Question

When two molecules of methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), react with oxygen, they combine with three \(\mathrm{O}_{2}\) molecules to form two \(\mathrm{CO}_{2}\) molecules and four \(\mathrm{H}_{2} \mathrm{O}\) molecules. (a) Write a balanced equation for this reaction. (b) How many \(\mathrm{H}_{2} \mathrm{O}\) molecules are formed when 10 methanol molecules react? (c) If \(30 \mathrm{O}_{2}\) molecules react, how many methanol molecules react?

Short answer

The balanced equation for the reaction is \(2 \mathrm{CH}_{3} \mathrm{OH} + 3\mathrm{O}_{2} \rightarrow 2\mathrm{CO}_{2} + 4 \mathrm{H}_{2} \mathrm{O}\). 20 molecules of H2O are formed when 10 molecules of methanol react. When 30 O2 molecules react, it is required 20 methanol molecules.

Step-by-step solution

Write Unbalanced Equation

Start by writing the unbalanced chemical equation for the reaction, using the given information:\n \(2 \mathrm{CH}_{3} \mathrm{OH} + \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + 2 \mathrm{H}_{2} \mathrm{O}\)

Balance the Equation

Balance the equation. Adjust the coefficients to match the number of each atom on the reactant side with the product side: \n\(2 \mathrm{CH}_{3} \mathrm{OH} + 3\mathrm{O}_{2} \rightarrow 2\mathrm{CO}_{2} + 4 \mathrm{H}_{2} \mathrm{O}\) The equation says that 2 methanol molecules react with 3 oxygen molecules to produce 2 carbon dioxide molecules and 4 water molecules.

Determine the Number of H2O Molecules

The stoichiometric coefficients in the balanced equation are in the ratio of 2:4 for methanol to water. This means, for every 2 molecules of methanol that react, 4 molecules of water are produced. Thus, if 10 methanol molecules react, the number of water molecules formed will be \(4/2 * 10 = 20\)

Determine Number of Methanol Molecules

The stoichiometric coefficients in the balanced equation are in the ratio of 2:3 for methanol to oxygen. This means, for every 3 molecules of oxygen that react, 2 molecules of methanol are needed. Thus, if 30 oxygen molecules react, the number of methanol molecules required will be \(2/3 * 30 = 20\)

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that involves calculating the quantities of reactants and products in a chemical reaction. It is a foundational concept that enables us to predict the outcomes of molecular reactions and balance chemical equation equations. To understand stoichiometry, it is crucial to comprehend the mole concept, which represents a standard quantity of particles, such as atoms or molecules.

In the given exercise, we delve into stoichiometry by examining the reaction of methanol with oxygen to produce carbon dioxide and water. With stoichiometric calculations, we can precisely determine how many water molecules will form when a certain number of methanol molecules react (part b) as well as how many methanol molecules are needed for a given amount of oxygen (part c). The balanced chemical equation provides the mole ratio of the reactants to the products, which is essential for these calculations.

Molecular Reactions

Molecular reactions describe the process of chemical transformation from reactants to products at the molecular level. These transformations often involve breaking and forming of chemical bonds, leading to new substances. The key to understanding molecular reactions lies in knowing the reactants involved, conditions of the reaction, and the products formed.

For instance, in the given exercise, the molecular reaction between methanol and oxygen involves a combustion process. Here, methanol is oxidized by oxygen, resulting in a release of energy. The balanced chemical equation gives insight into the molecular-level details of this reaction, such as the number of reactants consumed and the number of products formed. Understanding the molecular stoichiometry of the reactants and products helps us to describe these processes quantitatively.

Chemical Reaction Equations

Chemical reaction equations provide a symbolic representation of a chemical reaction by using chemical formulas to depict the reactants and products, along with their stoichiometric coefficients, which convey the relative amounts of each substance. Balancing these equations is a necessary practice in chemistry to ensure that the law of conservation of mass is upheld. It states that mass is neither created nor destroyed in a chemical reaction.

In our exercise, part a demonstrates the balancing of a chemical equation for the combustion of methanol with oxygen. The balanced equation, which is the outcome of steps 1 and 2 in the solution, shows that two methanol molecules react with three oxygen molecules to yield two carbon dioxide and four water molecules. This balanced equation is indispensable as it forms the basis for stoichiometric calculations and predicts the amounts of each substance involved in the reaction.