Problem 31 - 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

(a) 159.70 g/mol, (b) 117.16 g/mol, (c) 176.14 g/mol

Step 1: Identify the Elements and Their Atomic Masses

For each compound, list the elements it is composed of, and find the atomic masses from the periodic table. - **Fe (Iron):** 55.85 g/mol - **O (Oxygen):** 16.00 g/mol - **B (Boron):** 10.81 g/mol - **Cl (Chlorine):** 35.45 g/mol - **C (Carbon):** 12.01 g/mol - **H (Hydrogen):** 1.01 g/mol

Step 2: Calculate Molar Mass of \\(\mathrm{Fe}_{2} \mathrm{O}_{3}\\)

The formula for iron (III) oxide is \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). Calculate its molar mass:\[\text{Molar mass of } \mathrm{Fe}_{2} \mathrm{O}_{3} = 2 \times 55.85 + 3 \times 16.00 = 111.70 + 48.00 = 159.70 \, \text{g/mol}\]

Step 3: Calculate Molar Mass of \\(\mathrm{BCl}_{3}\\)

The formula for boron trichloride is \(\mathrm{BCl}_{3}\). Calculate its molar mass:\[\text{Molar mass of } \mathrm{BCl}_{3} = 1 \times 10.81 + 3 \times 35.45 = 10.81 + 106.35 = 117.16 \, \text{g/mol}\]

Step 4: Calculate Molar Mass of \\(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\\)

The formula for ascorbic acid (vitamin C) is \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\). Calculate its molar mass:\[\text{Molar mass of } \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} = 6 \times 12.01 + 8 \times 1.01 + 6 \times 16.00 = 72.06 + 8.08 + 96.00 = 176.14 \, \text{g/mol}\]

Key Concepts

iron (III) oxide

Iron (III) oxide, also known as ferric oxide, is a naturally occurring compound composed of iron and oxygen. It is represented by the chemical formula \( \mathrm{Fe}_{2} \mathrm{O}_{3} \). In this compound, two iron (Fe) atoms combine with three oxygen (O) atoms. Ferric oxide is commonly found in nature as the mineral hematite and plays a significant role in various industrial applications, including steelmaking.

To understand the molar mass for iron (III) oxide, it is important to realize its composition:

• Iron (Fe): Each iron atom contributes about 55.85 g/mol.
• Oxygen (O): Each oxygen atom contributes about 16.00 g/mol.

To find the molar mass of iron (III) oxide, you calculate:\[\text{Molar mass of } \mathrm{Fe}_{2} \mathrm{O}_{3} = 2 \times 55.85 + 3 \times 16.00 = 159.70 \, \text{g/mol}\]This total molar mass means that one mole of iron (III) oxide weighs 159.70 grams.

boron trichloride

Boron trichloride is a chemical compound with the formula \( \mathrm{BCl}_{3} \). This compound consists of one boron (B) atom and three chlorine (Cl) atoms. Boron trichloride is used in organic chemistry as a reagent to introduce boron into molecules. It is also utilized in the preparation of other boron compounds and in the electronics industry.

To calculate the molar mass of boron trichloride:

• Boron (B): Contributes 10.81 g/mol.
• Chlorine (Cl): Each atom contributes 35.45 g/mol.

The calculation for the molar mass is:\[\text{Molar mass of } \mathrm{BCl}_{3} = 1 \times 10.81 + 3 \times 35.45 = 117.16 \, \text{g/mol}\]So, the molar mass is 117.16 g/mol, indicating that one mole of boron trichloride weighs this amount in grams.

ascorbic acid

Ascorbic acid, commonly known as vitamin C, is a vital nutrient for humans. It is an antioxidant and is crucial for the maintenance of connective tissue. The chemical formula for ascorbic acid is \( \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} \), reflecting its composition of carbon (C), hydrogen (H), and oxygen (O) atoms.

To determine the molar mass of ascorbic acid:

• Carbon (C): Each carbon atom contributes 12.01 g/mol.
• Hydrogen (H): Each hydrogen atom contributes 1.01 g/mol.
• Oxygen (O): Each oxygen atom contributes 16.00 g/mol.

The calculation of the molar mass is done by summing the contributions of these atoms:\[\text{Molar mass of } \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} = 6 \times 12.01 + 8 \times 1.01 + 6 \times 16.00 = 176.14 \, \text{g/mol}\]Thus, each mole of ascorbic acid weighs 176.14 grams, indicating its presence in chemical reactions and supplementation.