Question

Which has more number of atoms, $100\mathrm{grams}$ of sodium or $100\mathrm{grams}$ of iron (Given, atomic mass of $\mathrm{Na}=23\mathrm{u},\mathrm{Fe}=56\mathrm{u}$)?

Answer 1

Step 1: Determine number of atoms in $\mathbf{100}\mathbf{}\mathbf{grams}$ of sodium

• Atomic mass of $\mathrm{Na}=23\mathrm{u}$
• Gram atomic mass of $\mathrm{Na}=23\mathrm{g}$
• $23\mathrm{g}$ of $\mathrm{Na}$ contains $=6.022\times {10}^{23}\mathrm{atom}$
• Calculate the number of atoms in $100\mathrm{grams}$ of sodium is as follows:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{atoms}\mathrm{in}100\mathrm{g}\mathrm{Na}& =& \frac{6.022\times {10}^{23}\times 100\bcancel{\mathrm{g}}}{23\bcancel{\mathrm{g}}}\mathrm{atom}\\ & =& 2.6182\times {10}^{24}\mathrm{atom}\end{array}$

Step 2: Determine number of atoms in $\mathbf{100}\mathbf{}\mathbf{grams}$ of iron

• Atomic mass of $\mathrm{Fe}=56\mathrm{u}$
• Gram atomic mass of $\mathrm{Fe}=56\mathrm{g}$
• $56\mathrm{g}$ of $\mathrm{Fe}$ contains $=6.022\times {10}^{23}\mathrm{atom}$
• Calculate the number of atoms in $100\mathrm{grams}$ of iron is as follows:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{atoms}\mathrm{in}100\mathrm{g}\mathrm{Fe}& =& \frac{6.022\times {10}^{23}\times 100\bcancel{\mathrm{g}}}{56\bcancel{\mathrm{g}}}\mathrm{atom}\\ & =& 1.0753\times {10}^{24}\mathrm{atom}\end{array}$

Therefore, $\mathbf{100}\mathbf{}\mathbf{grams}$ of sodium contains more number of atoms than $\mathbf{100}\mathbf{}\mathbf{grams}$ of iron.