Question

Show, with calculations, how the following data illustrate the law of multiple proportions: Compound 1: 77.6 mass \(\%\) xenon and 22.4 mass \(\%\) fluorine Compound 2: 63.3 mass \(\%\) xenon and 36.7 mass \(\%\) fluorine

Short answer

The mass ratios for the fluorine in the two compounds are in a small whole number ratio of 2:1, illustrating the law of multiple proportions.

Step-by-step solution

- Determine the mass ratios

For Compound 1, the mass ratio of xenon to fluorine is \ \( \frac{77.6 \%}{22.4 \%} = \frac{77.6}{22.4} = 3.464 \). For Compound 2, the mass ratio of xenon to fluorine is \ \( \frac{63.3 \%}{36.7 \%} = \frac{63.3}{36.7} = 1.725 \).

- Simplify the mass ratios

Convert the mass ratios to simpler fractional forms: \ \( 3.464 \approx \frac{12}{3.464/12} = 4 \), and \ \( 1.725 \approx \frac{12}{1.725/12} = 2.0 \).

- Compare the simplified ratios

Observe the simplified mass ratios of Compound 1 and Compound 2: 4 and 2, respectively. The ratio of these two simplified mass ratios is \ \( \frac{4}{2} = 2 \), which is a small whole number.

- Apply the law of multiple proportions

The law of multiple proportions states that if two elements form more than one compound, then the ratios of the masses of the second element that combine with a fixed mass of the first element are in ratios of small whole numbers. As shown, the ratio between the masses of fluorine that combine with a fixed mass of xenon in the two compounds is a small whole number (2:1), illustrating the law of multiple proportions.

Key concepts

Mass Ratios

Mass ratios are a key part of understanding chemical compounds. It refers to the proportion of the mass of one element to the mass of another element in a compound. In the given exercise, we calculated the mass ratios for xenon (Xe) and fluorine (F) in two compounds. For Compound 1, the ratio was calculated as 3.464, while for Compound 2 it was 1.725. Simplifying these ratios to smaller fractions, we found they approximate to simple whole numbers, 4 and 2 respectively. This simplification is crucial as it illustrates the law of multiple proportions.

By comparing these simplified ratios, we discovered that their ratio is 2, a small whole number. This result aligns with the law of multiple proportions, indicating a consistent relationship between the masses of elements in different compounds.

Chemical Compounds

Chemical compounds are substances formed by the chemical combination of two or more elements. These elements are present in fixed ratios, which can be determined by mass. For the compounds provided in the exercise, xenon and fluorine combine in specific mass percentages to create two distinct compounds.

Understanding the mass percentages and converting them to mass ratios allows us to see the fixed proportions in which these elements combine. By calculating the mass ratio of xenon to fluorine in both compounds, we see that these ratios simplify to small whole numbers, highlighting a fundamental principle in chemistry. The consistency of these mass ratios between compounds helps in identifying chemical compounds and understanding their properties.

Atomic Theory

Atomic theory is the foundation of modern chemistry. It proposes that all matter is made up of atoms, which are the smallest units of an element that retain the properties of that element. The law of multiple proportions, which was illustrated in the provided exercise, is rooted in atomic theory.

According to atomic theory, elements can combine in different ways to form various compounds. However, when they do so, they do it in fixed ratios of small whole numbers. This principle is clearly visible in the relationship between xenon and fluorine in the given compounds. The mass ratios derived from the percentages in the exercise—3.464 and 1.725—simplify to whole numbers, showing that the elements combine in simple, predictable ways.

This predictability is one of the reasons atomic theory is so powerful in understanding and predicting the results of chemical reactions. The law of multiple proportions, shown through these calculations, supports the fundamental idea that atoms combine in specific, observable ratios.