Question

Sulfur and oxygen form both sulfur dioxide and sulfur trioxide. When samples of thesc are decomposed, the sulfur dioxide produces 3.49 \(\mathrm{g}\) oxygen and 3.50 \(\mathrm{g}\) sulfur, while the sulfur trioxide produces 6.75 \(\mathrm{g}\) oxygen and 4.50 g sulfur. Calculate the mass of oxygen per gram of sulfur for each sample and show that these results are consistent with the law of multiple proportions.

Short answer

For sulfur dioxide, the mass ratio of oxygen to sulfur is 3.49 g / 3.50 g = 0.997 g O/g S. For sulfur trioxide, the mass ratio is 6.75 g / 4.50 g = 1.5 g O/g S. The ratio between the two mass ratios (sulfur trioxide to sulfur dioxide) is 1.5 / 0.997 which simplifies to approximately 1.5, a simple whole number, confirming the Law of Multiple Proportions.

Step-by-step solution

Calculate the mass ratio for sulfur dioxide

To calculate the mass of oxygen per gram of sulfur in sulfur dioxide, divide the mass of oxygen by the mass of sulfur. For sulfur dioxide: Mass ratio (Oxygen to Sulfur) = Mass of Oxygen / Mass of Sulfur = 3.49 g O / 3.50 g S.

Calculate the mass ratio for sulfur trioxide

Similarly, for sulfur trioxide, calculate the mass of oxygen per gram of sulfur: Mass ratio (Oxygen to Sulfur) = Mass of Oxygen / Mass of Sulfur = 6.75 g O / 4.50 g S.

Evaluate the results in relation to the Law of Multiple Proportions

According to the Law of Multiple Proportions, if two elements form more than one compound, the ratios of the masses of the second element that combine with a fixed mass of the first element will be ratios of small whole numbers. Calculate the ratio of the two oxygen-to-sulfur mass ratios obtained in steps 1 and 2. This ratio should be a simple whole number ratio if the Law of Multiple Proportions is valid in this case.

Key concepts

Chemical Stoichiometry

Chemical stoichiometry is the cornerstone of preparing and analyzing chemical reactions. It quantifies the relationships between the amounts of reactants and products in a chemical reaction. Understanding stoichiometry is essential because it allows chemists to predict how much product will form from certain amounts of reactants or how much of a reactant is necessary to create a desired quantity of product.

In our exercise, we examined the composition of sulfur dioxide and sulfur trioxide compounds. By taking precise measurements of sulfur and oxygen, students can understand the stoichiometry of the two compounds. It is important to note that stoichiometry is not only about balancing equations but also involves understanding the ratio of the masses of elements involved and how these ratios relate to the molecular composition of the substances.

Mass Ratio Calculations

Mass ratio calculations are a fundamental part of understanding chemical reactions. They involve determining the ratio of the mass of one substance to the mass of another. These ratios reveal the relative amounts of substances in a chemical compound or reaction, which are critical for tasks ranging from recipe formulation in industrial processes to adjusting reactants in a laboratory synthesis.

In our sulfur and oxygen example, the mass ratios are calculated by dividing the mass of oxygen by the mass of sulfur for each compound. Such calculations showed that sulfur dioxide and sulfur trioxide have different mass ratios of oxygen to sulfur, a concept that reinforces the precision required for stoichiometric calculations in chemistry. Mastering mass ratio calculations can deepen a student's understanding of chemical relationships and lead to better experimental outcomes.

Molecular Composition

Molecular composition refers to the elements that make up a molecule and their specific arrangement within that molecule. It's a way of describing what a molecule is 'made of' and how those components are connected. This concept is not only about knowing which atoms are present but understanding how they interact and bond together to give a compound its unique characteristics.

For example, sulfur dioxide (SO2) and sulfur trioxide (SO3) are composed of sulfur and oxygen, but in different ratios. The molecular composition defines the properties of these compounds, such as their physical state, reactivity, and role in chemical processes like acid rain formation. Teaching students about molecular composition is crucial for their ability to discern the differences between similar compounds and predict chemical behaviors.

Stoichiometric Principles

Stoichiometric principles are the rules and guidelines that govern the quantitative aspects of chemical reactions. These principles ensure that atoms are conserved in a reaction and help chemists convert between masses, volumes, and moles of reactants and products. One such principle is the Law of Conservation of Mass, which states that matter cannot be created or destroyed in an ordinary chemical reaction. Another principle related to our exercise is the Law of Definite Proportions, which posits that a chemical compound always contains exactly the same proportion of elements by mass.

In relation to the Law of Multiple Proportions, this law provides a more detailed lens to examine the variances when elements form more than one compound. This legislation further reveals that for our sulfur compounds, the mass ratios align with stoichiometric principles by giving ratios of small whole numbers. By understanding stoichiometric principles, students gain the ability to predict the outcomes of reactions and comprehend the fundamental rules that underpin all of chemical practice.