I was under the impression that chemistry almost exclusively involves valence electrons because there isn't enough energy to strip off electrons located closer to the nucleus.
If that is true, and elements in the same period have similar properties because they have the same number of valence electrons, then why is $\ce{SiO2}$ a solid and $\ce{CO2}$ a gas? Surely a difference in mass by a factor of 2.5 can't be that big a deal.
Is it because of a van der Waals force difference, because silicon has extra electrons which result in compounds being formed from it being more symmetrical than those formed from carbon?
Answer
It is because of the structure of the $\ce{CO2}$. Two of carbon's valence electrons hybridize into two $sp$ hybrid orbitals. As a result, the molecule is one dimensional with an angle of 180$^\circ$ between bonds and completely non-polar. The $\ce{Si}$, on the other hand, does not form such bonds and the angle is far from 180°, which in conjunction with oxygens high electronegativity makes it quite polar. Thus the interaction between neighboring $\ce{Si}$ and $\ce{O}$ atoms of different $\ce{SiO2}$ molecules is much higher and as a consequence you need much more energy to break the solid, giving it an increased melting point.
The mass (as discussed in various comments) does not play any role here since it is a matter of interaction or forces. The gravitational pull of single atoms or molecules is ridiculously small and never finds any considerations in such calculations (as it should!).
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