Question

A sample of ascorbic acid (vitamin C) is synthesized in the laboratory. It contains \(1.50 \mathrm{~g}\) of carbon and \(2.00 \mathrm{~g}\) of oxygen. Another sample of ascorbic acid isolated from citrus fruits contains \(6.35 \mathrm{~g}\) of carbon. How many grams of oxygen does it contain? Which law are you assuming in answering this question?

Short answer

The natural sample of ascorbic acid contains \(8.47 \mathrm{~g}\) of oxygen. We assumed the law of constant composition (law of definite proportions) in our calculations, which states that a chemical compound always has the same proportion of its constituent elements by mass.

Step-by-step solution

Determine the mass ratio of carbon to oxygen in the synthesized sample

In the synthesized sample, we are given the mass of carbon and oxygen as \(1.50 \mathrm{~g}\) and \(2.00 \mathrm{~g}\), respectively. We can calculate the mass ratio of carbon to oxygen by dividing the mass of carbon by the mass of oxygen: \[ \text{Mass ratio} = \frac{\text{Mass of Carbon}}{\text{Mass of Oxygen}} = \frac{1.50 \mathrm{~g}}{2.00 \mathrm{~g}} \]

Calculate the mass ratio of carbon to oxygen

Now we can compute the mass ratio of carbon to oxygen in the synthesized sample: \[ \text{Mass ratio} = \frac{1.50 \mathrm{~g}}{2.00 \mathrm{~g}} = 0.75 \]

Determine the mass of oxygen in the natural sample using the mass ratio

Since we are assuming the law of constant composition, the mass ratio of carbon to oxygen in the natural sample will be the same as the synthesized sample. We can now determine the mass of oxygen using the mass of carbon (\(6.35 \mathrm{~g}\)) in the natural sample and the mass ratio we found in Step 2: \[ \text{Mass of Oxygen} = \frac{\text{Mass of Carbon}}{\text{Mass ratio}} = \frac{6.35 \mathrm{~g}}{0.75} \]

Calculate the mass of oxygen in the natural sample

Finally, we compute the mass of oxygen in the natural sample: \[ \text{Mass of Oxygen} = \frac{6.35 \mathrm{~g}}{0.75} = 8.47 \mathrm{~g} \] So the natural sample of ascorbic acid contains \(8.47 \mathrm{~g}\) of oxygen. In answering this question, we assumed the law of constant composition (law of definite proportions), which states that a chemical compound always has the same proportion of its constituent elements by mass.

Key concepts

Chemical Composition

The chemical composition of a substance refers to the identity and quantity of the elements that make up that substance. For instance, ascorbic acid, commonly known as vitamin C, consists of carbon, hydrogen, and oxygen in specific proportions. These proportions are consistent across any sample of ascorbic acid, whether synthesized in a lab or isolated from natural sources, such as citrus fruits.

Understanding chemical composition is crucial because it defines the distinct characteristics of a compound, ranging from its physical properties, like melting and boiling points, to its reactivity with other substances. In the given exercise, ascorbic acid’s chemical composition directs us to expect the same carbon-to-oxygen mass ratio in all samples, providing the foundation for solving the problem.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It involves calculations to determine the quantities of substances consumed and produced. The principles of stoichiometry rest on the balanced chemical equation and abide by the law of conservation of mass, which implies that matter cannot be created or destroyed in an ordinary chemical reaction.

For the exercise involving ascorbic acid, stoichiometry allows us to extend the known mass of one element (carbon) to uncover the associated mass of another (oxygen), upholding the consistent stoichiometric ratio derived from a separate sample. This correlation facilitates the prediction of how much oxygen is present in a natural sample based on its carbon content.

Mass Ratio in Compounds

The mass ratio in compounds is a fixed value that indicates the ratio of the masses of one element to another within a chemical compound. This concept is a direct result of the law of constant composition, also known as the law of definite proportions, which dictates that a given compound always contains the same elements in the same proportions by mass.

In the provided exercise, the task was to find the mass of oxygen in a natural sample of ascorbic acid based on a known mass of carbon using the mass ratio obtained from a synthesized sample. The consistent mass ratio (calculated to be 0.75 for carbon to oxygen) is fundamental in ensuring that despite the differing sources or conditions of synthesis, ascorbic acid maintains its specific mass ratio, thereby guaranteeing its unique chemical identity.