Problem 88 - 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 complete combustion of C3H8 and CH3CH2COCH3 produces the largest number of moles of H2O (6.0 moles), while the complete combustion of C2H5OH produces the least moles of H2O (4.5 moles).

Step 1: 1. Write balanced combustion reactions for each compound

To determine the number of moles of H2O produced by the complete combustion of each compound, we need to write out the balanced chemical equations: For C2H5OH: \[ C_2H_5OH + 3O_2 \rightarrow 2CO_2 + 3H_2O \] For C3H8: \[ C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \] For CH3CH2COCH3: \[ CH_3CH_2COCH_3 + 5O_2 \rightarrow 4CO_2 + 4H_2O \]

Step 2: 2. Calculate the moles of H2O produced

Since we start with 1.5 moles of each compound, we can now calculate the moles of H2O produced by multiplying the coefficient of H2O in each balanced equation by 1.5 moles: For C2H5OH: \[ 3 \cdot 1.5 \: \text{moles H}_2O = 4.5 \: \text{moles H}_2O \] For C3H8: \[ 4 \cdot 1.5 \: \text{moles H}_2O = 6.0 \: \text{moles H}_2O \] For CH3CH2COCH3: \[ 4 \cdot 1.5 \: \text{moles H}_2O = 6.0 \: \text{moles H}_2O \]

Step 3: 3. Compare the moles of H2O produced and determine the largest and smallest

Now that we have calculated the moles of H2O produced by each compound when completely combusted, we can compare these values: - C2H5OH produces 4.5 moles of H2O. - C3H8 produces 6.0 moles of H2O. - CH3CH2COCH3 produces 6.0 moles of H2O. From this comparison, it's clear that the complete combustion of C3H8 and CH3CH2COCH3 produces the largest number of moles of H2O (6.0 moles), and the complete combustion of C2H5OH produces the least moles of H2O (4.5 moles).

Key Concepts

Balanced Chemical Equations

A balanced chemical equation is crucial for understanding the stoichiometry of a reaction. It tells us not only how reactants turn into products but also the proportions in which they do so. In a chemical equation, like the combustion reactions given for organic compounds, every atom on one side of the equation must appear in the same quantity on the other side.
The equations for the combustion of ethanol \[ C_2H_5OH + 3O_2 \rightarrow 2CO_2 + 3H_2O \],propane \[ C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \], and acetone \[ CH_3CH_2COCH_3 + 5O_2 \rightarrow 4CO_2 + 4H_2O \] show how oxygen combines with the compounds to produce carbon dioxide and water.

• The coefficients in front of molecules indicate the number of molecules or moles involved.
• Balancing ensures that mass is conserved and calculations on products like water can be accurately made.

Atoms can't be created or destroyed, so balanced equations help in understanding chemical transformations accurately.

Moles of Water

Calculating moles of water from combustion requires the balanced chemical equations from the previous section. The coefficients of the water molecules in these equations are key. For example, these coefficients tell us the ratio of water produced per mole of the compound combusted.
In our specific chemical reactions:

• Ethanol (\(C_2H_5OH\)) produces 3 moles of water per mole of ethanol.
• Propane (\(C_3H_8\)) results in 4 moles of water per mole of propane combusted.
• Acetone (\(CH_3CH_2COCH_3\)) similarly produces 4 moles of water per mole.

To find out how much water these reactions would yield, multiply the coefficients with the moles present, in this case, 1.5 moles. So, ethanol, propane, and acetone produce 4.5, 6.0, and 6.0 moles of water respectively.
Understanding moles helps chemists predict the outcomes of reactions quantitatively—it's the bridge between the macroscopic world that we can see and weigh and the microscopic world of atoms and molecules.

Organic Compounds Combustion

Combustion of organic compounds is a chemical reaction where the compound reacts with oxygen to release energy, usually as heat and light. This reaction typically results in the formation of carbon dioxide and water. The combustion process involves breaking chemical bonds in the reactants and forming new ones in the products.
In an educational context, understanding combustion is significant because:

• It involves the basic principles of redox reactions, where oxidation involves the loss of electrons and reduction involves the gain of electrons.
• Organic compounds like ethanol \(C_2H_5OH\), propane \(C_3H_8\), and acetone \(CH_3CH_2COCH_3\) serve as good examples because they are commonly encountered in everyday life.
• Predicting the products of combustion and their amounts offers insight into energy production and efficiency.

Since all organic combustion reactions lead to the production of water and carbon dioxide, being familiar with these reactions and being able to balance them offers a solid foundation for more advanced study in chemistry and chemical engineering.