Question

An automobile gasoline tank holds 21 \(\mathrm{kg}\) of gasoline. When the gasoline burns, 84 \(\mathrm{kg}\) of oxygen is consumed, and carbon dioxide and water are produced. What is the total combined mass of carbon dioxide and water that is produced?

Short answer

The total combined mass of carbon dioxide and water produced is 105 \(\mathrm{kg}\).

Step-by-step solution

Identify the Conservation of Mass Principle

According to the law of conservation of mass, matter is neither created nor destroyed. This means that the total mass of the reactants must be equal to the total mass of the products in a chemical reaction.

Calculate the Total Mass of Reactants

The total mass of reactants is the sum of the mass of gasoline and the mass of oxygen. Calculate this as follows: Total mass of reactants = Mass of gasoline + Mass of oxygen = 21 \(\mathrm{kg}\) + 84 \(\mathrm{kg}\) = 105 \(\mathrm{kg}\).

Determine the Total Mass of Products

Since the mass is conserved, the total mass of the products, which is the combined mass of carbon dioxide and water, is equal to the total mass of the reactants. Therefore, the total combined mass of carbon dioxide and water is 105 \(\mathrm{kg}\).

Key concepts

Stoichiometry

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between the substances involved in chemical reactions. It's like a recipe for chemistry: just as a recipe specifies the amounts of each ingredient needed, stoichiometry provides the proportions of reactants and products involved in a reaction.

In our automobile gasoline problem, stoichiometry would typically require the balancing of the chemical equation for combustion to predict the amounts of products formed from a certain amount of reactants. However, this problem simplifies the process by using the conservation of mass principle to determine the mass of the products without explicitly balancing the equation.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, interact to form new substances, called products. During this process, bonds between atoms are broken and formed, which translates to substances changing their identities.

For example, burning gasoline in an engine involves a chemical reaction where gasoline reacts with oxygen. The products of this combustion reaction are carbon dioxide and water. Each chemical reaction is governed by specific rules, one of which is the law of conservation of mass.

Mass Conservation Principle

The mass conservation principle, or the law of conservation of mass, states that for any closed system subject to no external forces, the mass of the system must remain constant over time. This is because mass cannot be created or destroyed.

In practice, this means that during a chemical reaction, like the combustion of gasoline, the total mass of the reactants (gasoline and oxygen) will be the same as the total mass of the products (carbon dioxide and water). This principle is fundamental to the field of stoichiometry and dictates that we must account for all matter in a reaction, just as we would balance a checkbook.

Combustion Products

In combustion reactions, which are a type of chemical reaction, fuel combines with an oxidant, often oxygen, to form combustion products. These products typically include various gases; in the case of hydrocarbon fuels like gasoline, carbon dioxide (CO2) and water (H2O) are the primary products.

In our textbook problem, we're examining the combustion of gasoline in an automobile engine. The combustion products here are carbon dioxide and water— common byproducts of burning hydrocarbon fuels in the presence of oxygen.

Reactants and Products Mass

The mass of reactants and products in a chemical reaction is a pivotal concern in stoichiometry. According to the conservation of mass, the mass of the reactants before the reaction must be equal to the mass of the products after the reaction.

In the context of the given problem, the mass of reactants (gasoline and oxygen) totals 105 kg. Since no mass is lost or gained during the reaction, the mass of the products (carbon dioxide and water) must also sum up to 105 kg. Understanding this equality is vital in solving stoichiometric problems and predicting the outcomes of chemical reactions.