Problem 79 - A Complete Resource Book in Chemistry for JEE Main

Question

The weight of a single atom of oxygen is (a) \(5.057 \times 10^{23} \mathrm{~g}\) (b) \(1.556 \times 10^{23} \mathrm{~g}\) (c) \(2.656 \times 10^{-23} \mathrm{~g}\) (d) \(4.538 \times 10^{-23} \mathrm{~g}\)

Step-by-Step Solution

Answer

The weight of a single oxygen atom is \(2.656 \times 10^{-23} \, \text{g}\), which is option (c).

Step 1: Understand the Problem

We need to find the correct weight of a single oxygen atom from the given options. The atomic mass of an oxygen atom is approximately 16 atomic mass units (amu). We need to convert this mass into grams to compare it with the provided options.

Step 2: Convert Atomic Mass to Grams

Remember that 1 amu is equal to \(1.66 \times 10^{-24}\) grams. Therefore, the mass of an oxygen atom in grams is calculated by multiplying the atomic mass of oxygen with the conversion factor: \[ 16 \, \text{amu} \times 1.66 \times 10^{-24} \, \text{g/amu} = 2.656 \times 10^{-23} \, \text{g} \]

Step 3: Compare with Options

Now we compare the calculated weight with the given options: (a) \(5.057 \times 10^{23} \, \text{g}\) is positive and very large, as is (b) \(1.556 \times 10^{23} \, \text{g}\), which are implausibly large.(c) \(2.656 \times 10^{-23} \, \text{g}\) matches exactly with our calculated value.(d) \(4.538 \times 10^{-23} \, \text{g}\) is a possible value but doesn't match our calculation.

Key Concepts

Understanding the Oxygen Atom

Oxygen is a fundamental element on Earth, primarily responsible for the process of oxidation, including combustion and cellular respiration. It is represented in the periodic table with the symbol 'O' and has an atomic number of 8. This means each oxygen atom contains 8 protons in its nucleus.

Oxygen atoms are part of diatomic molecules, meaning they naturally pair to form O₂, which is what we commonly find in the air we breathe. The atomic weight of a single oxygen atom is approximately 16 atomic mass units (amu). This is a useful figure to know when engaging in calculations involving molecular masses or conversions involving moles and atoms.

Oxygen is crucial in living organisms as it is involved in the formation of water and organic compounds. It's also essential for the production of ATP, the energy currency of the cells. By understanding the basic properties and atomic makeup of oxygen, you can better appreciate its indispensable role in chemistry and biology.

AMU to Grams Conversion

When dealing with atoms and subatomic particles, the atomic mass unit (amu) is a convenient unit of measure. It was specifically devised to express atomic and molecular masses, helping chemists and physicists convey very small numbers with more manageable figures.

To convert amu to grams, we need to understand the conversion factor. 1 amu is equivalent to approximately \(1.66 \times 10^{-24}\) grams. This conversion factor is derived from defining the masses of subatomic particles, wherein the carbon-12 isotope (with exactly 12 amu) plays a reference role.

• The amu is defined such that the mass of a carbon-12 nucleus is precisely 12 amu.
• In practical calculations, using \(1.66 \times 10^{-24}\) grams for 1 amu allows transition from atomic-scale measurements to the gram scale.

This conversion is pivotal in translating complex atomic and molecular data into real-world understandings, such as predicting how much of a substance will react or be required for a reaction.

Calculating the Weight of a Single Oxygen Atom

The process of determining the weight of a single atom involves careful conversion from atomic mass units to grams. For an oxygen atom, with an atomic mass of 16 amu, the calculation becomes straightforward with the right data.

Applying the conversion factor for amu to grams, we calculate:

• Given: 1 amu = \(1.66 \times 10^{-24}\) grams
• Therefore, an oxygen atom's mass = \(16 \times 1.66 \times 10^{-24} = 2.656 \times 10^{-23}\) grams

This calculation lets us compare with the options provided in the exercise. By matching this calculated weight with the given options, we can accurately determine that the correct answer is indeed \(2.656 \times 10^{-23}\) grams.

Single atom weight calculations are crucial for accurately understanding chemical quantities in practical applications, such as in scientific experiments or industrial processes. This foundational step enables the translation of atomic-level theory into observable outcomes in the physical world.