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

Short answer

The mass ratio of carbon to oxygen in the first sample of ascorbic acid is \(0.75\). Using this ratio, there are approximately \(8.47 \mathrm{g}\) of oxygen in the second sample, which contains \(6.35 \mathrm{g}\) of carbon.

Step-by-step solution

Calculate the mass ratio of the elements in the first sample

First, we need to find out the mass ratio of carbon and oxygen in the first sample. We are given 1.50 grams of carbon and 2.00 grams of oxygen, so the mass ratio of carbon to oxygen is: \[\frac{\text{mass of carbon}}{\text{mass of oxygen}} = \frac{1.50}{2.00} = 0.75\]

Use the mass ratio to find the mass of oxygen in the second sample

Now, we'll use the calculated mass ratio from step 1 to find the mass of oxygen in the second sample. We're given that the second sample contains 6.35 grams of carbon. Let 'x' be the mass of oxygen in the second sample. \[0.75 = \frac{6.35}{x}\]

Solve for x

Now, we need to solve for 'x' to find out the mass of oxygen in the second sample: \[x = \frac{6.35}{0.75}\] \[x \approx 8.47\] So, there are approximately 8.47 grams of oxygen in the second sample of ascorbic acid.

Key concepts

Understanding Ascorbic Acid

Ascorbic acid, also known as vitamin C, is an essential nutrient for the human body. It's vital for the growth and repair of tissues. The chemical formula for ascorbic acid is \( \text{C}_6\text{H}_8\text{O}_6 \). This signifies six carbon atoms, eight hydrogen atoms, and six oxygen atoms in each molecule.

Ascorbic acid is found naturally in citrus fruits, such as oranges and lemons. But it can also be synthesized in the laboratory for various uses, such as in supplements and fortified foods. Understanding its composition is crucial in fields like nutrition and chemistry, as its structure and elemental makeup influence its function and benefits. By examining its components, we can see the intricate balance of elements that contribute to its effectiveness as a nutrient.

Concept of Mass Ratio

The mass ratio of a substance refers to the proportion of elements by mass within a compound. It's a crucial concept in chemistry that follows the law of constant composition, stating that a given compound will always contain the same proportion of elements by mass.

For instance, in the original exercise, the given ascorbic acid sample has 1.50 grams of carbon and 2.00 grams of oxygen. Therefore, its mass ratio is calculated as:

• Mass ratio = \( \frac{1.50}{2.00} = 0.75 \)

This ratio remains consistent across any sample of the same compound, whether it's synthesized in a lab or extracted from fruits.

Using the mass ratio, one can predict the mass of another element in a different sample of the same compound. This can be particularly useful in determining the constituency of larger samples, and ensures the consistency of chemical analysis across different environments and sources.

Chemical Sample Analysis in Practice

Chemical sample analysis involves examining the composition of substances to determine their structure and elemental makeup. This process is vital in achieving accurate results and understanding substances on a molecular level.

To analyze a chemical sample effectively:

• Identify the known quantities or masses of elements in a sample.
• Apply the concept of mass ratios to predict unknown masses.
• Utilize mathematical equations to calculate these unknowns accurately.

In the given exercise, after calculating the mass ratio of carbon to oxygen in the first sample of ascorbic acid (0.75), we used it to find the mass of oxygen in the second sample. By setting up the equation \( 0.75 = \frac{6.35}{x} \) and solving for \( x \), the mass of oxygen was determined to be approximately 8.47 grams.

This methodical approach underscores the importance of following consistent rules of chemical composition and analysis, allowing for reliable and repeatable results regardless of the source or size of the chemical sample.