Question

The mass of one steel screw is $4.11\mathrm{g}$. Find the mass of one mole of these steel screws. Compare this value with the mass of the Earth ($5.98\times {10}^{24}\mathrm{kg}$). Which one of the two is heavier and by how many times?

Answer 1

Step 1: Finding mass of one mole of screw

• Mass of one steel screw $4.11\mathrm{g}$
• Thus, mass of one mole of screw $=4.11\times {\mathrm{N}}_{\mathrm{A}}$
• $=4.11\times 6.022\times {10}^{23}$
• $$\begin{gathered} =2.475\times {10}^{24}\mathrm{g} \\ =2.475\times {10}^{21}\mathrm{kg} \end{gathered}$$

Step 2: Finding the ratio of mass of earth to the mass of 1 mole of screws

• $\frac{\mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{earth}}{\mathrm{Mass}\mathrm{of}1\mathrm{mole}\mathrm{of}\mathrm{screws}}=\frac{5.98\times {10}^{24}\mathrm{kg}}{2.475\times {10}^{21}\mathrm{kg}}$
• $\frac{\mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{earth}}{\mathrm{Mass}\mathrm{of}1\mathrm{mole}\mathrm{of}\mathrm{screws}}=2.4\times {10}^3$
• Mass of earth is $2400$ times the mass of screw
• The earth is $2400$ times heavier than a mole of screw.

Hence, the earth is $2400$ times heavier than a mole of screw.