Question

Calculate the total number of atoms present in '$m$' g of any substance, if the number of atoms in one molecule of that substance is '$k$' and gram molecular weight of the substance is '$w$' g/mol.

• A. $\frac{w}{m}\times 6.023\times {10}^{23}\times k$
• B. $\frac{m}{w}\times 6.023\times {10}^{-23}$
• C. $\frac{1}{w}\times 6.023\times {10}^{23}\times k$
• D. $\frac{m}{w}\times 6.023\times {10}^{23}\times k$

Answer 1

The correct option is D $\frac{m}{w}\times 6.023\times {10}^{23}\times k$

Mass of the substance = $m$ g

Number of atoms in one molecule of that substance = $k$
Gram molecular weight of the substance = $w$ g/mol
We know that, total number of atoms in a substance
=Total number molecules $\left(N_m\right)\times$ Number of atoms in each molecules
=$\left(N_m\right)\times k$ ......(1)
Total number of molecules equals
=Number of molecules $\left(N_m\right)$=$\frac{m}{w}\times N_A$ .........(2)
where, $N_A$ is an Avogadro number with a value of $6.023\times {10}^{23}$.
Substituting the equation number (2) in equation (1) we get

$\Rightarrow$ Total number of atoms in $m$ g of a compound $=\frac{m}{w}\times 6.023\times {10}^{23}\times k$