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 (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

The mass of one mole of a substance will increase two fold.

Step 1: Understanding Atomic Mass Unit Change

The problem states a change in the basis for the atomic mass unit (amu) from \( \frac{1}{12} \) the mass of a carbon atom to \( \frac{1}{6} \). Typically, the atomic mass unit is defined based on \( \frac{1}{12} \) of the mass of a carbon-12 atom.

Step 2: Effect on Molar Mass

The molar mass of a substance depends on the atomic mass of its constituent atoms. If the basis of the atomic mass unit is doubled (from \( \frac{1}{12} \) to \( \frac{1}{6} \), which is double the initial value), each atomic mass also doubles.

Step 3: Determine the Change in Mass of One Mole

Since the atomic masses would double with the new atomic mass unit, the mass of one mole of a substance, which is the sum of the atomic masses, also doubles. The molar mass is therefore increased two-fold.

Step 4: Select the Correct Option

Based on the analysis, if the atomic mass unit standard changes as described, the mass of one mole of a substance will increase by a factor of two. Thus, the correct answer is (b) increase two fold.

Key Concepts

Molar Mass

Molar mass is a key concept in chemistry that refers to the mass of one mole of a given substance. The molar mass of a substance is numerically equal to the sum of the atomic masses of all the atoms in a chemical formula expressed in grams per mole. This measurement allows chemists to easily convert between moles and grams when performing calculations related to chemical reactions and stoichiometry.
Let's break it down into simple bullet points:

• Molar mass is expressed in grams per mole (g/mol).
• It is calculated by summing up the atomic masses of each element within a compound.
• Molar mass is essential for converting moles to grams and vice versa.

The importance of understanding molar mass lies in its utility for determining the proportions of elements in chemical reactions. When the basis of the atomic mass unit changes, as in the original exercise, the moar mass calculations are directly affected. If the atomic mass unit increases from \(\frac{1}{12}\) to \(\frac{1}{6}\) of a carbon atom, molar masses subsequently double because they are based on the summation of atomic masses.

Atomic Mass

Atomic mass is the mass of an individual atom, typically measured in atomic mass units (amu). Traditionally, atomic mass is based on \(\frac{1}{12}\) of the mass of a carbon-12 atom. However, if the atomic mass unit definition changes, as proposed in the initial exercise, it implies that every measured atomic mass would also change.
Understanding atomic mass:

• Atomic mass is usually measured in amu, where 1 amu is the mass of \(\frac{1}{12}\) of a carbon atom.
• It is a fundamental property of atoms and is often found on the periodic table.
• Atomic mass influences the physical and chemical properties of elements.

If you change the baseline of atomic mass units, as in changing from \(\frac{1}{12}\) to \(\frac{1}{6}\) of a carbon atom, the calculated atomic masses for all elements effectively double, leading to proportional changes in calculations of molar mass and chemical reactions.

Mole Concept

The mole concept is a cornerstone of chemistry that allows scientists to relate the mass of substances to the number of atoms or molecules they contain. One mole is defined as exactly \(6.022 \times 10^{23}\) (Avogadro's number) entities, which can be atoms, molecules, or other particles. This concept provides a bridge between the atomic and macroscopic worlds.
Key points of the mole concept:

• One mole contains \(6.022 \times 10^{23}\) particles, which is Avogadro's number.
• Mole concept links atomic scale measurements to laboratory scale.
• It's essential for quantifying elements and compounds in chemical reactions.

Adjusting the atomic mass unit as shown in the initial exercise also impacts the mole concept. Since the number of entities per mole remains constant, but the mass of each entity changes if the unit of atomic mass changes, the resultant molar mass calculations reflect these shifts. Therefore, correct comprehension of the mole concept is crucial for proper interpretation and application of chemical quantities and formulas.