Question

If \(1.5 \mathrm{~mol}\) of each of the following compounds is completely combusted in oxygen, which one will produce the largest number of moles of \(\mathrm{H}_{2} \mathrm{O}\) ? Which will produce the least? Explain. \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}, \mathrm{C}_{3} \mathrm{H}_{8}, \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCH}_{3}\)

Short answer

When completely combusted in oxygen, C2H5OH (Ethanol) will produce the least number of moles of H2O (4.5 moles), while C3H8 (Propane) and CH3CH2COCH3 (Butanone) both produce the largest number of moles of H2O (6 moles).

Step-by-step solution

Write the balanced combustion reactions for each compound

For each compound, we need to write a combustion reaction that includes the compound reacting with oxygen (O2) to produce carbon dioxide (CO2) and water (H2O). Then, balance the reaction. 1. Combustion reaction for C2H5OH: \(C_{2}H_{5}OH + 3O_{2} \rightarrow 2CO_{2} + 3H_{2}O\) 2. Combustion reaction for C3H8: \(C_{3}H_{8} + 5O_{2} \rightarrow 3CO_{2} + 4H_{2}O\) 3. Combustion reaction for CH3CH2COCH3: \(CH_{3}CH_{2}COCH_{3} + 5O_{2} \rightarrow 4CO_{2} + 4H_{2}O\)

Analyze the stoichiometry of each reaction

Here, we'll determine the moles of H2O produced when 1.5 moles of each compound reacts with oxygen completely. 1. For C2H5OH: According to the balanced combustion reaction, 1 mole of C2H5OH will produce 3 moles of H2O. So, when 1.5 moles of C2H5OH react completely, the number of moles of H2O produced will be: \(1.5 \times 3 = 4.5\) moles 2. For C3H8: 1 mole of C3H8 produces 4 moles of H2O. So, when 1.5 moles of C3H8 react completely, the number of moles of H2O produced will be: \(1.5 \times 4 = 6\) moles 3. For CH3CH2COCH3: 1 mole of CH3CH2COCH3 produces 4 moles of H2O. So, when 1.5 moles of CH3CH2COCH3 react completely, moles of H2O produced will be: \(1.5 \times 4 = 6\) moles

Identify the compound producing the largest and least moles of H2O

Now, we can compare the moles of H2O produced from each reaction to determine which will produce the largest and least amounts: - C2H5OH produces 4.5 moles of H2O. - C3H8 produces 6 moles of H2O. - CH3CH2COCH3 produces 6 moles of H2O. From the values above, we can see that when combusted in oxygen, C2H5OH (Ethanol) will produce the least number of moles of H2O (4.5 moles), while C3H8 (Propane) and CH3CH2COCH3 (Butanone) both produce the largest number of moles of H2O (6 moles).

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a given reaction, ensuring no waste of materials and efficient resource management.

For every chemical reaction, stoichiometry uses the coefficients of each substance to determine the ratios they react or form with. These coefficients represent the number of moles of a substance. When we know the amount of one reactant, we can use stoichiometry to calculate the amount of another reactant or product needed or produced based on this molar ratio.

In the given exercise, stoichiometry is used to calculate the number of moles of water produced during the combustion of different organic compounds. By understanding the balanced chemical equations, we can utilize the stoichiometric coefficients to find out how many moles of water (H2O) are produced when a specific amount (in moles) of the compound reacts with oxygen.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions, showing the reactants and products along with their physical states. They display the conservation of mass principle by ensuring that the same number of each type of atom appears on both the reactant and product sides of the equation.

A balanced chemical equation has equal numbers of each type of atom on both sides, achieved by adjusting coefficients, which tell us how many molecules or moles of each compound participate in the reaction. Balancing chemical equations is essential for studying reaction stoichiometry, as it ensures the molar ratios used for calculations are correct.

In the exercise we're discussing, balanced chemical equations for the combustion of various compounds were written to understand the formation of water. It is fundamental for determining the amounts of products generated from the known quantities of reactants, assisting in predicting which compound will produce the largest or smallest amount of water.

Mole Concept

The mole concept is a fundamental principle in chemistry that connects the mass of a substance with the number of particles it contains. One mole is defined as the amount of substance that contains Avogadro's number (approximately 6.022 x 10^23) of particles, which could be atoms, molecules, ions, or electrons.

The mole allows chemists to count particles by weighing them. It bridges the microscopic world of atoms and molecules with the macroscopic world of grams and kilograms. Using the molar mass, which is the mass of one mole of a substance, we can convert between the mass of a substance and the number of moles it represents.

In the solution to our exercise, moles are used to quantify how much of each compound is reacting. With the mole concept, it is possible to compare the number of moles of water produced by the combustion of different amounts of organic compounds based on the balanced chemical equation for their combustion.