Question

If a mole is defined to be $3 \times {10^{24}}$ (instead of Avogadro’s Number, $6 \times {10^{23}}$ ), what would be the mass of one mole of Argon atoms? (Atomic mass of Ar on conventional scale is 40)
(A) 40 gm
(B) 200 gm
(C) 20 gm
(D) 8 gm

Answer 1

Hint : The molar mass of a substance is the mass in grams of one mole of that substance. This mass is given by the atomic weight of the chemical unit that makes up that substance in atomic mass units (amu). The number 6.022 × 10²³ is known as Avogadro's number or Avogadro's constant. The concept of the mole can be used to convert between mass and number of particles.

Complete Step By Step Answer:
Given: Atomic mass of Argon is 40 gm according to conventional scale
To find: Mass of 1 mole of argon atoms according to new convention
The mass of one mole of atoms of a pure element in grams is equivalent to the atomic mass of that element.
Since, atomic mass of Argon is 40 gm, it means that one mole of Argon weighs 40 gm
1 mole of Argon contains $6 \times {10^{23}}$ atoms according to conventional scale
Therefore, mass of $6 \times {10^{23}}$ atoms = 40 gm
Mass of 1 atom = $\dfrac{{40}}{{6 \times {{10}^{23}}}}$ gm
According to the new convention given in the question
1 mole contains $3 \times {10^{24}}$ atoms
Mass of $3 \times {10^{24}}$ atoms = $3 \times {10^{24}} \times \dfrac{{40}}{{6 \times {{10}^{23}}}}$
= 200 gm
Therefore, mass of one mole of argon atoms according to new convention = 200 gm
Hence, option (B) is correct.

Note :
The identity of a substance is defined not only by the types of atoms or ions it contains, but by the quantity of each type of atom or ion. For example, water and hydrogen peroxide are alike in that their respective molecules are composed of hydrogen and oxygen atoms.