Question

The element chromium forms three different oxides (that contain only chromium and oxygen). The percentage of chromium (number of grams of chromium in \(100 \mathrm{~g}\) oxide) in these compounds is \(52.0 \%, 68.4 \%,\) and \(76.5 \%\). Do these data conform to the law of multiple proportions? Explain why or why not.

Short answer

Yes, the mass ratios conform to the law of multiple proportions.

Step-by-step solution

Calculate the Mass of Oxygen in Each Oxide

For each oxide, subtract the percentage of chromium from 100% to find the percentage of oxygen. \[\text{Oxygen in First Oxide} = 100\% - 52.0\% = 48.0\%\]\[\text{Oxygen in Second Oxide} = 100\% - 68.4\% = 31.6\%\]\[\text{Oxygen in Third Oxide} = 100\% - 76.5\% = 23.5\%\]

Determine the Mass Ratios of Chromium to Oxygen

Convert the percentages into mass ratios of chromium to oxygen by dividing the percentage of chromium by the percentage of oxygen for each oxide.\[\text{Ratio for First Oxide} = \frac{52.0}{48.0}\]\[\text{Ratio for Second Oxide} = \frac{68.4}{31.6}\]\[\text{Ratio for Third Oxide} = \frac{76.5}{23.5}\]

Simplify the Mass Ratios

Simplify each mass ratio by dividing both the numerator and denominator by their greatest common divisor (GCD) to get the simplest form of each ratio.\[\text{Simplified Ratio for First Oxide} = \frac{52.0}{48.0} \approx 1.08\]\[\text{Simplified Ratio for Second Oxide} = \frac{68.4}{31.6} \approx 2.16\]\[\text{Simplified Ratio for Third Oxide} = \frac{76.5}{23.5} \approx 3.26\]

Compare the Simplified Ratios

Compare the ratios from each oxide to check if the ratios are whole numbers or whole number multiples of each other (Law of Multiple Proportions).\[\text{Comparative Ratios: } 1.08 : 2.16 : 3.26\],

Conclusion on Law of Multiple Proportions

Since the ratios approximately form whole number multiples (1, 2, 3), they conform to the law of multiple proportions, indicating that the ratios of the masses of oxygen that combine with a fixed mass of chromium can be expressed by small whole numbers.

Key concepts

Mass Ratios

Understanding mass ratios is crucial when discussing chemical compounds. In simple terms, mass ratios show how much of each element is present relative to others in a compound. For chromium oxides, we can calculate this by comparing the mass of chromium to that of oxygen.
To obtain these ratios, first determine the mass percentage of each element. In the given chemical oxides, we subtract the chromium percentage from 100 to find the oxygen's mass percentage.
Once the percentages are known, they need to be converted into mass ratios. This is achieved by dividing the mass percentage of chromium by that of oxygen. The results give us an understanding of how these elements are proportioned in the compound.
Simplifying these ratios helps us identify patterns, particularly those aligned with the law of multiple proportions. When these ratios approximate whole numbers or simple multiples, they provide insight into the compound's stoichiometry and molecular construction.

Chemical Oxides

Chemical oxides are compounds that feature an element combined with oxygen. In our context, chromium oxides are formed between chromium and oxygen. Each oxide has unique properties, dictated by the specific ratio of chromium to oxygen atoms present.
The calculation of mass percentages for each element in these oxides is an essential step in analyzing their composition. Knowing these percentages allows for the calculation of how much chromium is combined with a certain amount of oxygen across different oxides.
This leads us to appreciate how variations in oxide composition reflect different ratios of mass per element. Through these variations, we come closer to understanding how different chromium oxides are configured.
Chemical oxides are a key player in studying chemical properties and reactivity. By examining their composition and mass ratios, we gain indispensable insights into their chemistry.

Chromium Oxides

Chromium oxides are a class of chemical compounds that consist of chromium and oxygen. These oxides exist in multiple forms, each with a distinct composition, which affects their physical and chemical behavior.
In the exercise provided, the different chromium oxides are identified by their percentage of chromium content: 52.0%, 68.4%, and 76.5%. These represent the varying amounts of chromium in each compound relative to oxygen.
The analysis of chromium oxides involves calculating the respective mass of oxygen and chromium. By understanding these ratios, and simplifying them, it can be ascertained whether these compounds follow the law of multiple proportions. This law stipulates that for a fixed mass of one element, the mass ratios of the other vary between small whole numbers.
This characteristic helps us categorize unknown oxides and predict the potential formation and stability of new chromium oxide compounds. Consequently, studying chromium oxides is not only about knowing their composition but also about comprehending their implications in the broader landscape of chemistry.