Question

Portland cement acts as the binding agent in concrete. A typical Portland cement has the following composition:

Assuming that the impurities contain no Ca, Al, or Fe, calculate the mass percent of these elements in this Portland cement.

Short answer

The mass percent of these elements can be calculated.

Step-by-step solution

Finding molar mass of elements

The molar mass of the elements can be calculated as,

$\begin{array}{rcl}C{a}_{3}Si{O}_5& =& 3\left(40.08\right)+1\left(28.09\right)+5\left(16\right)\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\\ & =& 228.32\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\\ C{a}_{2}Si{O}_4& =& 2\left(40.08\right)+1\left(28.09\right)+4\left(16\right)\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\\ & =& 172.24\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\\ C{a}_{3}A{l}_2{O}_5& =& 3\left(40.08\right)+2\left(26.98\right)+6\left(16\right)\\ & =& 270.19\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\\ C{a}_{2}AlFe{O}_5& =& 2\left(40.08\right)+1\left(26.98\right)+1\left(55.84\right)+5\left(16\right)\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\\ & =& 242.98\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\\ CaS{O}_4·2H_{2}O& =& 1\left(40.08\right)+1\left(32.06\right)+6\left(32\right)+4\left(1.008\right)\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\\ & =& 172.17\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.\end{array}$

Calculating mass percent of calcium

The mass percent of calcium can be calculated as,

$\begin{array}{rcl}\mathrm{Percent}\mathrm{of}\mathrm{Cain}\mathrm{cement}& =& 26.33\mathrm{percent}+11.63\mathrm{percent}+5.34\mathrm{percent}+2.63\mathrm{percent}+0.81\mathrm{percent}\\ & =& 46.74\mathrm{percent}\end{array}$

Calculating mass percent of elements

The mass percentage of all other elements can be calculated as,

$\begin{array}{rcl}\mathrm{Percent}\mathrm{Al}\mathrm{in}{\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6& =& \frac{2\left(26.98\right)}{270.91}\times \frac{12}{100}\\ & =& 2.4\mathrm{Percent}\\ \mathrm{Percent}\mathrm{Al}\mathrm{in}{\mathrm{Ca}}_2{\mathrm{AlFeO}}_5& =& \frac{1\left(26.98\right)}{242.98}\times 100\\ & =& 0.88\mathrm{percent}\end{array}$

The total percentage of aluminium can be calculated as,

$\begin{array}{rcl}\mathrm{Percent}\mathrm{Al}\mathrm{in}\mathrm{cement}& =& 2.4\mathrm{Percent}+0.88\mathrm{percent}\\ & =& 3.28\mathrm{percent}\end{array}$

To calculate the mass percent of Iron,

$\begin{array}{rcl}\mathrm{Percent}\mathrm{Fe}\mathrm{in}{\mathrm{Ca}}_2{\mathrm{AlFeO}}_5& =& \frac{1\left(55.84\right)}{242.98}\times \frac{8}{10}\\ & =& 1.84\mathrm{percent}\end{array}$

Fe is only one compound. The total mass percent can be calculated as 1.84 %.

Mass percent of impurities can be 46.74%Ca, 3.28%Al and 1.84%Fe.