Give the IUPAC and common names and structures of all ethers having the molecular formula \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}\).

Ethers are a class of organic compounds characterized by an oxygen atom bonded to two carbon atoms. This can be represented generically as \text{R}-O-\text{R}', where R and R' are hydrocarbons (alkyl or aryl groups). The key feature of ethers is the oxygen linkage between two carbon chains or rings. In ethers, the oxygen atom's lone pairs slightly repel the adjacent groups, creating a relatively stable and non-polar molecule. Examples in our context would compose combinations of a total of five carbons, fitting into the molecular formula \(\text{C}_5 \text{H}_{12} \text{O}\). Common examples of ethers include diethyl ether (\(\text{C}_2\text{H}_5\text{O}\text{C}_2\text{H}_5\)). Their stability and solubility properties make them useful in various chemical reactions, especially as solvents or intermediates in organic synthesis.

IUPAC nomenclature is a standardized method of naming organic compounds to ensure clarity and consistency. For ethers, the system focuses on two main parts: the alkyl groups attached to the oxygen and the longest carbon chain.
When naming ethers according to IUPAC rules:

• Identify the longest carbon chain attached to the oxygen atom, which becomes the parent hydrocarbon.
• Name the other group as an alkoxy substituent (e.g., \(\text{methoxy}\text{-}\text{, ethoxy}\text{-}\text{, propoxy}\text{-}\text{, etc}\text{.}\text{, etc}\text{.)}\text{.}\).
• Number the parent chain starting from the end nearest the alkoxy substituent for lowest locants.

For instance, one possible ether with \(\text{C}_5 \text{H}_{12} \text{O}\) would be named 1-methoxybutane, where a methoxy group (\(\text{CH}_3 \text{O}\text{-}\)) is attached to a four-carbon chain (\(\text{butane}\)). In this method, each ether derivative of \(\text{C}_5 \text{H}_{12} \text{O}\) can be systematically named, considering all different possible combinations.

Understanding organic chemistry structures is essential to grasping the composition of ethers. Structural formulas depict the arrangement of atoms and bonds within a molecule. Steps to draw these structures for ethers with \(\text{C}_5 \text{H}_{12} \text{O}\) include:

• Calculate the degree of unsaturation to determine potential double bonds, triple bonds, or rings. However, for \(\text{C}_5 \text{H}_{12} \text{O}\), expect straight or branched chains since there are no triple/double bonds.
• Combine carbon atoms to ensure all valencies are satisfied, remembering ethers feature one oxygen linked to two different carbon-containing groups.
• Explore all possible configurations, for instance, mixing one-carbon (methyl,\(\text{CH}_3\)) with four-carbons (butyl,\(\text{C}_4\text{H}_9\)), two with three, and more.

For example, structures include 1-ethoxypropane, 1-methoxybutane, and diethyl ether (Don’t confuse them with cyclic ethers unless specified). These visual arrangements offer insight into the molecule's reactivity and physical properties.

Molecular formula analysis involves determining the various combinations of atoms that result in the same molecular formula, here \(\text{C}_5\text{H}_{12}\text{O}\).
To analyze this specific ether:

• First, confirm the number of carbons, hydrogens, and oxygen aligns with possible ether structures. Ethers won't have double bonds but will have single bonds covalently connecting the oxygen.
• Break down the 5 carbon atoms into potential groups: permutations could yield 3+2 (propoxyethane), 4+1 (butoxy methane), among others. List each feasible structure.
• Utilize methods like condensation reaction details or mechanistic steps to visualize how these structures could form in practical scenarios.

By meticulously inspecting the molecular formula, one can confirm no isomers are omitted and ensure compliance with the unique characteristics of ethers. Advanced molecular formula scrutiny will adjust for stereo-isomers (if existing) and possible reaction pathways for these configurations.