Question

Consider 80.0-g samples of two different compounds consisting of only carbon and oxygen. One of the compounds consists of 21.8 g of carbon, and the other has 34.3 g of carbon. Determine the ratio in whole numbers of the masses of carbon that combine with 1.00 g of oxygen between the two compounds.

Short answer

The ratio in whole numbers of the masses of carbon that combine with 1.00 g of oxygen between the two compounds is 1:2.

Step-by-step solution

Calculate the Mass of Oxygen in Both Compounds

First, we will calculate the mass of oxygen in both compounds. Since the total mass of each compound is 80.0 g, we can find the mass of oxygen in the compounds by subtracting the mass of carbon from the total mass. For the first compound: Mass of oxygen = Total mass - Mass of carbon Mass of oxygen = 80.0 g - 21.8 g = 58.2 g For the second compound: Mass of oxygen = Total mass - Mass of carbon Mass of oxygen = 80.0 g - 34.3 g = 45.7 g

Determine the Mass of Carbon that Bonds with 1 g of Oxygen in Both Compounds

Next, we will calculate the mass of carbon that combines with 1 g of oxygen for both compounds. For the first compound: Mass of carbon combined with 1 g of oxygen = (Mass of carbon) / (Mass of oxygen) = 21.8 g / 58.2 g = 0.374 g of carbon For the second compound: Mass of carbon combined with 1 g of oxygen = (Mass of carbon) / (Mass of oxygen) = 34.3 g / 45.7 g = 0.750 g of carbon

Calculate the Ratio of the Masses of Carbon that Combine with 1.00 g of Oxygen between the Two Compounds

Finally, we will find the ratio of the masses of carbon that combined with 1.00 g of oxygen between the two compounds. Ratio = (Mass of carbon in the first compound that combined with 1 g of oxygen) / (Mass of carbon in the second compound that combined with 1 g of oxygen) = 0.374 g / 0.750 g ≈ 0.499 Now we need to convert this ratio to whole numbers. For simplicity, we can round it to the nearest whole number: Ratio ≈ 1/2 Therefore, the ratio in whole numbers of the masses of carbon that combine with 1.00 g of oxygen between the two compounds is 1:2.

Key concepts

Law of Multiple Proportions

The Law of Multiple Proportions is a fundamental principle in chemistry formulated by John Dalton. It states that if two elements form more than one compound between them, then the ratios of the masses of the second element which combine with a fixed mass of the first element will be ratios of small whole numbers.
For example, if we have two compounds made from the same elements, like carbon and oxygen in our original exercise, the different ratios of the second element with a fixed quantity of the first must be simple whole numbers.
This is seen in the exercise when we compare the two compounds with carbon combining with oxygen. The calculation of the carbon to oxygen mass in the two compounds leads to a simple whole number ratio of 1:2, confirming the Law of Multiple Proportions.
This law is significant because it reinforces the concept of atoms as discrete entities that combine in fixed ratios, providing strong evidence for the atomic theory of matter.

Mass Ratio

Mass ratio in chemistry denotes the proportion of the mass of one component to another within a compound. It is a simple but crucial tool for understanding stoichiometry and the composition of substances.
In the given exercise, we start by calculating the mass of oxygen by subtracting the known mass of carbon from the total mass of the compound, which allowed us to find a specific mass ratio of elements within each compound.
For both compounds, we determined the mass of carbon that combines with 1 g of oxygen. This involves dividing the mass of carbon by the mass of oxygen in each case to get a ratio that tells us how much carbon is proportionally contained per gram of oxygen.
Such mass ratios can highlight differences in compound formulas and help us deduce chemical compositions in more complex reactions or mixtures.

Chemical Compounds

Chemical compounds are substances formed by two or more different elements bonded together in specific proportions. They are characterized by a definite composition and unique properties.
In our exercise, the compounds consist solely of carbon and oxygen. Each compound's specific mass of carbon and oxygen reflects its unique chemical formula, even though the elements are the same.
Different compounds formed by the same elements can exist in varying stoichiometric forms, which explains variations in composition, such as differing mass ratios.
This is a clear demonstration of how not only the presence of elements but their proportions in compounds affect their chemical identity and properties.
Understanding these aspects is key to delving deeper into chemistry, as compounds are the basis of reactions and the substances we encounter generally in the laboratory and everyday life.