Problem 3 - General Chemistry: Principles and Modern Applications

Question

A 0.406 g sample of magnesium reacts with oxygen, producing \(0.674 \mathrm{g}\) of magnesium oxide as the only product. What mass of oxygen was consumed in the reaction?

Step-by-Step Solution

Answer

The mass of oxygen that was consumed in the reaction is \(0.268 \mathrm{g}\).

Step 1: Understanding the Conservation of Mass

The law of conservation of mass states that matter cannot be created nor destroyed. Therefore, the sum of the masses of the reactants, magnesium and oxygen, before the reaction must be equal to the sum of the masses of the products, in this case magnesium oxide, after the reaction.

Step 2: Calculate the mass of Oxygen

The problem provides the masses of magnesium (\(0.406 \, \mathrm{g}\)) and of magnesium oxide (\(0.674 \, \mathrm{g}\)) produced. The difference in mass between the magnesium oxide produced and the magnesium used will be the mass of oxygen involved in the reaction. So, subtract the mass of magnesium from the mass of magnesium oxide to find the mass of oxygen: \(0.674 \mathrm{g} - 0.406 \mathrm{g} = 0.268 \mathrm{g}\).

Step 3: Concluding the solution

So, the mass of oxygen consumed in the reaction was \(0.268 \mathrm{g}\). It's important to remember that the law of conservation of mass allows us to make these types of calculations. Regardless of how substances within a closed system interact with one another, or change forms, their total mass will always remain the same.

Key Concepts

Chemical Reactions

During a chemical reaction, substances called reactants interact to form new substances known as products. In the exercise, magnesium is the reactant, and when it reacts with oxygen, the product formed is magnesium oxide.

Chemical reactions are often represented by chemical equations, which give us an overview of the number of atoms involved.

• The equation must be balanced, meaning the number of each type of atom on the reactant side equals the number on the product side.
• For the reaction between magnesium and oxygen, it can be represented as: \(2\, \text{Mg} + \text{O}_2 \rightarrow 2\, \text{MgO}\).

Understanding how atoms rearrange during these processes is crucial for grasping the basics of chemistry.

Mass Calculations

Mass calculations in chemistry allow us to understand how the Law of Conservation of Mass applies to chemical reactions. In this example, we need to find out how much oxygen was involved in forming magnesium oxide.

According to the Law of Conservation of Mass, the mass of the reactants must equal the mass of the products. Thus, if we know two of the masses (magnesium and magnesium oxide), we can calculate the third (oxygen):

• Mass of magnesium oxide = Mass of magnesium + Mass of oxygen.
• Rearrange to find the oxygen mass: Mass of oxygen = Mass of MgO - Mass of Mg = 0.674 g - 0.406 g = 0.268 g.

This simple subtraction helps us learn the importance of precise measurements in chemical reactions to maintain mass consistency.

Stoichiometry

Stoichiometry is the quantitative relationship between the amounts of reactants and products in a chemical reaction. It helps us predict how much product we can make from a given amount of reactant.

This exercise is an example of stoichiometric calculations which derive from balanced chemical equations. The coefficients in a balanced equation tell us the ratio of moles of reactants needed to form the products. For magnesium and oxygen:

• The balanced equation tells us 2 moles of magnesium react with 1 mole of oxygen.
• This 2:1 ratio also holds true for masses, considering the molecular weights of the substances involved.

By understanding stoichiometry, we can determine exactly how much of each reactant is needed to produce a certain amount of product, ensuring nothing is wasted in chemical processes.