Problem 35 - Chemistry A Molecular Approach

Question

Two different compounds containing osmium and oxygen have the following masses of oxygen per gram of osmium: 0.168 and \(0.3369 \mathrm{~g} .\) Show that these amounts are consistent with the law of multiple proportions.

Step-by-Step Solution

Answer

The ratio of the two masses of oxygen per gram of osmium (0.3369 g to 0.168 g) is approximately 2, demonstrating that these amounts comply with the law of multiple proportions.

Step 1: Understanding the Law of Multiple Proportions

The law of multiple proportions states that when two elements (in this case osmium and oxygen) form more than one compound, the different masses of one element (oxygen in this case) that combine with a fixed mass of the other element (osmium) are in the ratio of small whole numbers.

Step 2: Calculate the Ratio of the Two Oxygen Masses

To show that the two given compounds are consistent with the law of multiple proportions, we calculate the ratio of the two different masses of oxygen per gram of osmium. The masses are 0.168 g and 0.3369 g, so their ratio is:\[ \frac{0.3369 \mathrm{g}}{0.168 \mathrm{g}} = 2.006 \]

Step 3: Analyzing the Ratio

Our calculated ratio is approximately 2, which means that for one compound to another, the amount of oxygen combines with osmium in a ratio that is a simple whole number, consistent with the law of multiple proportions.

Key Concepts

Understanding Chemical Compounds

Chemical compounds are a cornerstone of chemistry; they are substances composed of two or more different elements that are bonded together in fixed proportions. A familiar example would be water, which always consists of two hydrogen atoms for every one oxygen atom, abbreviated as H₂O. When studying compounds, we look at both qualitative aspects, such as what elements are present, and quantitative aspects, such as how much of each element is present.

In the provided exercise regarding osmium and oxygen, we see how these two elements can combine in different ratios to form distinct chemical compounds. Understanding the behavior of these elements when they bond can help us predict the properties and reactions of new compounds they may form.

Exploring Elemental Ratios

The elemental ratio in a compound tells us how the mass of one element compares to the mass of another within the same compound. This concept is crucial when categorizing compounds and understanding their formulas. For instance, carbon dioxide always has a carbon-to-oxygen mass ratio of 1:2.27. If we have two samples of carbon dioxide from different sources, the ratio must remain consistent.

The exercise demonstrates the law of multiple proportions through the comparison of two different masses of oxygen that combine with a fixed mass of osmium. We see that the elemental ratio, in this case, reflects a small whole number ratio, precisely matching the law's prediction. Understanding these ratios allows chemists to determine the empirical formulas of compounds, giving us insight into the compounds' actual structure.

Stoichiometry and Its Role

Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is grounded on the principle that, under normal chemical conditions, matter is neither created nor destroyed. Stoichiometry relies on the balanced chemical equation of a reaction where the coefficients represent the relative amounts of each substance involved.

Understanding stoichiometry allows us to predict how much of a chemical is needed to react with a given amount of another and what quantity of product will result. In the exercise, stoichiometry is implicitly used when comparing the mass ratios of oxygen to osmium in the compounds formed. It helps us confirm that the chemical behavior of these elements adheres to the law of multiple proportions, thus reinforcing the importance of stoichiometry in comprehending and predicting chemical phenomena.