Question

If we consider that 1/6, in place of 1/12, the mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will
(A) be a function of the molecular mass of the substance
(B) remain unchanged
(C) increase two-fold
(D) decrease twice

Answer 1

Hint: The ratio of the average atomic mass of the atom to the unified atomic mass unit is known as the relative atomic mass. According to IUPAC, the relative atomic mass of an element from a specified source is the ratio of the average mass per atom of the element to $1/{{12}^{th}}$ the mass of the 12 Carbon atom.

Complete Step by step answer:
-According to mole concept, one mole of any substance is the amount of a substance that contains as many particles or entities as there are in atoms in exactly 12g (or 0.0012 kg) of the 12C isotope.
-Mass of one mole of a substance $={{N}_{A}}\text{(Avagadro }\!\!'\!\!\text{ s constant)}\times \text{Mass of 1 atom (amu)}$
-We know that the relative atomic mass of a substance is the ratio of the actual atomic mass of the substance to that of the one-twelfth mass of the C-atom, that is
$\begin{align}
  & x=\dfrac{\text{Actual atomic mass of the substance}}{\dfrac{1}{12}\times 12} \\
 & \Rightarrow x=\dfrac{\text{Actual atomic mass of the substance}}{1} \\
\end{align}$
-According to question, the relative atomic mass of a substance is changed and made to be the ratio of actual mass of the substance to one-sixth of the mass of C-atom. In other words, we are now considering 1/6 in the place of 1/12.
So, now the Avagadro’s number becomes half since the weight of carbon corresponding to the atomic weight becomes half, that is 5 gm instead of 12 g. Now, the relative mass of a substance will be- The relative atomic mass of the substance $=\dfrac{x}{\left( \dfrac{1}{6}\times 12 \right)}=\dfrac{x}{2}$
Therefore, we can say that the final relative atomic mass of the substance is decreased to half of the initial relative atomic mass of the substance.

Hence, the correct answer is option D.

Note: Another way of solving this question is by considering the number of moles to be equal to Avagadro’s number. When we consider the 1/6 in place of 1/12, since the mass of the carbon atom is still the same, so new amu1 = amu2 (where amu1 is new amu and amu2 is the old amu unit). So, new Avagadro’s number becomes half because the weight of carbon corresponding to atomic weight becomes 6 gm in place of 12 gm. Let us consider, ${{N}_{A}}1$ be the value of new Avagadro’s number and ${{N}_{A}}2$ be the value of old Avagadro’s number (that is ${{N}_{A}}2=6.022\times {{10}^{23}}$)
We know that the mass of one substance $={{N}_{A}}\times amu$
So, the new atomic mass ${{N}_{A}}1\times amu=\dfrac{{{N}_{A}}}{2}\times 2amu={{N}_{A}}\times amu=\text{old atomic weight}$.