Problem 70 - Chemistry and Chemical Reactivity

Question

Calculate the molar mass of each of the following compounds: (a) \(\mathrm{Fe}\left(\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{O}_{7}\right)_{2},\) iron (II) gluconate, a dietary supplement (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{SH},\) butanethiol, has a skunk-like odor (c) \(\mathrm{C}_{20} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{2},\) quinine, used as an antimalarial drug

Step-by-Step Solution

Answer

(a) 446.14 g/mol; (b) 90.19 g/mol; (c) 324.42 g/mol.

Step 1: Identify the Elements and Their Atomic Masses

For each compound, list each element present and note its atomic mass. Assume the atomic masses are as follows: Fe: 55.85 g/mol, C: 12.01 g/mol, H: 1.01 g/mol, O: 16.00 g/mol, S: 32.07 g/mol, N: 14.01 g/mol.

Step 2: Write the Molecular Formula of Iron (II) Gluconate

The formula is \(\mathrm{Fe}\left(\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{O}_{7}\right)_{2}\). This indicates 1 iron atom, 12 carbon atoms, 22 hydrogen atoms, and 14 oxygen atoms in one formula unit.

Step 3: Calculate the Molar Mass of Iron (II) Gluconate

Multiply the number of each type of atom by its atomic mass and sum them up: \[\text{Molar mass} = \left(2 \times 55.85\right) + \left(12 \times 12.01\right) + \left(22 \times 1.01\right) + \left(14 \times 16.00\right) = 446.14 \, \text{g/mol}.\]

Step 4: Write the Molecular Formula of Butanethiol

The formula is \(\mathrm{C}_{4}\mathrm{H}_{10}\mathrm{S}\), indicating 4 carbon atoms, 10 hydrogen atoms, and 1 sulfur atom.

Step 5: Calculate the Molar Mass of Butanethiol

Multiply the number of each type of atom by its atomic mass and sum them up: \[\text{Molar mass} = \left(4 \times 12.01\right) + \left(10 \times 1.01\right) + \left(1 \times 32.07\right) = 90.19 \, \text{g/mol}.\]

Step 6: Write the Molecular Formula of Quinine

The formula is \(\mathrm{C}_{20} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{2}\), indicating 20 carbon atoms, 24 hydrogen atoms, 2 nitrogen atoms, and 2 oxygen atoms.

Step 7: Calculate the Molar Mass of Quinine

Multiply the number of each type of atom by its atomic mass and sum them up: \[\text{Molar mass} = \left(20 \times 12.01\right) + \left(24 \times 1.01\right) + \left(2 \times 14.01\right) + \left(2 \times 16.00\right) = 324.42 \, \text{g/mol}.\]

Key Concepts

Molecular Formula

A molecular formula is a representation of a chemical compound which indicates the actual number of each type of atom present in a molecule. It gives us a direct insight into the composition of the compound.
For example, in iron (II) gluconate, the molecular formula is \( \mathrm{Fe}\left(\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{O}_{7}\right)_{2}\). This formula tells us that in one formula unit, there are:

• 1 iron atom,
• 12 carbon atoms,
• 22 hydrogen atoms,
• and 14 oxygen atoms.

Understanding the molecular formula helps in calculating the molar mass, as it clearly shows the number and type of atoms. Similarly, the molecular formula for butanethiol is \( \mathrm{C}_{4}\mathrm{H}_{10}\mathrm{S} \), while for quinine it is \( \mathrm{C}_{20} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{2} \).
This initial step of identifying the molecular formula is crucial as it acts as the foundation for any further calculation or analysis.

Atomic Mass

Atomic mass, typically expressed in grams per mole (g/mol), is the mass of an individual atom of an element. Recognizing the atomic mass of each element is vital in computations involving chemical compounds.
For example, in the problem at hand, we have the following atomic masses:

• Iron (Fe): 55.85 g/mol
• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.01 g/mol
• Oxygen (O): 16.00 g/mol
• Sulfur (S): 32.07 g/mol
• Nitrogen (N): 14.01 g/mol

Knowing these masses allows us to calculate the molar mass of compounds by multiplying the atomic mass of each element by the number of times it appears in the molecular formula.

Chemical Compounds

Chemical compounds are substances formed from two or more elements chemically bonded together. They often have distinct physical and chemical properties compared to their individual elements.
Each compound has a unique molecular formula that shows its elemental composition and provides a roadmap for determining its characteristics, such as molar mass. In our examples:

• Iron (II) Gluconate: \( \mathrm{Fe}\left(\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{O}_{7}\right)_{2} \)
• Butanethiol: \( \mathrm{C}_{4}\mathrm{H}_{10}\mathrm{S} \)
• Quinine: \( \mathrm{C}_{20} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{2} \)

The ability to calculate molar mass is pivotal when studying chemical reactions since it allows us to understand the amounts and proportions of substances involved. This foundational understanding aids predictions and explanations of how compounds behave in different scenarios.

Elemental Composition

Elemental composition refers to the proportion of each element within a compound. Understanding this enables insights into the compound's structure and properties.
The elemental composition of a compound can be determined from its molecular formula. For example, in iron (II) gluconate:

• Each molecule contains 1 iron atom, which is a fundamental part of its structure.
• Carbon, hydrogen, and oxygen appear in higher quantities, influencing its properties and function.

By knowing the elemental composition, chemists can derive crucial information like the percentage composition, which indicates the relative amount of each element in the total compound.
This is essential for tailoring reactions and processes for desired outcomes, especially in fields such as pharmacology, where precise compound formulations are essential.