Question

Fulgurites are the products of the melting that occur when lightning strikes the earth. Microscopic examination of a sand fulgurite shows that it is a globule with variable composition that contains some grains of the definite chemical composition $\mathbf{\text{Fe}}\mathbf{}\mathbf{\text{46.01\% ,}}\mathbf{}\mathbf{\text{Si}}\mathbf{}\mathbf{\text{53.99\%}}$. Determine the empirical formula of these grains.

Short answer

The empirical formula is ${\text{Fe}}_3{\text{Si}}_7$

Step-by-step solution

Calculation of number of moles of each elements

Empirical formula is the simplest ratio in which atoms are arranged in a moleculeand we need to calculate the number of moles to find the empirical formula.It can be calculated by dividing the given mass by the molar mass of the elements.

Given that the mass of $\text{Fe}$ ,

${\text{m}}_{\text{Fe}}=46.01\text{g}$

Mass of $\text{Si,}$

${\text{m}}_{\text{Si}}=53.99\text{g}$

Molar mass of $\text{Fe,}$

${\text{M}}_{\text{Fe}}=55.845{\text{gmol}}^{-1}$

Molar mass of $\text{Si,}$

${\text{M}}_{\text{Si}}=28.0855{\text{gmol}}^{-1}$

Number of moles of Fe,

${\text{n}}_{\text{Fe}}=\frac{46.01}{55.845}=0.8239\text{mol}$

Number of moles of Si,

${\text{n}}_{\text{Si}}=\frac{53.99}{28.0855}=1.9223\text{mol}$

Step 2: Simplification of ratios

The smallest value is of iron, i.e., 0.8239 mol. Now, we have to divide the number of moles of each element by the smallest value.

$\text{Fe =}\frac{0.8239}{0.8239}=1$

$\text{Si =}\frac{1.9223}{0.8239}=2.333$

When we multiply both ratios with 3, we get the empirical formula as${\text{Fe}}_3{\text{Si}}_7$.