Question

If one atom of an element 'x' weigh $6.643\times {10}^{-23}\mathrm{g}$. What will be the number of moles in 20 Kg?

Answer 1

Step 1: Calculating the number of atoms

Given that, the mass of 1 atom is $6.643\times {10}^{-23}\mathrm{g}$, and the total mass is $20\mathrm{kg}=20000\mathrm{gm}$

If $6.643\times {10}^{-23}\mathrm{g}$ is the weight of 1 atom

$\therefore$$20000\mathrm{gm}$ is the weight of

$$\begin{gathered} \frac{1}{6.643\times {10}^{-23}}\times 20000 \\ =3\times {10}^{26}\mathrm{atoms} \end{gathered}$$

Step 2: Calculating the number of moles

We know that

$\mathrm{Number}\mathrm{of}\mathrm{moles}=\frac{\mathrm{Number}\mathrm{of}\mathrm{atoms}}{\mathrm{Avogadro}\text{'}\mathrm{s}\mathrm{Number}}$

So, the number of moles is,

$$\begin{gathered} \therefore \mathrm{Number}\mathrm{of}\mathrm{moles}=\frac{3\times {10}^{26}}{6.022\times {10}^{23}} \\ \Rightarrow \mathrm{Number}\mathrm{of}\mathrm{moles}=498\approx 500 \end{gathered}$$

Therefore, the total number of moles that would weigh 20kg is around $500$moles.