Show, with calculations, how the following data illustrate the law of multiple proportions: Compound 1: 47.5 mass \(\%\) sulfur and 52.5 mass \(\%\) chlorine Compound 2: 31.1 mass \(\%\) sulfur and 68.9 mass \(\%\) chlorine

The mass ratio is a fundamental concept in chemistry that tells us how the mass of one element compares to another within a compound. It is calculated by dividing the mass percentage of one element by the mass percentage of another. This ratio helps us understand the relative amounts of each element in a compound.

In the given exercise, we find the mass ratios of sulfur to chlorine in two different compounds. For Compound 1, the mass of sulfur is 47.5% and chlorine is 52.5%. The mass ratio is \(\frac{47.5}{52.5}\) which equals 0.9048. For Compound 2, the mass of sulfur is 31.1% and chlorine is 68.9%. Here, the mass ratio is \(\frac{31.1}{68.9}\) which equals 0.4514.

To find how these compounds are related, we compare these mass ratios. We divide the mass ratio of Compound 1 by the mass ratio of Compound 2, which gives \(\frac{0.9048}{0.4514}\) that equals approximately 2.004. This ratio, simplified to a simple whole number, is essential to applying the law of multiple proportions.

Chemical compounds are substances made up of two or more elements that are chemically bonded together. Each compound has a unique composition that is defined by the elements involved and their respective ratios. For example, in the given exercise, we have two compounds containing sulfur and chlorine.

Compound 1 has 47.5% sulfur and 52.5% chlorine, while Compound 2 has 31.1% sulfur and 68.9% chlorine. Despite having the same two elements, the different proportions of sulfur and chlorine result in distinct compounds. The law of multiple proportions helps us understand these differences by examining how the ratios of elements compare across different compounds.

This distinctive composition dictates the compound's properties and its behavior in chemical reactions, making the study of mass ratios and element proportions crucial in chemistry.

The sulfur to chlorine ratio helps illustrate the law of multiple proportions, which states that when elements combine into more than one compound, the ratios of the masses of the second element that combine with a fixed mass of the first element can be expressed as a ratio of small whole numbers.

In our case study, the sulfur to chlorine ratios in Compound 1 and Compound 2 are calculated as follows:

• For Compound 1: The ratio is \(\frac{47.5}{52.5} = 0.9048 \)
• For Compound 2: The ratio is \(\frac{31.1}{68.9} = 0.4514 \)

To illustrate the law of multiple proportions, we compare these two ratios: we divide them \(\frac{0.9048}{0.4514} \), obtaining approximately 2.004. This translates to a simple whole number ratio of 2:1.

This confirms that sulfur and chlorine form two different compounds with different mass ratios that adhere to the law of multiple proportions. Understanding these ratios is crucial for predicting compound formation and analyzing chemical reactions.