Finding a stoichiometric coefficient

[rustynail]

Hello, I am currently taking a college level chemistry class. I am struggling with this problem, any help would be greatly appreciated.

Homework Statement

We have a certain quantity of

$$CuSO_{4} \cdot \gamma H_{2}O$$

If our sample is formed of (25,5% Cu), (12% S), (57,7% O) and (4.04% H), what is the value of gamma ?

Homework Equations

None given.

The Attempt at a Solution

I have determined the mass of 1mol of each element, the mass of 1mol of CuSO_4 (111.611g) and really, I'm stuck there.

Please don't spoil the fun for me, just give me some hints.

(edit) : I have done this much more :

Mass of 1mol Cu = 63.546g

(63.546g/111.611g)*100 = 56.94% Cu in CuSO_4

56.94%/25.5% = 2.2328 (increment factor)

So the mass of the hydrated CuSO_4 should be

111.611g * 2,2328= 249.21g

249.21g - 111.611g = 137.6g H2O

and 137.6g/18(g/mol)= 7.6 mol H2O

but it does not give me an integer...

 

[AGNuke]

Try some Approximations in calculations. For example, Molar Mass of Cu is good as 63.5.

 

[rustynail]

thanks AGNuke, you mean that some approximations could get me closer to an integer coefficient? Do you think my attempt at a solution made sense?

 

[AGNuke]

No. You can apply the percentage "after" you had taken the molar mass of all the compound (including the hydration) part in consideration.
Take molar mass of compound as M[CuSO₄]+γ[M(H₂O)]

Also, you took the molar mass of CuSO₄ incorrect.

And don't panic if you don't get answer in integer. Just try rounding them up or down.

 

[DeeNos]

Hello! It looks like you have made some good progress so far. To find the stoichiometric coefficient (gamma), you will need to use the molar ratio between Cu and H2O in the compound CuSO4·γH2O. This means that for every 1 mole of Cu, there should be γ moles of H2O.

You have already calculated the mass of 1 mole of Cu and the mass of 1 mole of CuSO4. To find the mass of 1 mole of H2O, you can subtract the mass of 1 mole of CuSO4 from the total mass of the compound. Then, use the molar mass of H2O to convert this mass to moles.

Once you have the moles of H2O, you can use the molar ratio between Cu and H2O to solve for gamma. Remember, the molar ratio is the ratio of moles of one element to moles of another in a compound.

I hope this helps! Keep up the good work and don't hesitate to ask for more clarification if needed. Good luck!