Problem 109 - Introductory Chemistry Atoms First

Question

A \(110.99-g\) sample of a compound containing only calcium and chlorine is found to contain \(40.98 \mathrm{~g}\) of calcium. (a) How many grams of chlorine are in the compound? (b) What is the percent by mass of calcium in the compound? (c) What is the percent by mass of chlorine in the compound?

Step-by-Step Solution

Answer

(a) 70.01 g of chlorine are in the compound. (b) The percent by mass of calcium in the compound is 36.87%. (c) The percent by mass of chlorine in the compound is 63.13%.

Step 1: Calculate the mass of chlorine in the compound.

To find the mass of chlorine in the compound, subtract the mass of calcium from the total mass of the compound. Mass of chlorine = Total mass of the compound - Mass of calcium = 110.99 g - 40.98 g

Step 2: Calculate the percent by mass of calcium in the compound.

To find the percent by mass of calcium in the compound, divide the mass of calcium by the total mass of the compound and multiply by 100. Percent by mass of calcium = \(\frac{\text{Mass of calcium}}{\text{Total mass of the compound}} \times 100\)

Step 3: Calculate the percent by mass of chlorine in the compound.

To find the percent by mass of chlorine in the compound, divide the mass of chlorine by the total mass of the compound and multiply by 100. Percent by mass of chlorine = \(\frac{\text{Mass of chlorine}}{\text{Total mass of the compound}} \times 100\) Now, let's plug the values and calculate the answers.

Step 4: Calculate the mass of chlorine and the percentage of each element.

Mass of chlorine = 110.99 g - 40.98 g = 70.01 g Percent by mass of calcium = \(\frac{40.98 \,\text{g}}{110.99 \,\text{g}} \times 100 = 36.87 \% \) Percent by mass of chlorine = \(\frac{70.01 \,\text{g}}{110.99 \,\text{g}} \times 100 = 63.13 \% \) So, (a) there are 70.01 grams of chlorine in the compound, (b) the percent by mass of calcium in the compound is 36.87%, and (c) the percent by mass of chlorine in the compound is 63.13%.

Key Concepts

Percent Composition

Understanding the percent composition is crucial in chemistry as it not only assists in identifying the chemical but also aids in determining its purity and helps with stoichiometric calculations during reactions. It is defined as the percentage by mass of each individual element within a compound.

In the given exercise, the percent composition is calculated by dividing the mass of each element by the total mass of the compound, and then multiplying the result by 100 to get a percentage. This concept is vitally important because it serves as a bridge between the mass of substances and the mole concept, which is a fundamental principle in stoichiometry.

To clarify further with the given example, for calcium (Ca), the percent composition is computed as follows:
Percent by mass of calcium = \(\frac{40.98 \,\text{g}}{110.99 \,\text{g}} \times 100 = 36.87 \%\). This shows that in the sample, 36.87% of the mass is attributable to calcium.

Chemical Compounds

Chemical compounds are pure substances formed by the chemical combination of two or more elements in a specific ratio. Each compound has a unique composition as represented by a chemical formula. The compound in question only contains calcium and chlorine, indicating that it is likely a salt with a set ratio of these two elements.

In identifying a chemical compound, knowing its percent composition like the example provided helps us understand the substance's molecular or empirical formula, though additional information may be needed for complete determination. For compounds with more complex structures, the percent composition becomes an even more powerful tool as it helps to decipher the molecular makeup from a macroscopic perspective.

The relationship between the elements in a compound is governed by chemical bonds, which are the result of interactions between the valence electrons of the combining atoms. The types of chemical bonds, ionic or covalent, influence the compound's properties including its percent composition.

Mole Concept

At the heart of stoichiometry lies the mole concept, a fundamental unit in chemistry used to express amounts of a chemical substance. It allows chemists to count particles (atoms, molecules, ions, etc.) in a way that is analogous to counting objects in the everyday world. One mole is defined as Avogadro's number (\(6.022 \times 10^{23}\) particles) of the substance.

The mole concept is tightly tied to the mass of substances because the mass of one mole of a compound is equal to its molar mass, which can be found by adding the atomic masses of the constituent elements. This interplay between moles, mass, and the number of particles forms the foundation for quantitative analysis in chemistry.

In applications to the exercise above, you would need the molar mass of calcium and chlorine to convert the percent composition to moles for further stoichiometric calculations. For example, to determine the molar quantity of calcium in the given sample, you would divide the mass of calcium by its molar mass. This mole calculation is an essential stepto arriving at a deeper understanding of the composition and reactivity of chemical compounds.