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If carbon monoxide can exist then why can't we have silicon monoxide? Both carbon and silicon belong to group 14 and have similar chemical properties.

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Short answer: It does, but unstable and hard to detect reliably..

Long answer.

First of all, we should look at structure of carbon dioxide and silicon dioxide. It is pretty easy to see that silicon forms polymeric dioxide with no double bonds, while carbon forms molecules with two double bonds. It is not an anomaly, obtaining silicon compounds with double bonds $\ce{Si-E}$ is tricky at best. This is attributed to larger atom size and more diffuse $p$-orbitals for silicon, making formation of double bonds unfavoured in most circumstances.

Now, let's look at carbon monooxide. It is a molecule with bonding very similar to that in dinitrogen molecule. The carbon atom has formal negative charge and oxygen has formal positive charge. However, because of high electronegativity of oxygen, electron density is pulled back towards oxygen, so the resulting dipole moment is diminutive. The molecules contains not double, but triple bond, making formation of similar molecule for silicon highly unfavorable. Still, silicon monooxide can be detected in gas phase.

Now, why solid phase with composition $\ce{SiO}$ is not formed is a more interesting question. Unfortunately, such questions not always have an easy answer, as rules guarding stoichiometry of solid phases is often base on arcane concepts of atom packings and electron count. It is entirely possible, that such a phase would be obtained one day in some exotic conditions. For clarity, I would use sterical considerations. $\ce{Si-O-Si}$ fragment is roughly linear, while $\ce{Si}$ atom favors tetrahedral coordination. Going from here, only two simple phases with no dangling bonds can be formed, based on diamond structure. It is structures with either $\ce{Si}$ or $\ce{SiO4}$ units in the structure nodes. It IS an oversimplification, as silicon dioxide forms many rather esoteric crystal structures, because $\ce{Si-O-Si}$ fragment isn't perfectly linear, but is is close enough in my opinion.

Do not rely on oxidation states in prediction of existence of covalent compounds, +2 oxidation state for silicon is a thing. It exists in $\ce{Si6Cl12}$, adopting structure similar to cyclohexane.

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Since your question is a school-level question, I think the answer is as follows. Though carbon and silicon have similar electron configurations in their valence orbitals, silicon is one shell higher than carbon. That makes the bonding energies different. $\ce{Si}$ only has an oxidation number of $\ce{+4}$, so it must have $\ce{2}$ oxygens to form $\ce{SiO2}$. Carbon, however, can have an oxidation number of $\ce{+4}$, $\ce{-4}$ and $\ce{2}$, so it can form $\ce{CO}$.

In reality, $\ce{SiO}$ exists in nature. Silicon monoxide is the chemical compound with the formula $\ce{SiO}$ where silicon is present in the oxidation state $\ce{+2}$. In the vapour phase it is a diatomic molecule. When $\ce{SiO}$ gas is cooled rapidly, it condenses to form a brown/black polymeric glassy material, $\ce{(SiO)_{n}}$, which is available commercially and used to deposit films of $\ce{SiO}$.

Silica itself, or refractory materials containing $\ce{SiO2}$, can be reduced with $\ce{H2}$ or $\ce{CO}$ at high temperatures,

$$\ce{SiO2(s) + H2(g) ⇌ SiO(g) + H2O(g)}$$

As the $\ce{SiO}$ product is collected and removed, the equilibrium shifts to the right, resulting in the continued consumption of $\ce{SiO2}$.

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    $\begingroup$ Whether the glassy material is actually silicon monoxide is a widely disputed issue. See this paper to get an insight. $\endgroup$ – Corundum Jan 1 '16 at 18:35
  • $\begingroup$ The gist I think is that SiO is a very reactive species and only really exists in a gaseous state under "exotic" laboratory conditions on earth. $\endgroup$ – MaxW Jan 1 '16 at 19:14

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