Number of bridge oxygen atoms in a silicate mineral


> 
> Total number of oxygen atom(s) which act(s) as bridge between any two silicon atoms in a mineral with composition $\ce{MM’Si3O\_x}$ $(\ce{M}$ is the divalent metal ion and $\ce{M’}$ is the tetravalent metal ion).
> 
> 
> 


This is the question I have been stuck on. I do not understand how to approach it. Are we supposed to used the concepts of silicates? Like sheet silicate, chain silicate etc. or interstitial salts concepts?


Also, I don’t know whether it is possible to draw the structure as $x$ is a variable. Any hint would be appreciated.


P.S. Answer given is 3.




I am answering it to let others know that I have got the satisfactory answer, thanks to andselisk.


Since $\ce{M}$ is divalent and $\ce{M’}$ tetravalent, they exist as $\ce{\overset{2+}{M}}$ and $\ce{\overset{4+}{M’}},$ respectively. The anionic part is $\ce{[\overset{+4}{Si}\_3\overset{-2}{O}\_x]^6-},$ and taking oxidation numbers into consideration, $x = 9.$ $\ce{[Si3O9]^6-}$ moiety implies cyclic metasilicates:


[![Cyclic silicate anion [Si3O9]^6-](https://i.stack.imgur.com/TKNMs.png)](https://i.stack.imgur.com/TKNMs.png)


There are three bridging oxygen atoms per ring or per formula unit. A real life example for the mineral from the problem could be [benitoite $\ce{BaTiSi3O9}$](https://en.wikipedia.org/wiki/Benitoite).


 9