[Borek]

Again, borrowed question, with source to be given later.

Sample of the potassium chloride contaminated with some other salt is not losing its mass on roasting in air nor in chlorine. When 2.44 g of the mixture was treated with concentrated sulfuric acid, 0.896 L of HCl was produced (STP). Obtained clear solution was added to the excess concentrated solution of K₂CO₃, precipitate was filtered and roasted, yielding 0.400g of non-volatile residue.

What substance (and in what mass percentage) was present in the sample?

[Caustikola]

From my calculations and assumptions, i think AlCl3 is present; 22.5%

[Borek]

I am not going to comment on results till at least Wednesday or Thursday, unless someone will show convincing and correct calculations together with the result.

[Wastrel]

How difficult is this problem?  Should we ignore weirdness in the question and take the problem at face value?

If I had a fairly pedestrian answer that was out by about 1% should I work it through again, massage the maths a little and take it with a pinch of isotope variation or should I be throwing that away, correcting the HCl for deviation from ideal gas law and go looking for something squaratey?

[Borek]

If you are within 1% chances are you are OK. For sure you don't need corrections for non-ideality.

[Borek]

OK, it is Saturday already.

It is not AlCl₃. Easy to check: if the 2.44g sample contains 22.5% of AlCl₃ it means it contains 0.5490 g of AlCl₃ and 1.891 g of KCl, or 4.117x10^-3 moles of AlCl₃ and 0.02537 moles of KCl. So amount of HCl produced would be 3*4.117x10^-3+0.02537=0.03772 moles. 0.03772 moles times 22.4 L (we are at STP) gives 0.845 L, clearly less than it was collected in the experiment.

[Wastrel]

I make a mixture of 1.495g KCl and 0.945g MgCl₂ (about 38.7%) quite close.  Residue of MgO would be 0.400g and HCl produced would be about 0.894 L.

[Borek]

I make a mixture of 1.495g KCl and 0.945g MgCl₂ (about 38.7%) quite close.  Residue of MgO would be 0.400g and HCl produced would be about 0.894 L.

And that's the correct answer (book I use lists 38.9% of MgCl₂).

Question was from 11^th International Chemistry Olympiad.

[Wastrel]

This was strange question.  Concentrated sulphuric acid was added to the chloride and the resulting solution was clear, but by inference that is a solution of the sulphate in concentrated sulphuric acid rather than water.  We are told HCl was produced but it doesn't tell us it was the only gas, it's an assumption.

I have tidied my method for posterity.

Pure KCl would not give enough HCl gas so the adulterating salt must contain chloride.  So the mixture is _(1-p)KCl + _pMCl where p is the mole fraction of adulterant and M is just inert mass. 

The amount of HCl produced is 0.896/22.4 = 0.04 Moles which is the amount of chloride in the mixture.  So,

2.44 / ((1-p)*(39.1+35.5)+p*(M+35.5)) = 0.04
...
p = 13.6 /(39.1 - M)

The residue after roasting is almost certainly either a carbonate or an oxide.

For a carbonate M₂CO₃ the amount of mass we would expect is the number of moles of MCl multiplied by the molecular mass of the carbonate, which is,

0.04*p*(M + 30) = 0.4
...
p = 10/(M+30)

We can now solve for M.

13.6 /(39.1 - M) = 10/(M+30)

13.6 (M+30) = 10(39.1 - M)

13.6M+408 = 391-10M
3.6M = -17

Negative masses for atoms are not valid so carbonates don't work and I struck off lithium chloride.

Same procedure for oxide, M₂O.
p = 10/(M+8)
and solve,
13.6 /(39.1 - M) = 10/(M+8)
...
23.6M = 282.2

When done to higher precision M=12.26..

M can be any number or fraction of an atom, so long as there is 1 chloride ion per M of other stuff.  Close solutions with oxide products were magnesium chloride and titanium tetrachloride but unless it forms a double salt with potassium chloride the latter wouldn't have survived the roasting in air/chlorine part.  Aluminium trichloride does do this I think incidentally but the mass's weigh off.

After picking magnesium, it's atomic mass per chloride then provides two slightly different values for p according to which measurement you use, the volume of HCl or the mass of oxide.  Maybe an effect due to rounding atomic masses.