Question

What are the formula masses of water, \(\mathrm{H}_{2} \mathrm{O}\), propene, \(\mathrm{C}_{3} \mathrm{H}_{6}\), and 2-propanol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}\) ?

Short answer

The formula masses are 18 amu for H₂O, 42 amu for C₃H₆, and 60 amu for C₃H₈O.

Step-by-step solution

Identify the atomic masses

First, we need to know the atomic masses of the elements involved, which can be found on the periodic table. Hydrogen (H) has an atomic mass of approximately 1 amu (atomic mass unit), Carbon (C) is about 12 amu, and Oxygen (O) is approximately 16 amu.

Calculate the formula mass of water (H₂O)

Water has the chemical formula \(\mathrm{H}_{2}\mathrm{O}\). This means it contains 2 hydrogen atoms and 1 oxygen atom. The formula mass is calculated as follows: \(2 \times 1\,\text{amu (H)} + 1 \times 16\,\text{amu (O)} = 2 + 16 = 18\,\text{amu}\).

Calculate the formula mass of propene (C₃H₆)

Propene has the formula \(\mathrm{C}_{3}\mathrm{H}_{6}\). This implies it contains 3 carbon atoms and 6 hydrogen atoms. The formula mass is calculated as: \(3 \times 12\,\text{amu (C)} + 6 \times 1\,\text{amu (H)} = 36 + 6 = 42\,\text{amu}\).

Calculate the formula mass of 2-propanol (C₃H₈O)

2-Propanol has the formula \(\mathrm{C}_{3}\mathrm{H}_{8}\mathrm{O}\). Thus, it includes 3 carbon atoms, 8 hydrogen atoms, and 1 oxygen atom. The formula mass is calculated as: \(3 \times 12\,\text{amu (C)} + 8 \times 1\,\text{amu (H)} + 1 \times 16\,\text{amu (O)} = 36 + 8 + 16 = 60\,\text{amu}\).

Key concepts

Atomic Mass

Atomic mass is a crucial concept in chemistry that refers to the mass of an individual atom. It is usually expressed in atomic mass units (amu). One atomic mass unit is defined as one-twelfth the mass of a carbon atom (C) that contains six protons and six neutrons. This makes it a very small unit, ideal for expressing atomic-scale weights.

When looking up atomic masses, you often use the periodic table, where each element is listed along with its atomic mass. For example, hydrogen (H) has an atomic mass of about 1 amu, carbon (C) is approximately 12 amu, and oxygen (O) is around 16 amu. These values are averages of the isotopes available in nature.

Periodic Table

The periodic table is an organized way to display all the known chemical elements based on their atomic number, electron configurations, and recurring chemical properties. It was created to classify elements such that elements with similar properties are grouped together.

In the periodic table:

• Elements are arranged in order of increasing atomic number.
• Horizontal rows are called periods.
• Vertical columns are known as groups or families.

Each element's block in the table gives a lot of information, including the atomic number and atomic mass. This is how we identify the masses of hydrogen, carbon, and oxygen when calculating formula masses in chemical formulas.

Chemical Formula

A chemical formula represents a substance using symbols for its constituent elements. The formula shows:

• The types of atoms involved.
• The number of each type of atom in a molecule.

For instance, in water (H₂O), the formula indicates two hydrogen atoms and one oxygen atom. Similarly, propene is written as C₃H₆, containing three carbon atoms and six hydrogen atoms, and 2-propanol as C₃H₈O, comprising three carbons, eight hydrogens, and one oxygen atom.

By knowing the chemical formula, scientists can predict various properties of the compound, including its formula mass.

Water (H₂O)

Water is one of the simplest and most essential compounds for life, with a chemical formula of H₂O. This means each molecule of water consists of two hydrogen atoms and one oxygen atom.

To determine the formula mass of water:

• Multiply the atomic mass of hydrogen (1 amu) by the number of hydrogen atoms: 2 \( \times \) 1 amu = 2 amu
• Add the mass of one oxygen atom: 1 \( \times \) 16 amu = 16 amu
• Combine the masses: 2 amu + 16 amu = 18 amu

The formula mass of water is therefore 18 amu.

Propene (C₃H₆)

Propene, with the chemical formula C₃H₆, is an organic compound that is commonly used in the production of plastics. The formula indicates it has three carbon atoms and six hydrogen atoms.

To find the formula mass of propene:

• Calculate the total mass of carbon: 3 \( \times \) 12 amu (each carbon) = 36 amu
• Determine the mass contributed by hydrogen: 6 \( \times \) 1 amu (each hydrogen) = 6 amu
• Add these together: 36 amu + 6 amu = 42 amu

So, the formula mass of propene is 42 amu.

2-Propanol (C₃H₈O)

2-Propanol, also known as isopropanol or rubbing alcohol, has the chemical formula C₃H₈O. It contains three carbon atoms, eight hydrogen atoms, and one oxygen atom.

Here's how you calculate the formula mass of 2-propanol:

• Carbon's contribution: 3 \( \times \) 12 amu = 36 amu
• Hydrogen's contribution: 8 \( \times \) 1 amu = 8 amu
• Oxygen's contribution: 1 \( \times \) 16 amu = 16 amu
• Add them up: 36 amu + 8 amu + 16 amu = 60 amu

Thus, the formula mass of 2-propanol is 60 amu.