Name all the alcohols that have the formula \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O} .\) How many ethers have the formula \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}\) ?

To find the isomers of C5 alcohols having the formula C5H12O, we can attach the hydroxyl group (-OH) to different carbons: 1. Attach the -OH group to the first carbon: \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) - This is 1-pentanol. 2. Attach the -OH group to the second carbon: \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}(\mathrm{OH})\mathrm{CH}_{2} \mathrm{CH}_{3}\) - This is 2-pentanol. 3. Attach the -OH group to the third carbon: \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH})\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) - This is 3-pentanol. Naming all the alcohols, we have: 1-pentanol, 2-pentanol, and 3-pentanol.

To find the isomers of C5 ethers having the formula C5H12O, we can connect the oxygen atom to different carbon atoms: 1. Connect the oxygen atom to two methyl groups: \(\mathrm{CH}_{3}\mathrm{O}\mathrm{CH}_{3}\) - This is dimethyl ether. However, it has the formula C2H6O, not C5H12O. So, this is not a valid option. 2. Connect the oxygen atom to a methyl group and an ethyl group: \(\mathrm{CH}_{3}\mathrm{O}\mathrm{C}_{2} \mathrm{H}_{5}\) - This is ethyl methyl ether. 3. Connect the oxygen atom to a methyl group and an isopropyl group: \(\mathrm{CH}_{3}\mathrm{O}\mathrm{CH}( \mathrm{CH}_{3}) \mathrm{CH}_{3}\) - This is isopropyl methyl ether. 4. Connect the oxygen atom to two ethyl groups: \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O} \mathrm{C}_{2} \mathrm{H}_{5}\) - This is diethyl ether. To answer the question, there are 3 alcohols having the formula C5H12O: 1-pentanol, 2-pentanol, and 3-pentanol. There are 3 ethers having the formula C5H12O: ethyl methyl ether, isopropyl methyl ether, and diethyl ether.