Deducing a Molecular Formula from Mass Spectra

[PFuser1232]

Homework Statement

When reacted with a small quantity of water, SiCl₄ produces an oxychloride X, Si_xCl_yO_z. The mass spectrum of X shows peaks at mass numbers 133, 149, 247, 263 and 396. You should assume that the species responsible for all these peaks contain the ¹⁶O, ³⁵Cl and ²⁸Si isotopes only.

2. The attempt at a solution

The first step is fairly straightforward; the peak responsible for X is the 396 peak. Things start to get a little foggy when finding x, y and z.

$28x + 35y + 16z = 396$

How can I go about solving such an equation without using some sort of time-consuming trial and error method?

 

[Borek]

I would start assuming Si is bonded only to oxygen and chlorine (no Si-Si bonds) and there are no O-Cl bonds. That should give another equation, so you will be left with two unknowns only.

 

[PFuser1232]

I would start assuming Si is bonded only to oxygen and chlorine (no Si-Si bonds) and there are no O-Cl bonds. That should give another equation, so you will be left with two unknowns only.

I don't see why there can't be Si-Si bonds.

 

[PFuser1232]

I don't see why there can't be Si-Si bonds.

Same thing goes for O-Cl bonds.

 

[PFuser1232]

$28x + 35y + 16z = 396$
$x = z+1$
$y = 2x + 2$

Therefore:

$x = 3$
$y = 8$
$z = 2$

Which happens to me the right answer in my answer key. However, Si₄Cl₄O₉ and Si₈Cl₄O₂ are also given as acceptable alternatives.

 

[Borek]

It is not that Si-Si (or O-Cl) bonds are impossible, but in general in silicates silicon atoms are connected by an oxygen "bridge": Si-O-Si. Chlorine can replace oxygen, yielding Si-Cl, but it won't link two Si atoms like oxygen does.

Not sure what your equations are intended to mean. What I was hinting at is that all silicon valences are being used for bonds with oxygen and silicon, so 4x=y+2z.

 

[PFuser1232]

It is not that Si-Si (or O-Cl) bonds are impossible, but in general in silicates silicon atoms are connected by an oxygen "bridge": Si-O-Si. Chlorine can replace oxygen, yielding Si-Cl, but it won't link two Si atoms like oxygen does.

Not sure what your equations are intended to mean. What I was hinting at is that all silicon valences are being used for bonds with oxygen and silicon, so 4x=y+2z.

Could you please elaborate on how exactly you arrived at this equation? My reasoning was based on drawing a couple of structures wherein Si atoms are joined by O bridges and noticing the pattern of how the number of Si atoms varies with the number of O atoms ($x = z + 1$) and how the number of Cl atoms varies with the number of Si atoms ($y = 2x + 2$).

 

[Borek]

4x is a number of bonds that x atoms of silicone silicone can make. y+2z is number of bonds that y atoms of chlorine and z atoms of oxygen can make. All are used, and as silicon bonds only to oxygen or chlorine, 4x=y+2z.

It is just an analogy, you would use the same formula to describe an ionic compound where Si is always +4, Cl is -1 and oxygen is -2. Silicon oxychloride is not an ionic compound, but the analogy works.