Question

Arrange the following in Increasing order of mass:

1. One Atom of Silver
2. One mole atoms of $\mathrm{N}$
3. $2\mathrm{g}$ of Sodium
4. $6.022\times {10}^{22}$ Atoms of Calcium

Answer 1

According to the Mole concept,

$1$ Mole of an atom contains $6.022\times {10}^{23}$ number of Atoms.

And , $\mathrm{Number}\mathrm{of}\mathrm{Moles}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{Element}\mathrm{in}\mathrm{grams}}{\mathrm{Gram}\mathrm{atomic}\mathrm{mass}}$

(1.)Gram Atomic mass of Silver = $108\mathrm{g}$.

For One atom of Silver, By unitary method

If One Mole contains $6.022\times {10}^{23}$ number of atoms then $1$ atom contains $\frac{1}{6.022\times {10}^{23}}$ Number of Moles

Hence, Mass of Silver = $\frac{1}{6.022\times {10}^{23}}\times 108$ g

Mass of silver = $1.793\times {10}^{-22}$.g.

(2.)One mole Atoms Contain $6.022\times {10}^{23}$ number of Atoms

Hence, Number of Mole of $\mathrm{N}$ = $1$

Gram atomic mass of $\mathrm{N}$ = $14\mathrm{g}$

Hence, Mass of Nitrogen = $14\mathrm{g}$.

(3.) Given - $2\mathrm{g}$ of Sodium

(4.) $\mathrm{Number}\mathrm{of}\mathrm{moles}=\frac{\mathrm{Given}\mathrm{number}\mathrm{of}\mathrm{Atoms}}{\mathrm{Avogadro}\text{'}\mathrm{s}\mathrm{Number}}$

Hence, Number of moles = $\frac{6.022\times {10}^{22}}{6.022\times {10}^{23}}$

Number of Moles = $0.1$

Thus, Mass of Calcium = $0.1\times 40\mathrm{g}$

Mass of Calcium = $4\mathrm{g}$

Therefore Increasing Order of mass is (1)<(3)<(4)<(2).