[VanKwisH]

A 3.81-g geological sample, containing the mineral Boulangerite (Pb5Sb4S11) as the only lead-bearing compound, is subjected to chemical treatment in which the lead is quantitatively recovered as solid PbCl2. The mass of PbCl2 obtained is 2.36 g.
What was the percentage (by mass) of Pb5Sb4S11 in the sample?

Ok.... here's what i've done
1) found % of Pb in Pbcl = 74.5%
2) using the %, i found the actual amount of grams in PbCl
2.36g * 0.745 = 1.7582g
3)Found the % of Pb in Pb5Sb4S11 = 55.23

since i know that all the Pb in Pb5Sb4S11 comes from the PbCl
did what sung said and did
Amount of Pb5Sb4S11 = Amount of Pb extracted / % Pb in mineral
which is 1.7582 / 0.5523 = 3.18g
from that I did 3.18g / 3.81(the original mass of the
sample) and got 83.5%, but it was wrong. What am I missing?

[Borek]

I am not sure what you did. Go moles of PbCl₂ -> moles of Pb -> moles of boulangerite route, this is safer and more reliable.

Not that it gives different result, I got 3.18g of boulangerite as well, or 83.6% (small difference - have you used rounded intermediate results?)

[VanKwisH]

yes i did..
and apparently i can't just use mole ratios...
because this is a sample right... so it contains things other than just the boulagerite
so we can't determine the complete mole ratio according to my prof.

but apparently the answer is wrong... i've  checked my steps and they seem appropriate
so where do i go from here?

[Wreath]

I think you should use mole ratios, because you have no other ways where to put lead, right? So there may be other compounds, but you can stick to the lead - containing.
Well, i did those calculations: since we have mole ratios 1/5...
aA + bB   sS

w[%]=a/s*M(A)/M(S)*m_S/m_sample*100
w[%]=1/5*1875,75/278,1*2,36/3,81*100

and i did the same: 83,5%. you sure that's wrong?  

[Borek]

apparently i can't just use mole ratios...

Yes you can. In fact as you have arrived to the same result (3.18g) you have used them, even if not directly.

How many moles of PbCl₂ are created per every mole of boulangerite?