Problem 69 - Chemistry and Chemical Reactivity

Question

Calculate the molar mass of each of the following compounds: (a) \(\mathrm{Fe}_{2} \mathrm{O}_{3},\) iron(III) oxide (b) \(\mathrm{BCl}_{3},\) boron trichloride (c) \(\left.\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}, \text { ascorbic acid (vitamin } \mathrm{C}\right)\)

Step-by-Step Solution

Answer

Fe2O3: 159.70 g/mol; BCl3: 117.16 g/mol; C6H8O6: 176.14 g/mol.

Step 1: Identify the Elements and Their Atomic Masses for Fe2O3

The compound is iron(III) oxide and is denoted by \( \mathrm{Fe}_{2} \mathrm{O}_{3} \). This comprises iron (Fe) and oxygen (O). The atomic mass of iron is approximately 55.85 amu, and oxygen is approximately 16.00 amu.

Step 2: Calculate the Molar Mass of Fe2O3

In \( \mathrm{Fe}_{2} \mathrm{O}_{3} \), there are 2 iron atoms and 3 oxygen atoms. Calculate the molar mass as follows: \[ 2 \times 55.85 + 3 \times 16.00 = 111.70 + 48.00 = 159.70 \, \text{g/mol} \]

Step 3: Identify the Elements and Their Atomic Masses for BCl3

Boron trichloride is denoted by \( \mathrm{BCl}_{3} \). This includes boron (B) and chlorine (Cl). The atomic mass of boron is approximately 10.81 amu, and chlorine is approximately 35.45 amu.

Step 4: Calculate the Molar Mass of BCl3

In \( \mathrm{BCl}_{3} \), there is 1 boron atom and 3 chlorine atoms. Calculate the molar mass as follows: \[ 1 \times 10.81 + 3 \times 35.45 = 10.81 + 106.35 = 117.16 \, \text{g/mol} \]

Step 5: Identify the Elements and Their Atomic Masses for C6H8O6

Ascorbic acid (vitamin C) is denoted by \( \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} \). This includes carbon (C), hydrogen (H), and oxygen (O). The atomic mass of carbon is approximately 12.01 amu, hydrogen is 1.01 amu, and oxygen is 16.00 amu.

Step 6: Calculate the Molar Mass of C6H8O6

In \( \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} \), there are 6 carbon atoms, 8 hydrogen atoms, and 6 oxygen atoms. Calculate the molar mass as follows:\[ 6 \times 12.01 + 8 \times 1.01 + 6 \times 16.00 = 72.06 + 8.08 + 96.00 = 176.14 \, \text{g/mol} \]

Key Concepts

Atomic Mass

Every element on the periodic table has a unique atomic mass. Atomic mass is an average mass of atoms of an element, expressed in atomic mass units (amu). It reflects the mass of both protons and neutrons in the atomic nucleus. Understanding atomic mass is vital because it is a key component in calculating the molar mass of compounds. For instance, when dealing with compounds like iron(III) oxide or boron trichloride, knowing the atomic masses of the constituent elements is the first step in determining the entire compound's molar mass.

• Iron (Fe) has an atomic mass of approximately 55.85 amu.
• Oxygen (O) carries an atomic mass of about 16.00 amu.
• Boron (B) exhibits an atomic mass near 10.81 amu.
• Chlorine (Cl) possesses an atomic mass around 35.45 amu.

The atomic mass helps chemists precisely quantify the amount of each element in a chemical reaction.

Chemical Compounds

Chemical compounds are substances composed of two or more different elements combined in fixed ratios. They are bound together through chemical bonds and exhibit properties different from the individual elements. For example, water is not simply a mix of hydrogen and oxygen, but a specific arrangement of these atoms in a distinct molecule that gives water its unique properties.

In our exercises, we dealt with compounds such as iron(III) oxide, which combines iron and oxygen, and boron trichloride, which combines boron and chlorine. Each chemical compound has a formula that provides specific information about the types and numbers of atoms involved. For instance:

• In Fe iii O 2 O 3, the compound includes iron and oxygen atoms in a 2:3 ratio.
• For BCl 3, boron and chlorine are combined at a 1:3 ratio.

Understanding compounds involves not just knowing the formula, but also how these formulas contribute to calculating their molar masses.

Iron(III) Oxide

Iron(III) oxide, represented as \( \mathrm{Fe}_2\mathrm{O}_3 \), is a reddish-brown compound found in nature as hematite and often utilized as a pigment. This compound is composed of iron and oxygen atoms in a 2:3 ratio, as indicated by its chemical formula.

To calculate the molar mass:

• Identify the atomic masses: Iron (Fe) is about 55.85 amu, and oxygen (O) is about 16.00 amu.
• Multiply these atomic masses by the number of respective atoms in the formula: \( 2 \times 55.85 \) for iron and \( 3 \times 16.00 \) for oxygen.
• Add the results: \( 111.70 + 48.00 = 159.70 \, \text{g/mol} \).

This molar mass is essential in fields like geology and material science, where precise compositions are crucial.

Boron Trichloride

Boron trichloride, symbolized as \( \mathrm{BCl}_3 \), is a corrosive gas primarily used in the refining of aluminum, magnesium, zinc, and copper alloys. It consists of one boron atom and three chlorine atoms, as its formula suggests.

When calculating its molar mass, one must:

• Know the atomic masses: Boron (B) has an atomic mass of approximately 10.81 amu, and chlorine (Cl) is around 35.45 amu.
• Multiply these atomic masses by the number of atoms in each element: \( 1 \times 10.81 \) for boron and \( 3 \times 35.45 \) for chlorine.
• Add them up: \( 10.81 + 106.35 = 117.16 \, \text{g/mol} \).

Understanding these calculations helps in industrial and laboratory applications where boron trichloride's reactive qualities are utilized.

Ascorbic Acid

Ascorbic acid, or vitamin C, is crucial for the repair of tissues and enzymatic production of certain neurotransmitters. It is also an antioxidant. Its chemical formula \( \mathrm{C}_6\mathrm{H}_8\mathrm{O}_6 \) reveals it consists of carbon, hydrogen, and oxygen atoms.

To compute its molar mass, follow these steps:

• Identify the atomic masses: Carbon (C) is around 12.01 amu, hydrogen (H) about 1.01 amu, and oxygen (O) is 16.00 amu.
• Multiply the atomic masses by the number of each type of atom: \( 6 \times 12.01 \) for carbon, \( 8 \times 1.01 \) for hydrogen, and \( 6 \times 16.00 \) for oxygen.
• Add these values: \( 72.06 + 8.08 + 96.00 = 176.14 \, \text{g/mol} \).

Knowing ascorbic acid's molar mass is important for creating dietary supplements and understanding its biological interactions.