How many moles of ${\mathrm{SO}}_2$ have same mass as $3$ moles of Oxygen ?(Atomic mass : $\mathrm{S}$ = $32$, $\mathrm{O}$ = $16$)

Given - Atomic mass of $\mathrm{O}$ = $16$ and Atomic mass of $\mathrm{S}$ = $32$.

• Thus, Gram atomic mass of $\mathrm{O}$ = $16\mathrm{g}$ and Gram atomic mass of $\mathrm{S}$ = $32\mathrm{g}$.
• Gram molecular mass of ${\mathrm{SO}}_2$ = $1\times$[Gram atomic mass of $\mathrm{S}$] + $2\times$[Gram atomic mass of $\mathrm{O}$]
• Gram molecular mass of ${\mathrm{SO}}_2$ = $32+2\times 16$
• Gram molecular mass of ${\mathrm{SO}}_2$ = $64\mathrm{g}$
• Similarly, Gram molecular mass of $\mathrm{Oxygen}\left({\mathrm{O}}_2\right)$ = $32\mathrm{g}$

We Know,

$\mathrm{Number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{a}\mathrm{molecule}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{Molecule}\mathrm{in}\mathrm{Grams}}{\mathrm{Gram}\mathrm{Molecular}\mathrm{mass}}$.

• Hence, One mole of ${\mathrm{SO}}_2$ contains $64\mathrm{g}$ of ${\mathrm{SO}}_2$.
• Also, Three moles of $\mathrm{Oxygen}\left({\mathrm{O}}_2\right)$ has mass = $96\mathrm{g}$.
• So, if we want to have a mass of $96\mathrm{g}$
• Number of moles of ${\mathrm{SO}}_2$ = $\frac{96}{64}$
• Number of moles of ${\mathrm{SO}}_2$ = $1.5$.

Hence, $1.5$ moles of ${\mathrm{SO}}_2$ have same mass as $3$ moles of Oxygen Molecule.