Question

Are these data sets on chemical changes consistent with the law of conservation of mass? (a) A 7.5-g sample of hydrogen gas completely reacts with \(60.0 \mathrm{~g}\) of oxygen gas to form \(67.5 \mathrm{~g}\) of water. (b) A \(60.5-\mathrm{g}\) sample of gasoline completely reacts with \(243 \mathrm{~g}\) of oxygen to form \(206 \mathrm{~g}\) of carbon dioxide and \(88 \mathrm{~g}\) of water.

Short answer

(a) Data set is consistent with the law of conservation of mass, total mass = 67.5 g for both reactants and products. (b) Data set is not consistent, total mass of reactants = 303.5 g, products = 294 g.

Step-by-step solution

Understanding the Law of Conservation of Mass

The Law of Conservation of Mass states that mass is neither created nor destroyed in a chemical reaction. This means the total mass of the reactants should equal the total mass of the products in a reaction.

Assess Data Set (a)

Calculate the total mass of the reactants and the products. For reactants, add the mass of hydrogen gas to the mass of oxygen gas. For products, check the mass of water formed. Reactants: Hydrogen + Oxygen = 7.5 g + 60.0 g. Products: Water = 67.5 g.

Conclusion for Data Set (a)

Compare the total mass of reactants with the total mass of products. If the masses are the same, the data set is consistent with the law of conservation of mass. Total mass of reactants = 7.5 g + 60.0 g = 67.5 g. Total mass of products = 67.5 g.

Assess Data Set (b)

Similarly, calculate the total mass of the reactants and products for data set (b). Reactants: Gasoline + Oxygen = 60.5 g + 243 g. Products: Carbon Dioxide + Water = 206 g + 88 g.

Conclusion for Data Set (b)

Again, compare the total mass of reactants with the total mass of products for data set (b). Total mass of reactants = 60.5 g + 243 g = 303.5 g. Total mass of products = 206 g + 88 g = 294 g. The reactants and products have different masses, so the law is not followed based on the given data.

Key concepts

Chemical Reactions

Understanding chemical reactions is fundamental to grasping the concept of mass conservation. A chemical reaction involves the transformation of substances, known as reactants, into new substances, called products. Through bonds breaking and forming, atoms are rearranged in chemical reactions, like pieces in a game, assembled into new configurations.

Distinguishing between different types of chemical reactions is also important. There are synthesis reactions where compounds are formed, decomposition reactions where compounds break apart, and combustion reactions, which typically involve a substance reacting with oxygen to release energy. Importantly, during chemical reactions, the atoms themselves are not destroyed or created—they are simply shuffled from the reactants to the products.

Mass Conservation

The law of Conservation of Mass is a cornerstone of chemistry, stating that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time. This principle was first established by Antoine Lavoisier in the 18th century and implies that the mass of reactants in a chemical reaction must equal the mass of the products.

In the classroom, this law can be visualized through experiments where the mass of substances before and after a reaction is compared. Outside the classroom, it is evident in the balanced cycles of nature, such as the water cycle or the carbon cycle. Understanding this law is crucial for any study related to chemical reactions.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It involves using balanced chemical equations to calculate the masses, volumes, and number of moles of substances involved in a reaction. Stoichiometry is like a recipe for chemistry; it tells you how much of each ingredient—reactant—you need to end up with a certain amount of product.

To solve stoichiometry problems, you begin with a balanced chemical equation and utilize conversion factors that come from the coefficients in the equation. This way, you can predict yields of products or determine necessary quantities of reactants for a given reaction, ensuring that the recipes we follow in the laboratory can be replicated accurately and safely.

Reactants and Products

Reactants are the starting materials in a chemical reaction, while products are the substances formed as a result of that reaction. The conversion of reactants to products involves breaking old bonds and making new ones, a process that involves energy changes but does not create or destroy atoms.

In exercises dealing with the conservation of mass, students must keep track of all reactants and products to ensure that the total mass is accounted for. The law implies that for complete reactions, the sum of the masses of reactants should be the same as the sum of the masses of the products. Understanding the properties and behaviors of reactants and products is crucial for students to predict the outcomes of reactions and to apply concepts of stoichiometry effectively.