Question

A sample of the compound magnesium oxide is synthesized as follows. 60. g of magnesium is burned and produces \(100 .\) g of magnesium oxide, indicating that the magnesium combined with 40\. g of oxygen in the air. If \(30 .\) g of magnesium had been used, what mass of oxygen would have combined with it? What law of chemistry is used in solving this problem?

Short answer

20 g of oxygen combines with 30 g of magnesium; Law of Definite Proportions is used.

Step-by-step solution

Understand the Law of Chemistry

This problem involves the Law of Definite Proportions, which states that a chemical compound always contains exactly the same proportion of elements by mass.

Identify Proportions from Given Data

From the problem, we know that 60 g of magnesium combines with 40 g of oxygen to produce magnesium oxide. This establishes the ratio of magnesium to oxygen in the compound.

Calculate Ratio of Magnesium to Oxygen

To find the ratio, we divide the mass of oxygen by the mass of magnesium: \(\text{Ratio of oxygen to magnesium} = \frac{40 \, g}{60 \, g} = \frac{2}{3}.\ \)This means that for every 3 g of magnesium, 2 g of oxygen is needed.

Apply the Ratio to the New Scenario

Now, apply the ratio to the new situation with 30 g of magnesium. Using the ratio derived, we calculate the mass of oxygen required: \(\text{Mass of oxygen} = 30 \,g \times \frac{2}{3} = 20 \,g. \)This means 20 g of oxygen will combine with 30 g of magnesium.

Key concepts

Chemical Compound

A chemical compound is a substance made up of two or more different elements that are chemically bonded together. These elements are present in fixed proportions, and the compound itself exhibits unique properties compared to the individual elements. For example, when elements like magnesium and oxygen combine, they form a new compound known as magnesium oxide.
This combination of elements results in a substance that behaves differently than either magnesium or oxygen alone. Compounds are essential in chemistry because they are the building blocks of the various substances we encounter daily.

• Compounds are formed through chemical reactions.
• The properties of compounds are distinct from the elements that form them.
• A compound's chemical formula reflects the ratio of the elements involved.

Understanding chemical compounds is crucial as it helps us comprehend how elements interact to create the diverse materials around us.

Magnesium Oxide

Magnesium oxide (MgO) is a chemical compound composed of magnesium and oxygen. It is commonly produced by burning magnesium in the presence of oxygen, resulting in a white powder. This process is an example of a synthesis reaction where two elements unite to form a compound.
Magnesium oxide is known for its high melting point and is often used in materials requiring thermal resistance, such as refractory linings and furnace bricks. It also finds applications in medicine as a supplement and antacid.

• Formed by the combination of magnesium and oxygen.
• Has distinct properties like high thermal resistance.
• Used in various industrial and medical applications.

The study of magnesium oxide provides insights into how simple elements create compounds with useful properties.

Mass Ratio

The concept of mass ratio is central to understanding chemical compounds and reactions. It involves determining the proportion of each element by mass within a compound. In the scenario with magnesium oxide, we see that 60 g of magnesium reacts with 40 g of oxygen to produce the compound.
The mass ratio, \( \frac{40}{60} \ or \ \frac{2}{3} \), tells us that for every 3 grams of magnesium, 2 grams of oxygen are required. Mass ratio is crucial for predicting product amounts in chemical reactions and ensuring reactions occur with the desired proportions.

• A tool for understanding how elements combine in fixed ratios.
• Essential for quantitative analysis in chemical reactions.
• Helps maintain accuracy when scaling reactions up or down.

Mass ratio demonstrates the predictable nature of chemical compositions, as dictated by the Law of Definite Proportions.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the calculation of reactants and products in chemical reactions. It stems from the principles of the conservation of mass and the Law of Definite Proportions. These laws ensure that matter is neither created nor destroyed, and that elements combine in definite ratios.
In the exercise with magnesium oxide, stoichiometry allows us to determine how much oxygen is needed to react with a given mass of magnesium. By using the established ratio, \( \frac{2}{3} \), we calculated that 20 g of oxygen would combine with 30 g of magnesium.
This process involves:

• Applying known ratios to predict reaction outcomes.
• Ensuring balanced equations for chemical reactions.
• Quantifying the amount of reactants and products.

Mastering stoichiometry is essential for any chemist as it provides the mathematical framework for understanding and predicting chemical reactions.