Problem 66 - Chemistry

Question

Certain race cars use methanol (CH \(_{3} \mathrm{OH}\), also called wood alcohol) as a fuel. The combustion of methanol occurs according to the following equation:$$2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)$$In a particular reaction, 9.8 moles of \(\mathrm{CH}_{3} \mathrm{OH}\) are reacted with an excess of \(\mathrm{O}_{2}\). Calculate the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) formed.

Step-by-Step Solution

Answer

The number of moles of \(\mathrm{H}_{2} \mathrm{O}\) formed is 19.6

Step 1: Identify the relevant stoichiometric ratio

From the balanced chemical equation, you can see that the ratio between the moles of methanol (\(\mathrm{CH}_{3} \mathrm{OH}\)) and water (\(\mathrm{H}_{2} \mathrm{O}\)) is 2 : 4, or simplifying, 1 : 2. It means for every 1 mole of methanol reacted, 2 moles of water are formed.

Step 2: Use the identified ratio to compute the moles of water

We know that there are 9.8 moles of methanol reacted. We use our ratio to calculate the quantity of water produced. By multiplying the 9.8 moles of methanol by the stoichiometric ratio of 2 moles of water per mole of methanol, we get the number of moles of water produced.

Step 3: Calculation

The calculation becomes \(9.8 \: \text{moles CH}_{3} \text{OH} \times \frac{2 \: \text{moles H}_{2} \text{O}}{1 \: \text{mole CH}_{3} \text{OH}} = 19.6 \: \text{moles H}_{2} \text{O}\).

Key Concepts

Chemical Reactions

A chemical reaction involves the transformation of one or more substances into new substances. Each reaction follows a specific pattern, represented by a chemical equation. In these equations, reactants are substances that undergo change, while products are the new substances formed.

Every chemical equation must be balanced, meaning that the number of atoms for each element in the reaction must be the same on both sides of the equation. This reflects the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. Balance ensures that the quantities of reactants and products are in the right proportions.

• In a balanced chemical reaction, coefficients are used to ensure the same number of each type of atom appears on both sides.
• The equation given for the combustion of methanol is an example of a balanced chemical equation: \[ 2 \mathrm{CH}_{3} \mathrm{OH}(l) + 3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2} \mathrm{O}(l) \]

Understanding these coefficients is crucial, as they help in calculating the amounts of products formed from given reactants.

Mole Concept

The mole is a fundamental unit in chemistry used to express amounts of a chemical substance. One mole of any substance contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\). This concept enables chemists to count particles by weighing them.

In stoichiometry, the mole concept is crucial as it connects the macroscopic world (grams, liters) to the microscopic world (atoms, molecules, ions). It serves as the bridge between balanced chemical equations and real-world reactions.

• For instance, in the methanol combustion reaction, the mole ratio is used to relate moles of methanol to moles of water formed.
• This allows the calculation of the amount of product (water) from a given amount of reactant (methanol).

The key is to use the balanced chemical equation, which tells how many moles of one substance react with how many moles of another substance. This ensures precise calculations in chemical processes.

Combustion Reaction

Combustion reactions are a type of chemical reaction where a substance combines with oxygen to release energy. They are essential in various applications, such as powering engines or heating homes.

A common example of combustion is the burning of fuels, like in the reaction of methanol as demonstrated here. Combustion typically produces carbon dioxide and water as byproducts when a hydrocarbon or alcohol is burned in the presence of oxygen.

• The general form of a combustion reaction can be shown as: \[ \text{Fuel} + \text{Oxygen} \rightarrow \text{Carbon Dioxide} + \text{Water} \]
• Specific to the methanol example: \[ 2 \mathrm{CH}_{3} \mathrm{OH} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2} + 4 \mathrm{H}_{2} \mathrm{O} \]

In this case, the methanol serves as the fuel. The reaction with oxygen, a combustion reaction, results in energy, carbon dioxide, and water, consistent with many real-world applications of combustion.