Question

Verify by calculating that $240\mathrm{g}$ of calcium and $240\mathrm{g}$ magnesium elements have a mole ratio of $3:5$.

Answer 1

Mole

• The mole, symbol mol, is the SI unit of the amount of substance.
• The amount of a substance that contains the same number of elementary particles (ions, molecules, or atoms) as the number of atoms present in $12\mathrm{g}$ of carbon $\mathrm{C}12$ is called the mole.
• One mole of a substance contains $6.022\times {10}^{23}$ elementary entities.
• The formula is as follows:

$\mathrm{n}=\frac{\mathrm{m}}{\mathrm{M}}$

• $\mathrm{n}$ is the number of moles.
• $\mathrm{m}$ is the mass of an element.
• $\mathrm{M}$ is the molar mass of an element.

Calculate the number of calcium

• Mass of calcium $\left(\mathrm{Ca}\right)$, ${\mathrm{m}}_1=240\mathrm{g}$
• The molar mass of calcium, ${\mathrm{M}}_1=40\mathrm{g}{\mathrm{mol}}^{-1}$
• The number of moles of calcium is as follows:

$\begin{array}{rcl}{\mathrm{n}}_1& =& \frac{{\mathrm{m}}_1}{{\mathrm{M}}_1}\\ & =& \frac{240\mathrm{g}}{40\mathrm{g}{\mathrm{mol}}^{-1}}\\ & =& 6\mathrm{mol}\end{array}$

Calculate the number of magnesium

• Mass of magnesium $\left(\mathrm{Mg}\right)$, ${\mathrm{m}}_2=240\mathrm{g}$
• The molar mass of magnesium, ${\mathrm{M}}_2=24\mathrm{g}{\mathrm{mol}}^{-1}$
• The number of moles of magnesium is as follows:

$\begin{array}{rcl}{\mathrm{n}}_2& =& \frac{{\mathrm{m}}_2}{{\mathrm{M}}_2}\\ & =& \frac{240\mathrm{g}}{24\mathrm{g}{\mathrm{mol}}^{-1}}\\ & =& 10\mathrm{mol}\end{array}$

Calculate the mole ratio of calcium and magnesium

• Number of moles of calcium, ${\mathrm{n}}_1=6\mathrm{mol}$
• Number of moles magnesium, ${\mathrm{n}}_2=10\mathrm{mol}$
• The mole ratio is as follows:

$\begin{array}{rcl}\mathrm{n}& =& \frac{{\mathrm{n}}_1}{{\mathrm{n}}_2}\\ & =& \frac{6\bcancel{\mathrm{mol}}}{10\bcancel{\mathrm{mol}}}\\ & =& 3:5\end{array}$

• Therefore, the mole ratio of $240\mathrm{g}$ of calcium and $240\mathrm{g}$ of magnesium elements is $3:5$.
• Hence, verified.