Problem 28 - Introductory Chemistry Atoms First

Question

Suppose \(12.0 \mathrm{~g}\) of carbon \((\mathrm{C})\) reacts with \(70.0 \mathrm{~g}\) of sulfur (S) to give \(76.0 \mathrm{~g}\) of the compound carbon disulfide \(\left(\mathrm{CS}_{2}\right)\). In the process, all the carbon gets used up, but some elemental sulfur is left over. (a) For the law of conservation of matter to be obeyed, how much sulfur is unused? (b) What is the percent \(\mathrm{C}\) in \(\mathrm{CS}_{2} ?\) (c) What is the percent \(\mathrm{S}\) in \(\mathrm{CS}_{2} ?\) (d) What is the sum of the \(\% \mathrm{C}\) and \(\% \mathrm{~S}\) in \(\mathrm{CS}_{2} ?\)

Step-by-Step Solution

Answer

(a) The unused mass of sulfur is \(6.0 \mathrm{~g}\). (b) The percent of carbon in \(\mathrm{CS}_{2}\) is \(15.8 \% \). (c) The percent of sulfur in \(\mathrm{CS}_{2}\) is \(84.2 \% \). (d) The sum of the \% C and \% S in \(\mathrm{CS}_{2}\) is \(100 \% \).

Step 1: Calculate the mass of sulfur that reacted in the reaction

Since we know the mass of the compound CS₂ and carbon (12.0 g), we can calculate the mass of 'used' sulfur in the compound by the following: Used mass of sulfur = (Mass of CS₂) - (Mass of carbon)

Step 2: Calculate the unused mass of sulfur

Since we're given the initial mass of sulfur (70.0 g), the unused mass of sulfur can be calculated by subtracting the used mass of sulfur from the total mass: Unused mass of sulfur = (Initial mass of sulfur) - (Used mass of sulfur) b) & c) Calculate the percentage of C and S in CS₂

Step 3: Calculate the percentage of carbon in CS₂

To calculate the percentage of carbon in CS₂, we divide the mass of carbon by the mass of CS₂, then multiply the result by 100: Percent of carbon = \(\frac{Mass~of~carbon}{Mass~of~CS_{2}} \times 100\)

Step 4: Calculate the percentage of sulfur in CS₂

Similarly, to calculate the percentage of sulfur in CS₂, we divide the mass of used sulfur by the mass of CS₂, then multiply the result by 100: Percent of sulfur = \(\frac{Mass~of~used~sulfur}{Mass~of~CS_{2}} \times 100\) d) Calculate the sum of % C and % S in CS₂

Step 5: Calculate the sum of the percentages

Now that we have both percentages, add them to find the sum: Sum of percentages = (Percent of carbon) + (Percent of sulfur)

Key Concepts

Stoichiometry

In the realm of chemistry, stoichiometry is a vital concept employed to predict the outcomes of chemical reactions. Through stoichiometry, we study the quantitative relationships between the substances involved in reactions. It allows scientists and students to calculate the amounts of reactants required to produce a certain amount of product, making it a foundational pillar in chemical equations.

For example, if we have a chemical reaction where carbon reacts with sulfur to form carbon disulfide, knowing the stoichiometry of the reaction would tell us how many grams of each reactant we need to produce a specific amount of product. This is precisely what was done in the problem at hand, where the application of stoichiometric principles enables us to discern the amount of sulfur that actually participated in the reaction.

Chemical Reactions

Chemical reactions are processes in which substances, known as reactants, transform into new substances, called products. These transformations are governed by the law of conservation of matter, which states that matter cannot be created or destroyed in a closed system.

Understanding Reactants and Products

In the provided exercise, carbon and sulfur act as reactants to produce carbon disulfide as the product. The exercise walks us through understanding how much of each reactant is used and how much of the product is formed in the reaction.

Applying the Law of Conservation of Matter

By using the initial and final masses of reactants and products, we can apply the law of conservation of matter to find out how much sulfur remains unreacted after forming carbon disulfide. This is crucial for reinforcing the idea that the total mass remains constant, as matter is neither created nor lost, but rather conserved.

Percent Composition

Percent composition is an integral concept that provides information about the relative quantities of elements in a compound. It is determined by dividing the mass of each element in the compound by the total mass of the compound, then multiplying by 100 to get a percentage.

Calculating Percent Composition

In the exercise, the percent composition of carbon and sulfur in carbon disulfide is calculated to understand how much of each element contributes to the total mass of the compound. It helps illustrate the proportional makeup of the compound which is essential for understanding its properties and behavior.

Significance in Chemical Formulas

Knowing the percent composition also assists in verifying chemical formulas, as the percentage of elements must align with their ratios in the pure chemical compound. In the case of carbon disulfide, the percentages added together give us assurance that we have accounted for all the mass in the compound, in accordance with the law of conservation of matter.