Problem 67 - Chemistry The Central Science In Si Units

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. According to the law of constant composition, how many grams of oxygen does it contain?

Step-by-Step Solution

Answer

The citrus fruit sample contains approximately 8.47 g of oxygen.

Step 1: Understand the Law of Constant Composition

The law of constant composition states that any chemical compound will always contain its component elements in fixed ratio by mass, regardless of the source or how it was prepared. This means that the ratio of mass of carbon to mass of oxygen must be the same in both samples.

Step 2: Calculate the Carbon to Oxygen Mass Ratio in the Laboratory Sample

For the laboratory sample, we have 1.50 g of carbon and 2.00 g of oxygen. We can calculate the mass ratio as follows: \[ \text{Carbon to Oxygen ratio} = \frac{\text{Mass of Carbon}}{\text{Mass of Oxygen}} = \frac{1.50}{2.00} = 0.75 \].

Step 3: Apply the Ratio to the Citrus Fruit Sample to Find Oxygen Mass

Given that the carbon to oxygen mass ratio is 0.75, use this to calculate the mass of oxygen in the fruit sample where the mass of carbon is 6.35 g. Setting up the equation: \[ 0.75 = \frac{6.35}{\text{Mass of Oxygen}} \].

Step 4: Solve for the Mass of Oxygen in the Citrus Fruit Sample

Rearrange the equation from Step 3 to find the mass of oxygen: \[ \text{Mass of Oxygen} = \frac{6.35}{0.75} \]. Then calculate the value: \[ \text{Mass of Oxygen} \approx 8.47 \text{ g} \].

Key Concepts

Understanding Chemical Compounds

Chemical compounds are substances that are made up of two or more different elements that are bonded together in fixed proportions. This means that no matter where you find or how you make a compound, its basic composition remains the same. For example, water (H_2O) is always composed of hydrogen and oxygen in a 2:1 ratio.
This fixed composition is due to the way that atoms bond together to form compounds, which creates definite ratios of elements. In the case of ascorbic acid, a compound known commonly as vitamin C, it remains constant no matter if it's made in a lab or extracted from a fruit. Each molecule of ascorbic acid has the same number of carbon, hydrogen, and oxygen atoms.
Chemical compounds are essential in chemistry because they help us understand the properties and behaviors of different substances. Knowing the fixed ratio of elements in a compound allows scientists to predict how it will react with other substances and its potential uses in real life applications.

The Importance of Mass Ratio

The mass ratio in chemical compounds is a way to express the relative quantities of different elements present in a compound. This ratio is crucial because it ensures the consistency of a compound's properties. For instance, if you know that in one sample of a compound the atoms are combined in a specific mass ratio, any sample of that compound will have the same ratio, regardless of its source.
In our example, ascorbic acid, synthesized in a lab and isolated from citrus fruits, must have the same carbon to oxygen mass ratio. The law of constant composition ensures this consistency.
Understanding mass ratios also helps in performing calculations to determine the amount of one element in a sample if you know the amount of another element. This can be particularly useful in a lab setting, where precise measurements are crucial.

A Closer Look at Ascorbic Acid

Ascorbic acid, more commonly known as vitamin C, is a vital nutrient for humans. It's an organic compound mainly found in fruits and vegetables, especially citrus fruits like oranges and lemons. Lab synthesis of ascorbic acid mirrors its natural composition, which consists of carbon, hydrogen, and oxygen.
In our exercise, the challenge was to find the amount of oxygen in a sample of ascorbic acid when given the amount of carbon. By leveraging the known mass ratio from the laboratory, we can calculate this easily. This illustrates the real-world application of the law of constant composition: ensuring the consistent quality and efficacy of vitamin C supplements, regardless of how they are produced.

Unveiling Elemental Composition

Elemental composition refers to the percentage of each element within a compound. It's a fundamental characteristic that determines the compound's properties and behavior. Every molecule of a compound like ascorbic acid shares the same elemental composition.
Identifying a compound's elemental composition requires awareness of the fixed ratios with which elements combine. For example, in ascorbic acid, carbon, hydrogen, and oxygen combine in precise amounts that reflect its molecular structure.
Knowing the elemental composition is crucial not just for chemistry but for various industries where purity and concentration are key, like pharmaceuticals and food production. It ensures that products meet safety and efficiency standards through consistent and predictable properties.