Problem 67 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

\(\mathrm{BCl}_3\) has the highest weight percent of chlorine.

Step 1: Identify Molar Masses of Elements

For each compound, note the atomic masses. Chlorine (Cl) has an atomic mass of 35.5 g/mol, boron (B) has an atomic mass of 10.8 g/mol, aluminum (Al) has an atomic mass of 27.0 g/mol, arsenic (As) has an atomic mass of 75.0 g/mol, phosphorus (P) has an atomic mass of 31.0 g/mol, and gallium (Ga) has an atomic mass of 69.7 g/mol.

Step 2: Calculate Molar Mass of Each Compound

The molar mass of each compound can be calculated by summing the atomic masses of its constituent atoms. For example, \( \text{BCl}_3 = 10.8 + 3 \times 35.5 = 117.3 \) g/mol. Similarly, calculate for the other compounds.

Step 3: Determine the Mass of Chlorine in Each Compound

For each compound, the mass of chlorine is calculated by multiplying the number of chlorine atoms by its atomic mass. For example, in \( \text{BCl}_3 \), the mass of chlorine is \( 3 \times 35.5 = 106.5 \) g/mol.

Step 4: Calculate Weight Percent of Chlorine

The weight percent of chlorine is calculated by dividing the mass of chlorine by the molar mass of the compound and then multiplying by 100. For example, \( \text{%Cl in BCl}_3 = \frac{106.5}{117.3} \times 100 \approx 90.8\% \). Perform this calculation for the other compounds.

Step 5: Compare Weight Percents

Compare the calculated weight percent of chlorine for all the compounds to identify which one has the highest value.

Key Concepts

Molar Mass Calculation

Molar mass calculation is an integral part of chemistry for understanding the composition of various compounds. The molar mass of a compound is determined by adding up the atomic masses of all the elements that make up the compound. In simple terms, it's the 'weight' of a mole of that substance.Here's how you do it:

• Identify the chemical formula of the compound.
• Look up the atomic masses for each element in the formula. These are usually given in atomic mass units (amu) or grams per mole (g/mol).
• Multiply the atomic mass of each element by the number of times it appears in the formula.
• Add these values together to get the total molar mass.

For example, for the compound \( \mathrm{BCl}_3 \), the molar mass is calculated as follows: Add the atomic mass of boron (10.8 g/mol) to three times the atomic mass of chlorine (3 times 35.5 g/mol), giving you a total molar mass of 117.3 g/mol.

Atomic Mass

Atomic mass is a measure of the mass of one atom of an element. It is expressed in atomic mass units (amu), where one atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom. Key points to remember about atomic mass:

• Atomic masses are specific to each element; they represent a weighted average of all the isotopes of that element found in nature.
• Atomic mass is essential for calculating the molar mass of compounds, which involves these masses.
• In calculations, the atomic mass is often used as the weight of the element in grams per mole.

For example, chlorine's atomic mass is approximately 35.5 g/mol, which you'll use when calculating the molar mass of compounds involving chlorine.

Chemical Compounds

Chemical compounds are substances composed of two or more different elements that are chemically bonded together. These compounds can be represented using chemical formulas that show the types and numbers of atoms involved.Some fundamentals about chemical compounds:

• Chemical formulas provide essential information like which elements are present and in what ratio.
• Understanding the structure of a chemical compound is crucial for predicting its chemical behavior and properties.
• Compounds have different properties than the elements they contain, such as boiling and melting points, reactivity, and solubility.

For instance, in the compound \( \mathrm{PCl}_3 \), the formula indicates that one phosphorus atom is chemically bonded to three chlorine atoms.

Chlorine Content

Chlorine content in a compound is often calculated to understand its proportion within a mixture or solution. It is expressed as a weight percent, which is the ratio of the mass of chlorine to the total molar mass of the compound, multiplied by 100.To calculate chlorine content:

• First, determine the number of chlorine atoms in the compound.
• Calculate the total mass of chlorine by multiplying the number of chlorine atoms by the atomic mass of chlorine.
• Then divide this value by the total molar mass of the compound.
• Multiply the result by 100 to get the weight percent of chlorine.

For example, if you need to find the chlorine content in \( \mathrm{AlCl}_3 \), use the atomic mass of chlorine (35.5 g/mol) and the molar mass of the compound to compute the chlorine's weight percentage.