Question

Raunak took 5 moles of carbon atoms in a container and Krish also took 5 moles of sodium atoms in another container of the same weight.

(a) Whose container is heavier?

(b) Whose container has more number of atoms?

Answer 1

(a) The one has a heavier container:

Step 1: Given data

$$\begin{gathered} {\mathrm{n}}_{\mathrm{Na}}=5\mathrm{moles}; \\ {\mathrm{n}}_{\mathrm{C}}=5\mathrm{moles} \\ {M}_{Na}=23g/mol; \\ {M}_C=12g/mol \end{gathered}$$

Step: 2 Calculating the total mass of Na atoms

The total mass of the box containing Sodium:

$$\begin{gathered} {\mathrm{n}}_{\mathrm{Na}}=\frac{{\mathrm{W}}_{\mathrm{Na}}}{{\mathrm{M}}_{\mathrm{Na}}} \\ {\mathrm{W}}_{\mathrm{Na}}={\mathrm{n}}_{\mathrm{Na}}\times {\mathrm{M}}_{\mathrm{Na}}=5\times 23\mathrm{g}=115\mathrm{g} \end{gathered}$$

Step: 3 Calculating the total mass of C atoms

The total mass of the box containing Carbon:

$$\begin{gathered} {\mathrm{n}}_C=\frac{{\mathrm{W}}_C}{{\mathrm{M}}_C} \\ {\mathrm{W}}_C={\mathrm{n}}_C\times {\mathrm{M}}_C=5\times 12\mathrm{g}=60\mathrm{g} \end{gathered}$$

$\therefore$It can be analyzed that the mass of the container containing Sodium is heavier than the box containing Carbon, hence the container of Krish will be heavier than that of Raunak

(a) The one having a container with more number of atoms:

Step 1: Calculating the number of atoms of Na

Calculating the number of Sodium atoms in 5 moles of Sodium:

$$\begin{gathered} {\mathrm{n}}_{\mathrm{Na}}=\frac{\mathrm{No}.\mathrm{of}\mathrm{atoms}}{6.022\times {10}^{23}} \\ \mathrm{No}.\mathrm{of}\mathrm{atoms}={\mathrm{n}}_{\mathrm{Na}}\times 6.022\times {10}^{23} \\ \mathrm{No}.\mathrm{of}\mathrm{atoms}=5\times 6.022\times {10}^{23} \\ \mathrm{No}.\mathrm{of}\mathrm{atoms}=5\times 6.022\times {10}^{23} \\ \mathrm{No}.\mathrm{of}\mathrm{atoms}=30.11\times {10}^{23} \\ \mathrm{No}.\mathrm{of}\mathrm{atoms}=3.011\times {10}^{24} \end{gathered}$$

Step 2: Calculating the number of atoms of C

Calculating the number of Carbon atoms in 5 moles of Carbon:

$$\begin{gathered} {\mathrm{n}}_C=\frac{\mathrm{No}.\mathrm{of}\mathrm{atoms}}{6.022\times {10}^{23}} \\ \mathrm{No}.\mathrm{of}\mathrm{atoms}={\mathrm{n}}_C\times 6.022\times {10}^{23} \\ \mathrm{No}.\mathrm{of}\mathrm{atoms}=5\times 6.022\times {10}^{23} \\ \mathrm{No}.\mathrm{of}\mathrm{atoms}=5\times 6.022\times {10}^{23} \\ \mathrm{No}.\mathrm{of}\mathrm{atoms}=30.11\times {10}^{23} \\ \mathrm{No}.\mathrm{of}\mathrm{atoms}=3.011\times {10}^{24} \end{gathered}$$

$\therefore$Therefore, as the number of carbon atoms and the number of Sodium atoms is found out to be equal in number, Both Krish and Raunak have containers with the same number of atoms.