### Theory:

 1 Calculate the number of moles in $$46$$ $$g$$ of sodium.

Data:

Given mass of sodium $$= 46$$ $$g$$

Atomic mass or mass number of sodium $$= 23$$

Formula:

The formula to find the number of moles from the mass is,

$\mathit{Number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{moles}=\frac{\mathit{Mass}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{element}}{\mathit{Atomic}\phantom{\rule{0.147em}{0ex}}\mathit{mass}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{element}}$

Solution:

By substituting the values in the above formula, we get,

$\begin{array}{lll}\mathit{Number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{moles}& =& \frac{46}{23}\\ & =& 2\end{array}$

Hence, the number of moles in $$46$$ $$g$$ of sodium $$=2$$ $$moles$$

 2 Calculate the number of moles in $$5.6$$ $$L$$ of oxygen at STP.

Data:

Given volume of oxygen $$= 5.6$$ $$L$$

Molar volume of oxygen at STP $$= 22.4$$ $$L$$

Formula:

The formula to find the number of moles from the volume is,

$\mathit{Number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{moles}=\frac{\mathit{Given}\phantom{\rule{0.147em}{0ex}}\mathit{volume}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}{O}_{2}\phantom{\rule{0.147em}{0ex}}\mathit{at}\phantom{\rule{0.147em}{0ex}}\mathit{STP}}{\mathit{Molar}\phantom{\rule{0.147em}{0ex}}\mathit{volume}\phantom{\rule{0.147em}{0ex}}\mathit{at}\phantom{\rule{0.147em}{0ex}}\mathit{STP}}$

Solution:

By substituting the values in the above formula, we get,

$\begin{array}{lll}\mathit{Number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{moles}& =& \frac{5.6}{22.4}\\ & =& 0.25\phantom{\rule{0.147em}{0ex}}\mathit{moles}\end{array}$

Hence, the number of moles in $$5.6$$ $$L$$ of oxygen at STP$$=0.25$$ $$moles$$

 3 Calculate the number of moles of a sample that contains $$12.046\times10^{23}$$ atoms of iron.

Data:

Given the number of atoms of iron $$=12.046\times10^{23}$$

Avogadro's number $$=6.023\times10^{23}$$

Formula:

$\mathit{Number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{moles}=\frac{\mathit{Number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{atoms}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{iron}}{\mathit{Avogadro}\phantom{\rule{0.147em}{0ex}}\mathit{number}}$

Solution:

$\begin{array}{lll}\mathit{Number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{moles}& =& \frac{12.046×{10}^{23}}{6.023×{10}^{23}}\\ & =& 2\end{array}$

Hence, the number of moles of a sample that contains $$12.046\times10^{23}$$ atoms of iron$$=2$$ $$moles$$