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Chapter 1: Problem 67

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?

Short Answer

Expert verified
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 by step solution

01

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)
02

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) 脳 (1.50 g/2.00 g)
03

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) 脳 (1.50 g/2.00 g) = (6.35 g) 脳 (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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

(a) After the label fell off a bottle containing a clear liquid believed to be benzene, a chemist measured the density of the liquid to verify its identity. A \(25.0-\mathrm{mL}\) portion of the liquid had a mass of 21.95 g. A chemistry handbook lists the density of benzene at \(15^{\circ} \mathrm{C}\) as \(0.8787 \mathrm{~g} / \mathrm{mL}\). Is the calculated density in agreement with the tabulated value? (b) An experiment requires \(15.0 \mathrm{~g}\) of cyclohexane, whose density at \(25^{\circ} \mathrm{C}\) is \(0.7781 \mathrm{~g} / \mathrm{mL}\). What volume of cyclohexane should be used? (c) A spherical ball of lead has a diameter of \(5.0 \mathrm{~cm}\). What is the mass of the sphere if lead has a density of \(11.34 \mathrm{~g} / \mathrm{cm}^{3} ?\) (The volume of a sphere is \((4 / 3) \pi r^{3},\) where \(r\) is the radius.)

In \(2009,\) a team from Northwestern University and Western Washington University reported the preparation of a new "spongy" material composed of nickel, molybdenum, and sulfur that excels at removing mercury from water. The density of this new material is \(0.20 \mathrm{~g} / \mathrm{cm}^{3},\) and its surface area is \(1242 \mathrm{~m}^{2}\) per gram of material. (a) Calculate the volume of a (b) Calculate the surface area for \(10.0-\mathrm{mg}\) sample of this material. a \(10.0-\mathrm{mg}\) sample of this material. \((\mathbf{c})\) A \(10.0-\mathrm{mL}\) sample of contaminated water had \(7.748 \mathrm{mg}\) of mercury in it. After treatment with \(10.0 \mathrm{mg}\) of the new spongy material, \(0.001 \mathrm{mg}\) of mercury remained in the contaminated water. What percentage of the (d) What is the final mass mercury was removed from the water? of the spongy material after the exposure to mercury?

(a) A sample of tetrachloroethylene, a liquid used in dry cleaning that is being phased out because of its potential to cause cancer, has a mass of \(40.55 \mathrm{~g}\) and a volume of \(25.0 \mathrm{~mL}\) at \(25^{\circ} \mathrm{C}\). What is its density at this temperature? Will tetrachloroethylene float on water? (Materials that are less dense than water will float.) (b) Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is a gas at room temperature and pressure. However, carbon dioxide can be put under pressure to become a "supercritical fluid" that is a much safer dry-cleaning agent than tetrachloroethylene. At a certain pressure, the density of supercritical \(\mathrm{CO}_{2}\) is \(0.469 \mathrm{~g} / \mathrm{cm}^{3}\). What is the mass of a \(25.0-\mathrm{mL}\) sample of supercritical \(\mathrm{CO}_{2}\) at this pressure?

Give the derived SI units for each of the following quantities in base SI units: (a) acceleration = distance/time \(^{2}\) (b) force \(=\) mass \(\times\) acceleration (c) work \(=\) force \(\times\) distance (d) pressure = force/area (e) power = work/time (f) velocity \(=\) distance/time (g) energy \(=\) mass \(\times(\text { velocity })^{2}\)

(a) The speed of light in a vacuum is \(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}\). Calculate its speed in miles per hour. (b) The Sears Tower in Chicago is \(1454 \mathrm{ft}\) tall. Calculate its height in meters. \((\mathbf{c})\) The Vehicle Assembly Building at the Kennedy Space Center in Florida has a volume of \(3,666,500 \mathrm{~m}^{3}\). Convert this volume to liters and express the result in standard exponential notation. (d) An individual suffering from a high cholesterol level in her blood has \(242 \mathrm{mg}\) of cholesterol per \(100 \mathrm{~mL}\) of blood. If the total blood volume of the individual is \(5.2 \mathrm{~L}\), how many grams of total blood cholesterol does the individual's body contain?
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