= 2.4367 mols

No. of moles of ZnSO4xH20
= mass �€ molar mass
= 100 �€ (161 + 18x) mols
No. of moles of ZnSO4xH20
= 1/x X no. of moles of H2O
= 1/x X 2.4367
= i.e. 2.4367/x mols
Therefore, 2.4367/x = 100 �€ (161 + 18x)

Solving the equation,
100x = 2.4367 (161+18x)
56.1394x = 392.3087
x = 6.990
= 7 (whole no.)
Hence the formula is ZnSO4. 7H2O
There are 7 water molecules.

Please note that those missing symbols mean divide. i.e.

no. of moles = mass/molar mass

To find the formula of the hydrate, we need to determine the number of water molecules (x) associated with each formula unit of ZnSO4.

Let's break down the problem step-by-step:

Step 1: Calculate the molar mass of ZnSO4
The molar mass of ZnSO4 can be calculated by adding up the atomic masses of each element:
Zn: 65.38 g/mol
S: 32.06 g/mol
O (4 times): 16.00 g/mol = 64.00 g/mol

Molar mass of ZnSO4 = 65.38 g/mol + 32.06 g/mol + 64.00 g/mol = 161.44 g/mol

Step 2: Calculate the molar mass of H2O
The molar mass of H2O is calculated by adding the atomic masses of hydrogen and oxygen:
H (2 times): 1.01 g/mol = 2.02 g/mol
O: 16.00 g/mol

Molar mass of H2O = 2.02 g/mol + 16.00 g/mol = 18.02 g/mol

Step 3: Calculate the moles of ZnSO4
Moles of ZnSO4 = mass of ZnSO4 / molar mass of ZnSO4
Moles of ZnSO4 = 100 g / 161.44 g/mol

Step 4: Calculate the moles of water lost
Moles of water lost = mass of water lost / molar mass of water
Moles of water lost = 43.86 g / 18.02 g/mol

Step 5: Calculate the ratio of moles of water lost to moles of ZnSO4
Ratio = moles of water lost / moles of ZnSO4

Step 6: Simplify the ratio to whole numbers to find the formula of the hydrate
Multiply the ratio obtained in Step 5 by the smallest whole number to obtain a whole number ratio.

For example,
If the ratio calculated in Step 5 is 2.8, multiply by 5 to get a whole number ratio of 14.

The resulting ratio represents the number of water molecules associated with each formula unit of ZnSO4.

Therefore, the formula of the hydrate ZnSO4x�œH2O is ZnSO4·14H2O.

To find the formula of a hydrate, you need to determine the number of water molecules associated with each formula unit of the compound. In this case, you are given the mass of the hydrate and the mass of water that is given off when it is heated.

Here are the steps to solve this problem:

Step 1: Calculate the mass of the anhydrous salt.
Since the mass of the hydrate is given as 100g, and the mass of water given off is 43.86g, you can calculate the mass of the anhydrous salt (ZnSO4) by subtracting the mass of water from the total mass of the hydrate:

Mass of anhydrous salt = Mass of hydrate - Mass of water
= 100g - 43.86g
= 56.14g

So, the mass of the anhydrous salt (ZnSO4) is 56.14g.

Step 2: Calculate the molar mass of the anhydrous salt.
To find the formula, you need to know the molar mass of the anhydrous salt (ZnSO4). You can find the molar mass of ZnSO4 by looking up the atomic masses of zinc (Zn), sulfur (S), and oxygen (O) on the periodic table:
Zn: atomic mass = 65.38 g/mol
S: atomic mass = 32.06 g/mol
O: atomic mass = 16.00 g/mol (there are 4 oxygen atoms in ZnSO4)

Molar mass of ZnSO4 = (molar mass of Zn) + (molar mass of S) + (molar mass of 4 O)
= 65.38 g/mol + 32.06 g/mol + (4 * 16.00 g/mol)
= 161.38 g/mol

So, the molar mass of ZnSO4 is 161.38 g/mol.

Step 3: Calculate the number of formula units in the anhydrous salt.
This step involves dividing the mass of the anhydrous salt (obtained in Step 1) by the molar mass of the anhydrous salt (obtained in Step 2):

Number of formula units = Mass of anhydrous salt / Molar mass of anhydrous salt
= 56.14g / 161.38 g/mol
≈ 0.35 mol

So, there are approximately 0.35 moles of ZnSO4 in the sample.

Step 4: Calculate the number of moles of water.
Since the molar mass of water is 18.02 g/mol, you can calculate the number of moles of water that were given off when the hydrate was heated:

Number of moles of water = Mass of water / Molar mass of water
= 43.86g / 18.02 g/mol
≈ 2.44 mol

So, there are approximately 2.44 moles of water in the sample.

Step 5: Determine the ratio of water to anhydrous salt.
To find the formula of the hydrate, divide the number of moles of water by the number of moles of anhydrous salt:

Water : Anhydrous salt = 2.44 mol : 0.35 mol

To simplify this ratio, you can divide each mole value by the smallest value (0.35 mol):

Water : Anhydrous salt = 2.44 mol / 0.35 mol : 0.35 mol / 0.35 mol
= 6.97 : 1

So, the ratio of water to anhydrous salt is approximately 7:1.

Step 6: Write the formula of the hydrate.
Based on the ratio determined in Step 5, you can write the formula of the hydrate as:

ZnSO4 · 7H2O

Therefore, the formula of the hydrate is ZnSO4 · 7H2O.

I hope this explanation helps! Let me know if you have any further questions.