Question

A sample of ascorbic acid (vitamin \(\mathrm{C}\) ) 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 second sample of ascorbic acid, isolated from citrus fruits, contains 8.47 grams of oxygen. We assumed the Law of Definite Proportions in answering this question.

Step-by-step solution

Calculate the ratio of carbon to oxygen in the Laboratory sample.

First, we need to determine the ratio of carbon to oxygen in the laboratory sample of ascorbic acid. To do this, divide the mass of carbon by the mass of oxygen in the laboratory sample: Ratio of \(\frac{Carbon}{Oxygen} = \frac{1.50\,g\,Carbon}{2.00\,g\,Oxygen}\)

Simplify the ratio

Now, simplify the ratio to a whole number or simplest fraction: \(\frac{3}{4} = \frac{Carbon}{Oxygen}\) So there are 3 grams of carbon for every 4 grams of oxygen in ascorbic acid.

Use the proportion to find grams of oxygen in the second sample.

We can set up a proportion using the information we have for the second sample. We know that there are 6.35 grams of carbon in the second sample, and we want to find out how many grams of oxygen it contains. Since the ratio applies to both samples (because of the Law of Definite Proportions), we can write the proportion as: \(\frac{1.50\,g\,Carbon}{2.00\,g\,Oxygen} = \frac{6.35\,g\,Carbon}{x\,g\,Oxygen}\) Solve for x, to find the mass of oxygen: \(1.50 * x = 2.00 * 6.35\) \(x = \frac{2.00 * 6.35}{1.50}\) \(x = 8.47\,g\)

State the final answer

The second sample of ascorbic acid, isolated from citrus fruits, contains 8.47 grams of oxygen. The law that we assumed in answering this question is the "Law of Definite Proportions."

Key concepts

Stoichiometry

Stoichiometry is the field of chemistry that relates to measuring the quantitative relationships or ratios between reactants and products in chemical reactions. It is based on the conservation of mass where the mass of the reactants equals the mass of the products. Stoichiometry allows chemists to predict the amounts of substances consumed and produced in a given reaction.

Using stoichiometry in a problem-solving context usually involves understanding the mole concept, balancing equations, and using mole ratios. In the given example of ascorbic acid, stoichiometry is applied to determine the mass of oxygen in the second sample based on its known carbon content. The steps involve setting up a proportional relationship derived from a balanced chemical understanding of the substance's composition.

Chemical Composition

Chemical composition refers to the identity and quantity of the elements or compounds that make up a substance. Knowing the chemical composition of a substance is crucial for understanding its properties and behavior during a chemical reaction.

In the context of the exercise, chemical composition is integral to understanding how the same substance—ascorbic acid—from different sources has consistent elemental ratios. The concept of chemical composition underlies the principle that the ascorbic acid obtained from citrus fruits will have the same ratio of carbon to oxygen as the sample synthesized in the laboratory. This concept is foundational to the science of chemistry as it reflects the consistent and predictable nature of matter at a molecular level.

Mole Ratio

The mole ratio is a key concept in stoichiometry; it represents the ratio of moles of one substance to the moles of another substance in a chemical reaction. These ratios are derived from the coefficients of a balanced chemical equation, enabling the calculation of the quantities of reactants needed or products formed.

In our example problem, we express the relationship between carbon and oxygen in ascorbic acid as a mole ratio, even though the exercise deals with grams. The conversion to moles isn't shown but is implicit in the presumed chemical formula consistency. The mole ratio provides the bridge to use stoichiometry for converting between masses of different elements in a compound.

Ascorbic Acid Chemistry

Ascorbic acid, known as vitamin C, is an essential nutrient in the human diet and is known for its properties as an antioxidant. Chemically, it is C₆H₈O₆, which reveals that its mole ratio of carbon to oxygen is 6:6, or simplified to 1:1. However, the exercise simplifies the ratio further based on the given masses, not the chemical formula.

The understanding of ascorbic acid chemistry is crucial for solving this problem because it reinforces the notion that every sample of pure ascorbic acid must contain these elements in a definite proportion, regardless of its source. Assumptions about its uniformity across different samples are used when applying the Law of Definite Proportions.