Question

The three most stable oxides of carbon are carbon monoxide (CO), carbon dioxide \(\left(\mathrm{CO}_{2}\right),\) and carbon suboxide \(\left(\mathrm{C}_{3} \mathrm{O}_{2}\right) .\) The molecules can be represented as Explain how these molecules illustrate the law of multiple proportions.

Short answer

The Law of Multiple Proportions states that when two elements combine to form more than one compound, the ratios of the masses of the second element combined with a fixed mass of the first element are simple whole numbers. For the carbon oxides CO, CO2, and C3O2, we calculate the mass of oxygen combined with a fixed mass of carbon (12 g or 1 mole), which are 16 g (CO), 32 g (CO2), and 16 g (C3O2). The simple whole number ratios between these oxygen masses are 1:2 for CO and CO2, 1:1 for CO and C3O2, and 2:1 for CO2 and C3O2. These simple whole number ratios confirm the Law of Multiple Proportions for the most stable carbon oxides.

Step-by-step solution

Determine the molar masses of carbon and oxygen

To calculate the mass ratios, we first need to determine the molar masses of carbon and oxygen. The molar mass of carbon (C) is approximately 12 g/mol, and the molar mass of oxygen (O) is approximately 16 g/mol.

Calculate the mass ratios for each compound

In each compound, we'll take a fixed mass of carbon, for example, 12 g (1 mole of carbon), and calculate the mass of oxygen combined with it. For CO (carbon monoxide): 1 mole of C combines with 1 mole of O, so the mass of oxygen combined with 12 g of carbon is 16 g. For CO2 (carbon dioxide): 1 mole of C combines with 2 moles of O, so the mass of oxygen combined with 12 g of carbon is 2 * 16 g = 32 g. For C3O2 (carbon suboxide): 3 moles of C (36 g) combine with 2 moles of O (32 g). Therefore, for 1 mole of C (12 g), the mass of oxygen combined will be \(\frac{32}{3}\) * 12 = 16 g.

Determine the simple whole number ratios of oxygen masses

Now, we'll find the simple whole number ratios between the masses of oxygen combined with 12 g (1 mole) of carbon in each compound. For CO and CO2: The ratio of oxygen masses is 16:32 which can be reduced to 1:2. For CO and C3O2: The ratio of oxygen masses is 16:16 which can be reduced to 1:1. For CO2 and C3O2: The ratio of oxygen masses is 32:16 which can be reduced to 2:1.

Relate the whole number ratios to the Law of Multiple Proportions

We see that the ratios between the masses of oxygen combined with a fixed mass of carbon in the compounds CO, CO2, and C3O2 are simple whole numbers (1:2 and 1:1), which confirms the Law of Multiple Proportions. In this exercise, we've demonstrated that the law holds true for the most stable carbon oxides.

Key concepts

Understanding Carbon Compounds

Carbon is a versatile element capable of forming several stable compounds, primarily observed in its oxides. The three most common carbon oxides include carbon monoxide (CO), carbon dioxide (CO₂), and carbon suboxide (C₃O₂). Each compound showcases unique properties and compositions that are vital to understanding how elements combine.
Carbon monoxide consists of one carbon atom and one oxygen atom, while carbon dioxide contains one carbon atom and two oxygen atoms. Meanwhile, carbon suboxide has a more complex structure with three carbon atoms and two oxygen atoms.
These compounds are crucial examples of how carbon can combine in different ratios with oxygen, illustrating the versatility and reactivity of carbon. By understanding these compounds, we explore the foundational principles that govern chemical reactions and the formation of different chemical species.

Introducing Moles and Molar Mass

When working with chemical compounds, it is important to understand the concepts of moles and molar mass. A mole is a unit that helps us quantify the amount of a chemical substance. One mole contains Avogadro's number of particles, typically atoms or molecules, which is roughly 6.022 x 10²³ particles.
The molar mass is the mass of one mole of a given substance, measured in grams per mole (g/mol). For example, the molar mass of carbon is approximately 12 g/mol, and the molar mass of oxygen is approximately 16 g/mol.
In carbon compounds like CO and CO₂, knowing these molar masses helps us calculate how much oxygen is present for each given amount of carbon. Understanding moles and molar mass allows scientists to weigh and measure substances accurately for chemical reactions, ensuring precise calculations and results.

Exploring Chemical Ratios in Compounds

Chemical ratios reveal how different elements combine to form compounds. By examining the ratios of elements in compounds, we can verify laws such as the Law of Multiple Proportions. This law states that if two elements form more than one compound, the mass ratios of the second element that combine with a fixed mass of the first element can be reduced to small whole numbers.
Consider carbon compounds like CO, CO₂, and C₃O₂. By analyzing these, we calculate the mass of oxygen combining with a fixed mass of carbon. For CO, 12 grams of carbon combine with 16 grams of oxygen. For CO₂, the same 12 grams of carbon combine with 32 grams of oxygen. Finally, for C₃O₂, the ratio results in 12 grams of carbon combining again with 16 grams of oxygen, once simplified to one carbon.
The resulting mass ratios remain as simple whole numbers (1:2, 1:1), effectively demonstrating the Law of Multiple Proportions, instrumental in validating consistent chemical reactions across different compounds.