Problem 12 - A Complete Resource Book in Chemistry for JEE Main

Question

There are three isotopes of hydrogen and three naturally occurring isotopes of oxygen \(\left(\mathrm{O}^{16}, \mathrm{O}^{17}\right.\) and \(\left.\mathrm{O}^{18}\right)\). How many kinds of water are possible? (a) 9 (b) 16 (c) 8 (d) 18

Step-by-Step Solution

Answer

There are 27 kinds of water possible, but given options don't match this solution.

Step 1: Identify Variables

There are 3 isotopes of hydrogen ( rm{H}^1, rm{H}^2, rm{H}^3) and 3 isotopes of oxygen ( rm{O}^{16}, rm{O}^{17}, rm{O}^{18}). Each water molecule consists of 2 hydrogen atoms and 1 oxygen atom.

Step 2: Calculate Combinations of Hydrogen Atoms

Since a water molecule consists of two hydrogen atoms, we can select these two from the three available hydrogen isotopes. The number of ways to choose 2 hydrogen isotopes out of 3 is calculated using a combination formula: \( \binom{3}{2} = 3\). However, each pair can be identical or different, thus we actually have additional options due to the ability to pair them with repetitions (e.g., rm{H}^1-rm{H}^1, rm{H}^1-rm{H}^2, etc.). Therefore, we calculate it as: 3 options for first hydrogen, 3 options for the second hydrogen = 9 combinations.

Step 3: Calculate Combinations with Oxygen

For each of these 9 combinations of hydrogen atoms, we can then pair them with each of the 3 isotopes of oxygen. Therefore, the total number of combinations of hydrogen-oxygen is calculated as follows: 9 combinations with hydrogen * 3 options for oxygen, resulting in a total of 27 possible combinations.

Key Concepts

Hydrogen Isotopes

Hydrogen is the simplest and most abundant element in the universe. It is unique in that it has isotopes that vary only by the number of neutrons in the nucleus. The most common isotope is Protium

• Protium ( ¹H): Contains one proton and no neutrons. This is the most prevalent form of hydrogen found naturally, making up about 99.98% of the hydrogen in the universe.
• Deuterium ( ²H): Also known as heavy hydrogen, it contains one proton and one neutron. Deuterium is stable and is used in various scientific research applications, as well as in nuclear reactors. The chemical symbol is often represented as a 'D'.
• Tritium ( ³H): Contains one proton and two neutrons. Tritium is radioactive with a half-life of about 12 years. It is rare in nature and is often used in nuclear fusion reactions and luminescent devices.

Understanding these isotopes is crucial because they form the foundation for how water molecules can vary based on hydrogen's isotopic nature.

Oxygen Isotopes

Oxygen is vital for life and has three naturally occurring isotopes that differ in the number of neutrons:

• ¹⁶O: The most common isotope, constituting over 99% of oxygen found on Earth. It has 8 protons and 8 neutrons, making it stable.
• ¹⁷O: Comprises about 0.037% of natural oxygen. It has 8 protons and 9 neutrons. Though less common, ¹⁷O is stable and is used in various scientific investigations, particularly in the fields of paleoclimatology and geochemistry.
• ¹⁸O: Accounts for approximately 0.2% of Earth's oxygen. This isotope has 8 protons and 10 neutrons. Like ¹⁷O, it is stable and is also valuable for scientific applications, such as tracing atmospheric changes over time.

These isotopes are critical in science because their varying abundances can be used to gain insights into Earth's climate history and atmospheric processes.

Isotope Combinations

The concept of isotope combinations is fundamental in understanding how variations in elemental isotopes can create different molecular forms. For instance, when considering water molecules, combining hydrogen and oxygen isotopes can result in different forms of water. Each water molecule comprises two hydrogen atoms and one oxygen atom. Given:

• 3 hydrogen isotopes: ¹H, ²H, and ³H
• 3 oxygen isotopes: ¹⁶O, ¹⁷O, and ¹⁸O

To approach the combinations: - **Selecting Hydrogen**: For the two hydrogen atoms in a single water molecule, the possibilities expand with combination choices, such as ¹H- ¹H, ¹H- ²H, up to having different isotopes such as ²H- ³H.

• This gives us 9 potential combinations for hydrogen, as each can be identical or mixed.

- **Adding Oxygen**: Each hydrogen pair can pair with any of the 3 different oxygen isotopes. This results in 27 distinct possible water molecules. This understanding of molecular variation is significant in fields like chemistry and environmental science, as it allows scientists to trace ecological processes and chemical pathways in the environment.