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) \(\left.\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}, \text { ascorbic acid (vitamin } \mathrm{C}\right)\)

Short answer

(a) 159.70 g/mol; (b) 117.16 g/mol; (c) 176.14 g/mol.

Step-by-step solution

Understand the Concept

To calculate the molar mass of a compound, first, determine the atomic masses of each element in the compound. Atomic masses can be found on the periodic table and are expressed in atomic mass units (amu). The molar mass of the compound is the sum of the atomic masses of all the atoms present in one mole of the compound.

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

Iron (III) oxide has the formula \( \mathrm{Fe}_2 \mathrm{O}_3 \). To find its molar mass:- Iron (\( \mathrm{Fe} \)): Atomic mass = 55.85 amu- Oxygen (\( \mathrm{O} \)): Atomic mass = 16.00 amuCalculate the molar mass by multiplying the atomic masses by the number of each type of atom and summing up:\[(2 \times 55.85) + (3 \times 16.00) = 111.70 + 48.00 = 159.70 \, \text{g/mol}\]

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

Boron trichloride has the formula \( \mathrm{BCl}_3 \). To find its molar mass:- Boron (\( \mathrm{B} \)): Atomic mass = 10.81 amu- Chlorine (\( \mathrm{Cl} \)): Atomic mass = 35.45 amuCalculate the molar mass:\[(1 \times 10.81) + (3 \times 35.45) = 10.81 + 106.35 = 117.16 \, \text{g/mol}\]

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

Ascorbic acid has the formula \( \mathrm{C}_6 \mathrm{H}_8 \mathrm{O}_6 \). To find its molar mass:- Carbon (\( \mathrm{C} \)): Atomic mass = 12.01 amu- Hydrogen (\( \mathrm{H} \)): Atomic mass = 1.01 amu- Oxygen (\( \mathrm{O} \)): Atomic mass = 16.00 amuCalculate the molar mass:\[(6 \times 12.01) + (8 \times 1.01) + (6 \times 16.00) = 72.06 + 8.08 + 96.00 = 176.14 \, \text{g/mol}\]

Key concepts

Atomic Mass

Atomic mass refers to the mass of an individual atom of a chemical element. It is usually expressed in atomic mass units (amu), which are equivalent to grams per mole. This concept is fundamental when performing calculations involving molar mass. When atoms bond to form a molecule, the total mass of the molecule corresponds to the sum of the atomic masses of all the involved atoms.

Each element has a unique atomic mass, which is a reflection of the average mass of its isotopes, weighted by their abundance. For example:

• Iron (Fe) has an atomic mass of 55.85 amu.
• Oxygen (O) has an atomic mass of 16.00 amu.
• Boron (B) has an atomic mass of 10.81 amu.
• Chlorine (Cl) has an atomic mass of 35.45 amu.

Understanding atomic mass is essential when determining the molar masses of compounds, as it allows you to add up the mass contributions from each atom present in a compound.

Periodic Table

The periodic table is a graphical arrangement of all known chemical elements, organized by increasing atomic number, which corresponds to the number of protons in an atom's nucleus. The periodic table is a crucial tool in chemistry, as it provides essential information about the elements, including their atomic numbers, symbols, and atomic masses.

Elements in the periodic table are arranged in rows and columns to reflect similarities in chemical properties. Each element’s atomic mass is generally stated beneath its symbol in the table. This makes it easy to look up the necessary atomic masses when calculating molar masses of compounds.

• The periodic table is divided into different blocks, such as s-block, p-block, d-block, and f-block, based on the electron configurations of elements.
• Groups are the vertical columns in the periodic table, and elements within a group typically share similar chemical behaviors.
• Periods are the horizontal rows, and as you move across a period, the atomic number increases, and properties vary consistently.

Using the periodic table effectively can provide insights into how different elements will interact in chemical reactions, such as those needed to understand molar mass calculations.

Chemical Compounds

Chemical compounds are substances formed by the combination of two or more different elements in fixed ratios through chemical bonds. These compounds have distinct properties that differ from the individual elements that compose them. Here are some examples from the provided exercise:

- Iron (III) oxide, (\( \mathrm{Fe}_2 \mathrm{O}_3 \)), is a compound consisting of iron and oxygen atoms. It forms a red-brown crystalline solid, commonly known as rust.- Boron trichloride, (\( \mathrm{BCl}_3 \)), is a compound where one boron atom is bonded to three chlorine atoms.- Ascorbic acid (\( \mathrm{C}_6 \mathrm{H}_8 \mathrm{O}_6 \)), or vitamin C, consists of carbon, hydrogen, and oxygen. It is essential for human health, functioning as an antioxidant.

The properties of a chemical compound depend not only on the types of atoms it contains but also on how they are bonded. There are different types of chemical bonds, such as covalent bonds (where atoms share electrons) and ionic bonds (where atoms transfer electrons). The structure of these compounds influences their physical and chemical properties, making each compound unique. Understanding chemical compounds is crucial for calculating molar mass, as knowing the exact number of each type of atom within the compound allows for precise calculations.