A chemist heats a sample of copper(II) sulfate and finds that 63.9% of the mass is copper(II) sulfate and the other 36.1% by mass is the water. What is the formula of the hydrate?
Take a 100 g sample to give you
63.9 g CuSO4 and
36.1 g H2O
Convert to mols.
mols CuSO4 = grams/molar mass = ?
mols H2O = grams/molar mass = ?
Now find the ratio of the two with the smaller number no less than 1.00. The easy way to do that is to divide the smaller number by itself (thereby getting 1.00). Then divide the other number by the same small number. Round to whole numbers. That will give you (CuSO4)1.00.xH2O where x is the other whole number.
To determine the formula of the hydrate, we need to analyze the information provided.
First, we know that 63.9% of the sample's mass is copper(II) sulfate, and the remaining 36.1% is water. This indicates that the compound is a hydrate, meaning it contains water molecules within its crystal structure.
Next, we need to calculate the molar masses of copper(II) sulfate (CuSO4) and water (H2O).
- Copper(II) sulfate (CuSO4):
- Atomic mass of Cu = 63.55 g/mol
- Atomic mass of S = 32.07 g/mol
- Atomic mass of O (4 oxygen atoms) = 16.00 g/mol × 4 = 64.00 g/mol
- Molar mass of CuSO4 = 63.55 g/mol + 32.07 g/mol + 64.00 g/mol = 159.62 g/mol
- Water (H2O):
- Atomic mass of H (2 hydrogen atoms) = 1.01 g/mol × 2 = 2.02 g/mol
- Atomic mass of O = 16.00 g/mol
- Molar mass of H2O = 2.02 g/mol + 16.00 g/mol = 18.02 g/mol
Now, we can use the molar masses to calculate the ratio of copper(II) sulfate to water in the hydrate.
- Ratio of copper(II) sulfate to water:
- Copper(II) sulfate mass = 63.9% of the sample mass
- Water mass = 36.1% of the sample mass
Using the molar masses, we can calculate the number of moles for each component:
- Moles of copper(II) sulfate = (Copper(II) sulfate mass / Molar mass of CuSO4)
- Moles of water = (Water mass / Molar mass of H2O)
Finally, divide both mole values by the smaller mole value to obtain the ratio of moles and simplify it to get the smallest whole number ratio. The result will be the subscripts of the formula.
For example, if the ratio is 2:3, it means that there are 2 moles of copper(II) sulfate for every 3 moles of water. Thus, the formula of the hydrate is CuSO4 · 3H2O.
Perform the calculations using the provided percentages and molar masses to determine the formula of the hydrate.