Problem 170 - A Complete Resource Book in Chemistry for JEE Main

Question

If we consider that \(\frac{1}{6}\), in place of \(\frac{1}{12}\), mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will \([\mathbf{2 0 0 5}]\) (a) decrease twice (b) increase two fold (c) remain unchanged (d) be a function of the molecular mass of the substance

Step-by-Step Solution

Answer

(b) increase two fold

Step 1: Understanding the Concept of Moles

The molar mass is defined as the mass of one mole of a substance. Normally, it is based on the standard that one mole of carbon-12 (\(^{12}C\)) atoms weighs exactly 12 grams.

Step 2: Defining the Alternative Atomic Mass Unit

In this problem, we have been asked to consider an alternative atomic mass unit, using \(\frac{1}{6}\) instead of \(\frac{1}{12}\) of the mass of a carbon atom. Therefore, if the mass of a carbon atom was to be based on \(\frac{1}{6}\), the standard molar mass calculation for all elements would be effectively doubled.

Step 3: Calculating the Impact on Molar Mass

If the unit of atomic mass unit is doubled (from \(\frac{1}{12}\) to \(\frac{1}{6}\)), every element's relative atomic mass would proportionally be doubled as well. Thus, the mass of one mole of any substance in this altered system becomes twice that of the conventional system.

Step 4: Determining the Correct Option

From the analysis, if the atomic mass unit changes to \(\frac{1}{6}\) instead of \(\frac{1}{12}\), the molar mass will be twice as large. Therefore, the mass of one mole of a substance will increase two-fold.

Key Concepts

Mole Concept

The concept of a mole is fundamental in chemistry. A mole is a unit that measures the quantity of a substance. It is equivalent to Avogadro's number, approximately \(6.022 \times 10^{23}\) atoms, molecules, or particles. This is a crucial concept because it allows chemists to count particles by weighing them, linking the microscopic world of atoms to the macroscopic quantities we can see and measure.
The molar mass of a substance is expressed in grams per mole and provides the mass of this multitude of entities. By using the mole concept, we can relate a substance's mass to its chemical composition, thereby predicting reaction outcomes and products.

• Moles allow chemists to describe how substances interact in a reaction.
• Understanding moles helps in predicting the yields of reactions.
• It is used to convert between the mass of a substance and the amount of substance.

A solid grasp of the mole concept is essential for anyone studying chemical reactions and stoichiometry, providing a bridge between the atomic scale and real-world chemical quantities.

Atomic Mass Unit

The atomic mass unit (amu) serves as a standard unit for expressing atomic and molecular weights. One atomic mass unit is defined as one twelfth of the mass of a carbon-12 atom, the isotope of carbon which has 6 protons and 6 neutrons. This definition allows chemists to compare the masses of different atoms on a relative scale.
The idea of an atomic mass unit makes it convenient to express the tiny masses of individual atoms in understandable terms. For instance, if hydrogen has an atomic mass of approximately 1 amu, and oxygen roughly 16 amu, it tells us an oxygen atom is around 16 times heavier than a hydrogen atom.

• It allows consistency and accuracy when calculating molecular weights.
• Changes in how the amu is defined impact how we understand molar masses.
• An accurate amu definition ensures reliable chemical calculations.

By using the consistent standard of amu, chemists can ensure that their calculations are precise and comparable across different contexts and studies.

Carbon Atom

Carbon, situated in group 14 of the periodic table, is crucial in numerous chemical processes and the basis for organic chemistry. Its atomic number is 6, and its typical atomic mass is about 12 amu, the foundation for the definition of atomic mass units.
Carbon atoms can form stable bonds with many elements, including itself, which allows for the vast diversity of organic compounds. This unique ability gives rise to complex molecules essential to life, such as proteins, carbohydrates, and DNA.

• Carbon's ability to form four covalent bonds makes it extremely versatile.
• The carbon-12 isotope is critical for the definition of an atomic mass unit.
• Carbon atoms are fundamental in numerous chemical reactions, especially organic reactions.

Grasping the role of carbon atoms can shed light on the broader subject of organic chemistry and the importance of carbon-based life processes and materials.