Problem 86 - Chemistry The Central Science

Question

If \(1.5 \mathrm{~mol} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}, 1.5 \mathrm{~mol} \mathrm{C}_{3} \mathrm{H}_{8},\) and \(1.5 \mathrm{~mol} \mathrm{CH}_{3} \mathrm{CH}_{2}\) \(\mathrm{COCH}_{3}\) are completely combusted in oxygen, which produces the largest number of moles of \(\mathrm{H}_{2} \mathrm{O} ?\) Which produces the least? Explain.

Step-by-Step Solution

Answer

The compound which produces the largest number of moles of water when 1.5 moles are combusted is propane (C3H8) with 6.0 moles of H2O. Both ethanol (C2H5OH) and acetone (CH3CH2COCH3) produce the least number of moles of water with 4.5 moles of H2O each.

Step 1: Write down the combustion reactions

The combustion reactions of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}, \mathrm{C}_{3} \mathrm{H}_{8},\) and \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCH}_{3}\) are as follows: Ethanol (C2H5OH) combustion: \[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2} + 3 \mathrm{H}_{2} \mathrm{O}\] Propane (C3H8) combustion: \[\mathrm{C}_{3} \mathrm{H}_{8} + 5 \mathrm{O}_{2} \rightarrow 3 \mathrm{CO}_{2} + 4 \mathrm{H}_{2} \mathrm{O}\] Acetone (CH3CH2COCH3) combustion: \[\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCH}_{3} + 3.5 \mathrm{O}_{2} \rightarrow 3 \mathrm{CO}_{2} + 3 \mathrm{H}_{2} \mathrm{O}\]

Step 2: Calculate the number of moles of water produced

For each compound, we will calculate the number of moles of water produced when 1.5 moles are combusted. 1.5 moles of ethanol combustion: \[1.5 \times \frac{3}{1} = 4.5 \mathrm{~moles~H}_{2} \mathrm{O}\] 1.5 moles of propane combustion: \[1.5 \times \frac{4}{1} = 6.0 \mathrm{~moles~H}_{2} \mathrm{O}\] 1.5 moles of acetone combustion: \[1.5 \times \frac{3}{1} = 4.5 \mathrm{~moles~H}_{2} \mathrm{O}\]

Step 3: Compare the number of moles of water produced and draw conclusions

Based on the calculations above, the number of moles of water produced when 1.5 moles of each compound are combusted are: - Ethanol (C2H5OH): 4.5 moles of H2O - Propane (C3H8): 6.0 moles of H2O - Acetone (CH3CH2COCH3): 4.5 moles of H2O The compound which produces the largest number of moles of water is propane (C3H8), while ethanol (C2H5OH) and acetone (CH3CH2COCH3) both produce the least number of moles of water.

Key Concepts

Moles of Water

When substances undergo combustion, they react with oxygen to produce products such as carbon dioxide and water. Understanding the number of moles of water produced is essential in various chemical processes, including energy production and environmental analysis.

In a combustion reaction, you can use stoichiometry to determine the moles of water produced from a certain amount of reactant. This involves writing and balancing the chemical equation, and using the coefficients to relate the reactants to the product. For instance, if 1.5 moles of ethanol are combusted completely, the balanced chemical equation for this reaction tells us that 3 moles of water are produced per mole of ethanol. Therefore, multiplying 1.5 by the factor of 3 gives us 4.5 moles of water.

This fundamental concept is crucial because it allows chemists to predict the outcome of other chemical reactions simply by understanding these relationships in balanced equations.

Ethanol Combustion

Ethanol (C\(_2\)H\(_5\)OH) combustion is a reaction where ethanol reacts with oxygen (O\(_2\)) to produce water (H\(_2\)O) and carbon dioxide (CO\(_2\)). This chemical process releases energy, making ethanol a commonly used fuel.

In the combustion of ethanol, every molecule of ethanol produces three molecules of water. So, if you burn 1.5 moles of ethanol, using the balanced equation: C\(_2\)H\(_5\)OH + 3O\(_2\) \(\rightarrow\) 2CO\(_2\) + 3H\(_2\)O, you can calculate the number of water moles formed as 1.5 multiplied by 3, resulting in 4.5 moles of water.

This reaction is not only important in everyday applications like automobiles, but also in the production of energy from biofuels. Ethanol's role as a renewable energy source makes it significant in the quest for sustainable energy solutions.

Propane Combustion

Propane (C\(_3\)H\(_8\)) is a hydrocarbon that combusts in oxygen to produce carbon dioxide and water, releasing a significant amount of energy. This makes propane an excellent fuel choice for heating and cooking.

During propane combustion, as shown in the chemical equation C\(_3\)H\(_8\) + 5O\(_2\) \(\rightarrow\) 3CO\(_2\) + 4H\(_2\)O, 1 mole of propane yields 4 moles of water. Thus, burning 1.5 moles of propane results in 6.0 moles of water.

This makes propane combustion particularly efficient in terms of water production, when compared to other fuels such as ethanol or acetone. Its efficiency and energy output have made propane a staple in both residential and industrial energy applications.

Acetone Combustion

Acetone (CH\(_3\)CH\(_2\)COCH\(_3\)) is commonly known for its role as a solvent, but it can also undergo combustion. In a controlled environment, acetone reacts with oxygen to produce carbon dioxide and water.

According to the stoichiometry of the reaction CH\(_3\)CH\(_2\)COCH\(_3\) + 3.5O\(_2\) \(\rightarrow\) 3CO\(_2\) + 3H\(_2\)O, one mole of acetone will generate 3 moles of water. Hence, if 1.5 moles of acetone are combusted, 4.5 moles of water will be produced.

Although the water yield from acetone is similar to that from ethanol combustion, the application of acetone is different due to its solvent properties and volatility. This sheds light on the versatility in chemical uses beyond combustion.