Problem 25 - Introductory Chemistry Atoms First

Question

Volcanoes spew off hydrogen sulfide, a poisonous, bad-smelling gas. A \(100.00-\mathrm{g}\) sample of hydrogen sulfide gas was obtained from some strange volcanic planet. Analysis showed that \(94.08 \mathrm{~g}\) of it is the element sulfur. The rest of the sample consists of the element hydrogen. (a) What are the percentages by mass of sulfur and hydrogen in this sample? (b) Hydrogen sulfide from Earth has exactly the same percent compositions for \(\mathrm{S}\) and \(\mathrm{H}\) as hydrogen sulfide from the strange volcanic planet. Which law accounts for this?

Step-by-Step Solution

Answer

The mass of hydrogen in the \(100.00-\mathrm{g}\) sample is \(5.92 \mathrm{~g}\), and the percentages by mass of sulfur and hydrogen are \(94.08\%\) and \(5.92\%\) respectively. The Law of Definite Proportions (or Law of Constant Composition) accounts for the fact that hydrogen sulfide from Earth has the same percent compositions for S and H as hydrogen sulfide from the strange volcanic planet.

Step 1: Calculate the mass of hydrogen in the sample

To find the mass of hydrogen in this \(100.00-\mathrm{g}\) sample of hydrogen sulfide, simply subtract the mass of sulfur from the total mass of the sample: Mass of hydrogen = Total mass of sample - Mass of sulfur = \(100.00 \mathrm{~g} - 94.08 \mathrm{~g}\).

Step 2: Compute the percentages by mass of sulfur and hydrogen

To find the percentages by mass of sulfur and hydrogen, we'll divide the mass of each element by the total mass of the sample, and then multiply by 100. Percentage by mass of sulfur = (Mass of sulfur / Total mass of sample) × 100 Percentage by mass of hydrogen = (Mass of hydrogen / Total mass of sample) × 100

Step 3: Identify the law that accounts for the same percent compositions

After calculating the percentages by mass of sulfur and hydrogen, we'll identify the law that accounts for the fact that hydrogen sulfide from Earth has the same percent compositions for S and H as hydrogen sulfide from the strange volcanic planet. Now, let's perform the calculations: Step 1: Calculate the mass of hydrogen in the sample Mass of hydrogen = \(100.00 \mathrm{~g} - 94.08 \mathrm{~g} = 5.92 \mathrm{~g}\) Step 2: Compute the percentages by mass of sulfur and hydrogen Percentage by mass of sulfur = \(\frac{94.08 \mathrm{~g}}{100.00 \mathrm{~g}} \times 100 = 94.08\%\) Percentage by mass of hydrogen = \(\frac{5.92 \mathrm{~g}}{100.00 \mathrm{~g}} \times 100 = 5.92\%\) Step 3: Identify the law that accounts for the same percent compositions The law that accounts for the fact that hydrogen sulfide from Earth has the same percent compositions for S and H as hydrogen sulfide from the strange volcanic planet is the Law of Definite Proportions (or Law of Constant Composition). This law states that a given compound always contains exactly the same proportion of elements by mass.

Key Concepts

Percent Composition

Percent composition is an essential concept in chemistry that helps to describe the relative amounts of each element within a compound. It shows the percentage of each element's mass compared to the total mass of the compound. Think of percent composition as a recipe, where each ingredient's amount contributes to the whole dish. To calculate the percent composition for an element in a compound:

• First, determine the mass of the element in the sample.
• Divide the element's mass by the total mass of the sample.
• Multiply the result by 100 to convert it into a percentage.

For instance, in our exercise with hydrogen sulfide (\( \text{H}_2\text{S} \)), the sulfur's percent composition is calculated as \[(\frac{94.08 \text{ g}}{100.00 \text{ g}}) \times 100 = 94.08\%\]. Similarly, hydrogen's percent composition is \[(\frac{5.92 \text{ g}}{100.00 \text{ g}}) \times 100 = 5.92\%\]. This allows us to clearly express the makeup of the compound, in this case, showing that the compound is mostly sulfur by mass.

Law of Definite Proportions

The Law of Definite Proportions, also known as the Law of Constant Composition, is a fundamental principle in chemistry. It tells us that a chemical compound always contains the same elements in exactly the same proportions by mass, regardless of the sample's source or size.
This law ensures that water from any location consists of hydrogen and oxygen in a fixed mass ratio. The same principle applies to hydrogen sulfide, whether from Earth, a volcano, or a distant planet. In our exercise, both terrestrial and extraterrestrial hydrogen sulfide have the same percent compositions for sulfur and hydrogen. This consistency across samples is due to the Law of Definite Proportions.
Historically, this law helped distinguish between compounds and mixtures, as mixtures can vary in composition, while compounds do not. It's like knowing that a chocolate chip cookie will always contain a specific ratio of flour, sugar, and chocolate in precise cookie brand mixtures.

Elemental Analysis

Elemental analysis is a method used to determine the elemental composition of a sample. It is essential for identifying the substances within a sample and understanding their quantities.
In the context of hydrogen sulfide from our exercise, elemental analysis allowed scientists to measure how much sulfur and hydrogen were present in the sample. By doing so, they could calculate each element's mass, 94.08 g for sulfur and 5.92 g for hydrogen, and determine the sample's total mass.
Elemental analysis typically involves breaking down a compound to measure each element. Techniques like CHN Analysis, Inductively Coupled Plasma (ICP), or Mass Spectrometry are commonly used in laboratories. These techniques drive deeper understanding and accurate quantification of chemical compositions, thus supporting calculations like percent composition and validating the Law of Definite Proportions.