Animated Solution for Chemistry - Basic Concepts in Chemistry: If we consider that $1/6$, in place of $1/12$, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Have you ever wondered how we weigh things that are too small to see? In the macroscopic world, we use kilograms and pounds. But in the microscopic realm of atoms, we need a much smaller standard. This is where the Atomic Mass Unit (amu) comes into play.

Currently, the scientific community uses the Carbon-12 isotope as the universal gold standard. By definition, $1\text{ amu}$ is exactly $\frac{1}{12}$ the mass of a single ${}^{12}\text{C}$ atom. You can visualize this as taking a pizza, slicing it into twelve perfectly equal pieces, and declaring one slice as your standard unit of weight.

This problem introduces a fascinating thought experiment: What if we change the rules of the game? The question asks us to imagine a world where the new standard unit is $\frac{1}{6}$ the mass of a Carbon-12 atom instead of $\frac{1}{12}$.

Mathematically, this means our new reference unit is twice as heavy as the old one:

If you measure the mass of any atom using this new, heavier standard, its relative atomic mass will be cut in half. For example, if an atom weighed $24\text{ amu}$ under the old system, it would only weigh $12{\text{ amu}}^{\prime }$ under the new system.

Relative vs. Absolute

Here is where many students fall into a trap. The question does not ask about the relative atomic mass; it specifically asks about the mass of one mole of a substance.

To understand this, we must differentiate between a relative measurement and an absolute physical quantity. If you weigh $60\text{ kg}$ and suddenly decide to measure your weight in a new unit that is twice as heavy as a kilogram, your numerical weight drops to $30$. But did your actual physical body change? Did you lose half your mass? Absolutely not.

The mass of one mole of a substance is an absolute macroscopic quantity. A mole is simply a specific number of particles, known as Avogadro's Number ($N_A=6.022\times 10^{23}$).

The total mass of one mole is given by the master equation:

Did the actual, physical mass of the atom change in our thought experiment? No. Did Avogadro's number change? No.

Since neither the absolute mass of the individual atoms nor the number of atoms in a mole has been altered, the total mass of one mole remains exactly the same. Changing the ruler you use to measure an object does not change the physical reality of the object itself.

Therefore, the mass of one mole of the substance will remain unchanged.