Problem 106 - A Complete Resource Book in Chemistry for JEE Main

Question

Rearrange the following (I to IV) in the order of in creasing masses and choose the correct answer from (a), (b), (c), (d). (atomic masses: \(\mathrm{N}=14, \mathrm{O}=\) \(16, \mathrm{Cu}=63\) ). I. 1 molecule of oxygen II. 1 atom of nitrogen III. \(1 \times 10^{10} \mathrm{~g}\) molecular weight of oxygen IV. \(1 \times 10^{-18} \mathrm{~g}\) atomic weight of copper (a) II \(<\mathrm{I}<\mathrm{IV}<\mathrm{III}\) (b) IV < III < II < I (c) II \(<\mathrm{III}<\mathrm{I}<\mathrm{IV}\) (d) III \(<\) IV \(<\mathrm{I}<\mathrm{II}\)

Step-by-Step Solution

Answer

Correct order is (a): II < I < IV < III.

Step 1: Calculate mass of 1 molecule of oxygen (I)

The molecular mass of oxygen (O₂) is calculated as follows:\[ \text{Mass of O}_2 = 2 \times \text{atomic mass of oxygen} = 2 \times 16 = 32 \text{ amu} \] Thus, the mass of 1 molecule of oxygen is 32 amu.

Step 2: Calculate mass of 1 atom of nitrogen (II)

The atomic mass of a nitrogen atom is 14 amu.

Step 3: Calculate mass of given molecular weight of oxygen (III)

Given that the molecular weight of oxygen is \(1 \times 10^{10}\) grams, we express the mass directly as \(1 \times 10^{10} \text{ grams}\).

Step 4: Calculate mass of given atomic weight of copper (IV)

Given that the atomic weight of copper is \(1 \times 10^{-18}\) grams, we express the mass directly as \(1 \times 10^{-18} \text{ grams}\).

Step 5: Rank the masses in increasing order

Listing the calculated or given masses:1. Mass of 1 atom of nitrogen = 14 amu (atomic mass unit)2. Mass of 1 molecule of oxygen = 32 amu3. Mass of copper = \(1 \times 10^{-18} \text{ grams}\)4. Mass of molecular weight of oxygen = \(1 \times 10^{10} \text{ grams}\)When converted (considering 1 amu is approximately \(1.66 \times 10^{-24} \text{ grams}\)), the masses in increasing order are: 1 atom of nitrogen (II), 1 molecule of oxygen (I), atomic weight of copper (IV), molecular weight of oxygen (III).

Key Concepts

Molecular Mass

The concept of molecular mass is vital in understanding a variety of scientific and chemical calculations. Molecular mass is the total weight of all the atoms present in a molecule. It is usually measured in atomic mass units (amu).

• To calculate the molecular mass, add up the atomic masses of all the atoms in the molecule.
• For example, oxygen (O₂) is composed of two oxygen atoms. Since each oxygen atom has an atomic mass of 16 amu, the molecular mass of an oxygen molecule (O₂) is 32 amu.

The molecular mass has practical applications in real-world calculations, helping scientists determine the proportions of elements in compounds. This facilitates a greater understanding of reactions and compositions. Ideally, understanding molecular mass can simplify complex calculations and increase accuracy.

Oxygen Molecule

Oxygen, symbolized as O₂, is a diatomic molecule, meaning it is made up of two atoms of oxygen bonded together.

• Each oxygen atom in the molecule contributes 16 atomic mass units, making the entire oxygen molecule weigh 32 amu.
• This weight signifies the intrinsic mass that the molecule retains, independent of its environment.

Oxygen is a vital element found abundantly in the earth's atmosphere. It is essential for the respiration of many living organisms and is also used in various industrial processes. The molecular configuration of two bonded oxygen atoms gives it distinct characteristics, including stability and reactivity for crucial biological and chemical functions.

Nitrogen Atom

A nitrogen atom is a single atom of nitrogen with an atomic mass of 14 amu. The atomic structure of nitrogen consists of 7 protons and 7, typically 7, neutrons, and electrons in an outer shell.

• Nitrogen atoms form the basis for nitrogen molecules and are essential in creating amino acids, proteins, and nucleic acids.
• Nitrogen is a major component of the Earth’s atmosphere, constituting around 78% of it.

Understanding the atomic mass of nitrogen assists in determining its reactivity and role in various compounds. It's pivotal in fields such as agriculture, where nitrogen fertilizers enhance plant growth by providing essential nutrients. Knowing the atomic mass allows for more informed decisions regarding its use and manipulation.

Copper Atom Weight

The weight of a copper atom is noted as 63 amu, although it can vary slightly due to isotopic differences. This weight is a representation of the total number of protons and neutrons in the nucleus of the copper atom.

• Copper, with its excellent conductivity, is frequently used in electrical wiring and electronics.
• Understanding copper's atomic weight is critical for engineers and scientists when dealing with metal alloys and chemical reactions.

By comprehending the copper atomic weight, industries can optimize the use of copper in manufacturing and production processes. It also helps in calculating the quantities required in metallurgical processes. Copper's distinct weight and properties, including malleability and thermal conductivity, make it valuable across various industrial applications.