Problem 67 - Chemistry: The Central Science in SI Units, Global Edition

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 second sample of ascorbic acid isolated from citrus fruits contains \(4.76 \mathrm{~g}\) of oxygen, according to the law of constant composition.

Step 1: Calculate the ratio between the masses of carbon and oxygen in the first sample

First, we need to find the ratio between the masses of carbon and oxygen in the first sample. We can calculate this by dividing the mass of carbon by the mass of oxygen. Ratio = mass of carbon / mass of oxygen In the first sample, we have: Mass of carbon = 1.50 g Mass of oxygen = 2.00 g So the ratio between the masses of carbon and oxygen is: Ratio = (1.50 g)/(2.00 g)

Step 2: Calculate the mass of oxygen in the second sample.

Now, we will use the calculated ratio from Step 1 to find the mass of oxygen in the second sample. We do this by multiplying the mass of carbon in the second sample by the ratio we found in Step 1. Mass of carbon in the second sample = 6.35 g Ratio (from Step 1) = (1.50 g)/(2.00 g) Mass of oxygen in the second sample = (6.35 g) × (1.50 g/2.00 g)

Step 3: Calculate the final mass of oxygen in the second sample.

In this step, we will perform the actual multiplication to find the mass of oxygen in the second sample. Mass of oxygen = (6.35 g) × (1.50 g/2.00 g) = (6.35 g) × (0.75) Mass of oxygen = 4.76 g According to the law of constant composition, the second sample of ascorbic acid isolated from citrus fruits contains 4.76 grams of oxygen.

Key Concepts

Understanding Ratio Calculation

When looking into ratio calculations, we begin by understanding the comparison of two quantities. In chemistry, calculating the ratio of the masses of elements in a compound is crucial for understanding their proportions. This is particularly useful when applying the law of constant composition.

For example, given a compound containing different masses of carbon and oxygen, you would calculate the ratio by dividing the mass of one element by the mass of the other. In our case:

• Mass of carbon = 1.50 g
• Mass of oxygen = 2.00 g

The ratio of carbon to oxygen therefore becomes:\[\text{Ratio} = \frac{1.50 \, \text{g C}}{2.00 \, \text{g O}} = 0.75\]This means, for every gram of oxygen, there are 0.75 grams of carbon. Ratio calculations allow you to determine the consistent proportion of elements in different samples of the same compound.

Decoding Ascorbic Acid Samples

Ascorbic acid, commonly known as vitamin C, is a substance where understanding its composition is key for applications in both nutrition and chemistry. When dealing with ascorbic acid samples, recognizing that they follow the law of constant composition is essential.

Let's consider two different samples:

• The first sample synthesized in the lab contains 1.50 grams of carbon and 2.00 grams of oxygen.
• The second sample, isolated from citrus fruits, contains 6.35 grams of carbon.

Even though these samples come from different sources, according to the law of constant composition, they must exhibit the same mass ratio. Therefore, calculating the amount of oxygen in the second sample involves applying the previously determined carbon to oxygen ratio (0.75).

Using this ratio helps us understand the consistent nature of ascorbic acid's elemental makeup across various sources.

The Significance of Mass Ratio in Chemistry

Mass ratios in chemistry convey the consistent proportion of elements in a chemical compound, irrespective of the sample's size or source. This is rooted in the law of constant composition, which dictates that a chemical compound always contains the same elements in exactly the same proportions by mass.

So, when we encounter different samples of the same compound, even if from different locations or methods, they will follow the same mass ratio as shown:

• The ratio for ascorbic acid samples calculated from the lab synthesis is 0.75.
• This means that in the fruit-derived sample with 6.35 grams of carbon, the amount of oxygen calculated based on this consistent ratio is 4.76 grams.

Understanding mass ratios not only helps in predicting the behavior of compounds but also ensures accuracy when performing chemical analyses, ensuring that calculations reflect true chemical consistency across samples.