(1) A sample of the hydrate CuSO4.5H2O has a mass of 12.5g. (a) how many molecules of hydrogen are contained in this hydrate? If the hydrate is completely dehydrated.
1.51 x 10 ^23 molecules
1.51×10^23
5.00moles
Well, let's not "hydrate" the situation any further. To calculate the number of molecules of hydrogen in the hydrate, we need to find the molar mass of the compound first.
The molar mass of CuSO4 is approximately 159.6 g/mol, and the molar mass of H2O is approximately 18.0 g/mol. Since there are five water molecules (H2O) per CuSO4, the molar mass of CuSO4.5H2O is approximately:
(1 * 159.6 g/mol) + (5 * 18.0 g/mol) = 249.6 g/mol
Now, we can find the number of moles by dividing the mass of the hydrate (12.5 g) by its molar mass (249.6 g/mol):
12.5 g / 249.6 g/mol ≈ 0.05 mol
Since there are 2 hydrogen atoms per water molecule, and each mole of H2 contains 6.022 x 10^23 molecules (Avogadro's number), we'll have:
0.05 mol * 5 * 2 * 6.022 x 10^23 molecules/mol ≈ 6.022 x 10^22 molecules of hydrogen
So, approximately 6.022 x 10^22 molecules of hydrogen will be contained in the fully dehydrated hydrate.
That's a lot of "hydro-gems"! Now I'm ready to make some hydrating jokes. Do you need a laugh?
How many molecules of hydrogen
To find the number of molecules of hydrogen in the hydrate CuSO4 · 5H2O, you can follow these steps:
Step 1: Calculate the molar mass of the hydrate.
To do this, you need to determine the molar mass of each element present in the hydrate and multiply it by its respective subscript.
The molar mass of CuSO4 is:
Cu: 63.55 g/mol
S: 32.07 g/mol
O: 16.00 g/mol (x 4 because there are four oxygen atoms)
Total molar mass of CuSO4 is: 63.55 + 32.07 + (16.00 x 4) = 159.62 g/mol
The molar mass of H2O is:
H: 1.01 g/mol (x 2 because there are two hydrogen atoms)
O: 16.00 g/mol
Total molar mass of H2O is: 1.01 x 2 + 16.00 = 18.02 g/mol
The molar mass of the hydrate, CuSO4 · 5H2O, is the sum of the molar masses of CuSO4 and 5H2O:
Molar mass of CuSO4 · 5H2O = 159.62 + (18.02 x 5) = 249.72 g/mol
Step 2: Convert the mass of the hydrate to moles.
You can do this by dividing the mass of the hydrate by its molar mass:
Moles of hydrate = Mass of hydrate / Molar mass of hydrate
Moles of hydrate = 12.5 g / 249.72 g/mol = 0.0500 mol
Step 3: Determine the molar ratio.
For every one mole of CuSO4 · 5H2O, there are 5 moles of H2O.
Therefore, the moles of hydrogen atoms is 5 times the moles of the hydrate:
Moles of hydrogen = Moles of hydrate x 5
Moles of hydrogen = 0.0500 mol x 5 = 0.250 mol
Step 4: Convert moles of hydrogen to molecules.
To convert moles to molecules, you can use Avogadro's number, which is 6.022 × 10^23 molecules/mol.
Number of molecules of hydrogen = Moles of hydrogen x Avogadro's number
Number of molecules of hydrogen = 0.250 mol x 6.022 × 10^23 molecules/mol = 1.505 × 10^23 molecules
So, if the hydrate CuSO4 · 5H2O is completely dehydrated, it will produce 1.505 × 10^23 molecules of hydrogen.