Question

Without per forming detailed calculations, which of the following yields the same mass of \(\mathrm{CO}_{2}(\mathrm{g})\) per gram of compound as does ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) when burned in excess oxygen? (a) \(\mathrm{H}_{2} \mathrm{CO}\); (b) \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH} ;\) (c) \(\mathrm{HOCH}_{2} \mathrm{CHOHCH}_{2} \mathrm{OH}\) (d) \(\mathrm{CH}_{3} \mathrm{OCH}_{3} ;\) (e) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\)

Short answer

Hence, the compound that yields the same mass of \(CO_2(g)\) per gram of compound as does ethanol when burned in excess oxygen is Ethylene Glycol (\(HOCH_2CH_2OH\)).

Step-by-step solution

Identifying the number of carbon atoms in ethanol

Ethanol (\(CH_3CH_2OH\)) has two carbon atoms.

Checking each compound for the same number of carbon atoms

(a) Formaldehyde (\(H_2CO\)) - 1 carbon atom. (b) Ethylene glycol (\(HOCH_2CH_2OH\)) - 2 carbon atoms. (c) Glycerol (\(HOCH_2CHOHCH_2OH\)) - 3 carbon atoms. (d) Dimethyl ether (\(CH_3OCH_3\)) - 2 carbon atoms. (e) Phenol (\(C6H5OH\)) - 6 carbon atoms.

Finding the correct compound

The two compounds Ethylene glycol and Dimethyl ether both have two carbon atoms, same as ethanol. In addition, none of the compounds have atoms other than carbon, hydrogen, and oxygen. Therefore, both of these two compounds will yield the same mass of CO2 per gram of compound as Ethanol - if we assume complete combustion is possible in all cases. Thus, the key lies in realizing that one compound, Dimethyl Ether, is an ether and the other, Ethylene Glycol, is an alcohol. Alcohols, in general, will produce the same amount of CO2 as ethanol per gram of compound, because of the same type of functional group.

Key concepts

Ethanol Combustion

Ethanol combustion is a chemical reaction where ethanol (\(\text{CH}_3\text{CH}_2\text{OH}\)) reacts with oxygen gas to produce carbon dioxide (\(\text{CO}_2\)) and water (\(\text{H}_2\text{O}\)). This reaction occurs because ethanol is an organic compound known as an alcohol, which contains an -OH (hydroxyl) group.
The combustion process releases energy, which is why ethanol is commonly used as a fuel in various applications. During complete combustion, all of the carbon atoms in ethanol are oxidized to produce carbon dioxide:

\[ \text{C}_2\text{H}_5\text{OH} + 3\text{O}_2 \rightarrow 2\text{CO}_2 + 3\text{H}_2\text{O} \]
This balanced chemical equation demonstrates that for every molecule of ethanol burned, two molecules of \(\text{CO}_2\) are produced.

• It's important to ensure enough oxygen is present to achieve complete combustion.
• Incomplete combustion can occur if oxygen is limited, producing carbon monoxide instead of carbon dioxide.

Functional Groups in Chemistry

In chemistry, functional groups refer to specific groups of atoms within molecules that determine the main properties and reactivities of those molecules. Functional groups are like the building blocks of organic chemistry and include groups such as hydroxyl (-OH), carboxyl (-COOH), and amino (-NH2).

A functional group can drastically alter the behavior of the molecule they are part of.

• Alcohols such as ethanol contain a hydroxyl (-OH) group, making them more polar and capable of hydrogen bonding.
• Ethers, like dimethyl ether (\(\text{CH}_3\text{OCH}_3\)), contain an oxygen atom connected to two alkyl or aryl groups, affecting their boiling points and solubility.

Understanding functional groups is crucial for predicting how different compounds will react, especially during combustion and other chemical transformations.

Carbon Dioxide Production

Carbon dioxide (\(\text{CO}_2\)) production is a common outcome of many chemical reactions, primarily combustion. During the combustion of carbon-based compounds like ethanol, carbon is oxidized to carbon dioxide, releasing energy in the process.

In the provided exercise, the focus is on assessing which compounds produce similar amounts of \(\text{CO}_2\) per gram as ethanol during combustion.

• By analyzing the number of carbon atoms, we can predict \(\text{CO}_2\) production.
• Compounds with the same number of carbon atoms as ethanol (such as ethylene glycol and dimethyl ether) are likely to yield a similar mass of \(\text{CO}_2\) under similar conditions.

This knowledge is vital, especially in industrial applications and environmental science, where managing \(\text{CO}_2\) emissions is crucial for sustainability.