Question

An automobile gasoline tank holds \(42 \mathrm{~kg}\) of gasoline. When the gasoline burns, \(168 \mathrm{~kg}\) of oxygen are consumed and carbon dioxide and water are produced. What total combined mass of carbon dioxide and water is produced?

Short answer

The combined mass of carbon dioxide and water produced is 210 kg.

Step-by-step solution

Understand the Law of Conservation of Mass

The Law of Conservation of Mass states that mass is neither created nor destroyed in a chemical reaction. Therefore, the total mass of reactants before the reaction must equal the total mass of products after the reaction.

Calculate the Total Mass of Reactants

Calculate the total mass of reactants by adding the mass of gasoline and the mass of oxygen together. The mass of gasoline is given as 42 kg, and the mass of oxygen consumed is 168 kg.

Calculate the Total Mass of Products

Since the mass is conserved, the total mass of the products (carbon dioxide and water combined) will be equal to the total mass of the reactants. Simply add the mass of gasoline and oxygen to find the total mass after the reaction.

Key concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into new substances called products. These transformations occur as part of various interactions at the molecular level, where atoms are rearranged to create different compounds.

An everyday example is the burning of gasoline in a car engine. During this combustion reaction, gasoline reacts with oxygen to produce carbon dioxide and water. Understanding chemical reactions is important not only in chemistry but also in broader applications like environmental science, engineering, and medicine.

The balanced chemical equation provides a recipe for how much of each reactant is needed to produce a certain amount of product. This is crucial for calculating the amounts of substances consumed and produced in a reaction, as you will see in stoichiometry.

Mass Conservation

The Law of Conservation of Mass is a fundamental principle in chemistry stating that mass cannot be created or destroyed in a chemical reaction. It implies that the total mass of all reactants must be the same as the total mass of all products.

For example, if a gasoline tank holds 42 kg of gasoline and 168 kg of oxygen is consumed during combustion, the total initial mass is the sum of these two, which is 210 kg. According to the conservation of mass, the total mass of carbon dioxide and water produced must also be 210 kg.

This law is pivotal in understanding that even though substances change forms, the same amount of matter exists before and after a chemical reaction. It necessitates a balanced chemical equation and allows us to predict the quantity of an unknown product or reactant.

Stoichiometry

Stoichiometry is the aspect of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. In other words, it involves calculations to determine the amount of reactants needed to produce a certain amount of product, or vice versa.

Understanding stoichiometry is essential when performing a chemical reaction to be sure that the correct amount of each substance is used. This prevents the waste of chemicals and ensures that reactions proceed to completion. In the context of the automobile gasoline problem, stoichiometry would allow us to, theoretically, calculate the exact amounts of carbon dioxide and water produced, given the amounts of gasoline and oxygen.

The stoichiometric calculations rest on the balanced chemical equation and use mole ratios derived from it, making it a foundational tool for predicting the outcome of a chemical reaction.