A hydrate of copper (II) sulfate with formula CuSO4.xH2O has a molar mass of 250.0 g/mol. 2.545 g of hydrate is heated and 63.85% of the residue is found after heating.

a) Determine the value of x in the formula of the compound
b) What is the molecular formula of the hydrate?

CuSo4.xHO

a) Let's first calculate the mass of the residue after heating the hydrate. We know that 63.85% of the residue is found, so we can calculate:

Mass of residue = 63.85% x 2.545 g = 1.625 g

Next, we need to calculate the mass of CuSO4 in the hydrate. Subtracting the mass of the residue from the initial mass of the hydrate, we have:

Mass of CuSO4 = 2.545 g - 1.625 g = 0.92 g

The molar mass of CuSO4 is 159.61 g/mol. We can use this information to calculate the number of moles of CuSO4:

Number of moles of CuSO4 = Mass of CuSO4 / Molar mass of CuSO4
= 0.92 g / 159.61 g/mol
= 0.00577 mol

Now, let's find the number of moles of water (H2O). The molar mass of water is 18.015 g/mol. We can use this information to calculate the number of moles of water:

Number of moles of water = Mass of water / Molar mass of water
= (2.545 g - 0.92 g) / 18.015 g/mol
= 0.073 mol

Since the ratio of CuSO4 to water in the formula is 1: x, we can find the value of x by comparing the number of moles of CuSO4 and water. From the calculations above, we see that there are approximately 0.00577 moles of CuSO4 and 0.073 moles of water. To simplify the ratio, we can divide both by 0.00577 to get:

Number of moles of CuSO4 = 1
Number of moles of water = 0.073 / 0.00577 = 12.65

Therefore, the value of x in the formula CuSO4.xH2O is approximately 12.65.

b) Now that we know the value of x, we can write the molecular formula of the hydrate. The formula CuSO4.xH2O suggests that for every 1 mole of CuSO4, there are x moles of water. Since x is approximately 12.65, the molecular formula of the hydrate is CuSO4.12.65H2O.

To solve this problem, we need to use the concept of hydrates and molar mass. Let's break it down step by step:

a) Determining the value of x in the formula of the compound:
1. Calculate the percentage of water lost during heating: 100% - 63.85% = 36.15%.
2. Convert the mass of the water lost to moles. We know that the molar mass of water (H2O) is 18.015 g/mol, so:
moles of water lost = (mass of water lost) / (molar mass of water) = (2.545 g) / (18.015 g/mol)
3. The compound before heating consists of both the anhydrous salt and the water of hydration, so we must subtract the moles of water lost from the total moles of the compound before heating.
moles of anhydrous salt = total moles - moles of water lost
4. Now, we need to calculate the moles of the anhydrous salt. We can use the molar mass of the compound (250.0 g/mol) to convert the mass of the hydrate to moles:
moles of hydrate = (mass of hydrate) / (molar mass of hydrate) = (2.545 g) / (250.0 g/mol)
5. Finally, we can determine the value of x by equating the moles of the anhydrous salt and the moles of the hydrate, and solving for x:
moles of anhydrous salt = moles of hydrate - moles of water lost
x = (moles of hydrate - moles of anhydrous salt) / moles of water lost

b) Determining the molecular formula of the hydrate:
1. Calculate the moles of copper (II) sulfate (CuSO4) in the hydrate by multiplying the moles of the anhydrous salt by its coefficient in the formula, which is 1:
moles of copper (II) sulfate = moles of anhydrous salt * 1
2. To calculate the molecular formula, we need to find the ratio of moles of water to moles of copper (II) sulfate. Divide the moles of water by the moles of copper (II) sulfate:
ratio = moles of water / moles of copper (II) sulfate
3. Finally, we can write the molecular formula by multiplying the subscript x by the ratio we just found:
molecular formula = CuSO4 * ratio

By following these steps, you should be able to determine the value of x in the formula of the compound and find the molecular formula of the hydrate.

NAIL SNAIL NAIL SNAIL NAIL SNAIL NAIL SNAILNAIL SNAILNAIL SNAIL NAIL SNAIL NAIL SNAIL NAIL SNAIL NAIL SNAIL NAIL SNAIL NAIL SNAIL

mass hydrate before heat = 2.545 g

mass hydrate after heat = 2.545 x 0.6385 = 1.625 g = mass CuSO4
mass H2O = 2.545-1.625 = 0.9200 g
mols H2O = 0.9200/18 = 0.0511
mols CuSO4 = 1.625/159.6 = 0.01

Convert to integers and round to whole numbers for find answer to b. That will give you answer to a.
You can work this another way using the 250 g/mol in the problem and I did it another way.