Problem 113 - Chemistry and Chemical Reactivity

Question

Which of the following compounds has the highest mass percent of chlorine? (a) \(\mathrm{BCl}_{3}\) (b) \(\mathrm{AsCl}_{3}\) (c) \(\mathrm{GaCl}_{3}\) (d) \(\mathrm{AlCl}_{3}\) (e) \(\mathrm{PCl}_{3}\)

Step-by-Step Solution

Answer

\( \mathrm{BCl}_{3} \) has the highest mass percent of chlorine (90.77\%).

Step 1: Determine Atomic Masses

List the atomic masses of the elements involved: B: 10.81, As: 74.92, Ga: 69.72, Al: 26.98, P: 30.97, Cl: 35.45.

Step 2: Calculate Molar Masses of Each Compound

For each compound, compute the molar mass:- \( \mathrm{BCl}_{3} \): \( 10.81 + 3 \times 35.45 = 117.16 \)- \( \mathrm{AsCl}_{3} \): \( 74.92 + 3 \times 35.45 = 178.27 \)- \( \mathrm{GaCl}_{3} \): \( 69.72 + 3 \times 35.45 = 176.07 \)- \( \mathrm{AlCl}_{3} \): \( 26.98 + 3 \times 35.45 = 133.33 \)- \( \mathrm{PCl}_{3} \): \( 30.97 + 3 \times 35.45 = 137.32 \)

Step 3: Calculate Mass Percent of Chlorine

Find the mass percent of chlorine for each compound using the formula:\[ \text{Mass percent of Cl} = \left( \frac{3 \times 35.45}{\text{Molar mass of compound}} \right) \times 100 \]- \( \mathrm{BCl}_{3} \): \( \left( \frac{106.35}{117.16} \right) \times 100 = 90.77\% \)- \( \mathrm{AsCl}_{3} \): \( \left( \frac{106.35}{178.27} \right) \times 100 = 59.67\% \)- \( \mathrm{GaCl}_{3} \): \( \left( \frac{106.35}{176.07} \right) \times 100 = 60.41\% \)- \( \mathrm{AlCl}_{3} \): \( \left( \frac{106.35}{133.33} \right) \times 100 = 79.76\% \)- \( \mathrm{PCl}_{3} \): \( \left( \frac{106.35}{137.32} \right) \times 100 = 77.45\% \)

Step 4: Identify Compound with Highest Chlorine Percentage

Compare the mass percent of chlorine in each compound. The highest percent is for \( \mathrm{BCl}_{3} \) at 90.77\%.

Key Concepts

Molar Mass

Molar mass is a fundamental concept in chemistry used to express the mass of one mole of a given substance, typically in units of grams per mole (g/mol). It is crucial for understanding how much of each element is contained in a compound.
To calculate the molar mass, you sum up the atomic masses of all the atoms in the molecule. For example, in the compound \( \mathrm{BCl}_{3} \) (boron trichloride), you need to consider the atomic mass of boron and the atomic masses of the three chlorine atoms.
Finding molar mass involves these steps:

• Identify the number of atoms of each element in the compound.
• Multiply the atomic mass of each element by the number of atoms of that element in the compound.
• Add these values together to get the total molar mass of the compound.

This metric not only aids in calculating the mass percent of elements but also plays a vital role in stoichiometric calculations, making it easier to convert between moles and grams.

Chlorine Compounds

Chlorine compounds like \( \mathrm{BCl}_{3} \), \( \mathrm{AsCl}_{3} \), and \( \mathrm{PCl}_{3} \) consist of chlorine bonded with other elements. Chlorine is a highly reactive halogen and is commonly found as a part of numerous compounds.
These particular compounds tend to form strong covalent connections due to chlorine's high electronegativity. The different elements such as boron (B), arsenic (As), gallium (Ga), aluminum (Al), and phosphorus (P) create unique interactions with chlorine, affecting the overall properties of the compound.
Understanding chlorine compounds entails observing these aspects:

• The valency of chlorine and its role in forming bonds.
• The type of bonding (covalent or ionic) involved in the compound.
• The molecular structure and how it influences the compound’s chemical behavior.

Studying chlorine compounds helps in understanding different chemical reactions and their industrial applications like in water purification, pesticides, and even in some pharmaceuticals.

Atomic Mass

Atomic mass, often seen as atomic weight, is essential for determining the composition of elements. It tells us the average mass of atoms in an element and is measured in atomic mass units (amu).
For an element like chlorine, the atomic mass is typically around 35.45 amu.
This information is crucial when calculating molar mass and mass percent in compounds:

• Atomic mass influences the mass of the compound significantly, especially when elements have noticeably differing atomic masses.
• Knowing atomic masses allows us to determine the relative quantity of each element in compounds.

For example, in the compound \( \mathrm{AlCl}_3 \), knowing the atomic masses of aluminum and chlorine helps calculate the overall molar mass, aiding in deriving the mass percentage of any constituent element.

Chemical Calculations

Chemical calculations encompass a range of mathematical computations used in chemistry to determine quantities and relationships between substances in chemical reactions.
One key calculation is determining the mass percent of an element within a compound, which provides insight into the element's composition relative to the whole molecule.
The formula for mass percent is:\[\text{Mass percent} = \left( \frac{\text{Mass of element in compound}}{\text{Molar mass of compound}} \right) \times 100\]Here's how these calculations are applied:

• Compute the mass of the element of interest (e.g., chlorine) within the compound.
• Calculate the molar mass of the entire compound.
• Substitute these values into the mass percent formula to find the result.

These calculations are fundamental in fields like materials science, pharmaceuticals, and engineering, where understanding a material's composition and stoichiometry accurately impacts formulation and production processes.