Question

Calculate the volume of steam produced when a 4.0-kg brick made from pure kaolinite is completely dehydrated at $\mathbf{600}°\mathbf{C}$ and a pressure of 1.00 atm.

Short answer

The answer is 2220 L of volume.

Step-by-step solution

Stoichiometry

The stoichiometry of a chemical reaction depends on the balanced chemical equation. The mole ratio of the constituent compounds in the chemical reaction helps predict the yield.

Calculation

The chemical formula of kaolinite is ${\mathrm{Al}}_2{\mathrm{O}}_3·2{\mathrm{SiO}}_2·2{\mathrm{H}}_2\mathrm{O}$

On heating kaonilite, the following chemical reaction takes place:

${\mathrm{Al}}_2{\mathrm{O}}_3·2{\mathrm{SiO}}_2·2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{s}\right)\to {\mathrm{Al}}_2{\mathrm{O}}_3.2{\mathrm{SiO}}_2\left(\mathrm{s}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

The molar mass of Kaolinite is 258.15 g/mol.

Thus, from the balanced chemical equation, 1 mol of kaolinite forms 2 mol of water.

That is 258.15 g of kaolinite forms ---2 mol ${\mathrm{H}}_2\mathrm{O}$

Then, 4.0 kg kaolinite forms the following moles of water:

$\begin{array}{c}{\mathrm{n}}_{{\mathrm{H}}_2\mathrm{O}}=4000\mathrm{g}\times \frac{2\mathrm{mol}}{258.15\mathrm{g}}\\ =31.0\mathrm{mol}\end{array}$

Use ideal gas equation to calculate the volume occupied by steam under the given set of conditions of pressure and temperature:

$\begin{array}{c}\mathrm{PV}=\mathrm{nRT}\\ 1.00\mathrm{atm}\times \mathrm{V}=31.0\mathrm{mol}\times 0.0821\mathrm{L}.\mathrm{atm}.{\mathrm{mol}}^{-1}.{\mathrm{K}}^{-1}\times 873\mathrm{K}\\ \mathrm{V}=\frac{31.0\mathrm{mol}\times 0.0821\mathrm{L}.\mathrm{atm}.{\mathrm{mol}}^{-1}.{\mathrm{K}}^{-1}\times 873\mathrm{K}}{1.00\mathrm{atm}}\\ \mathrm{V}=2220\mathrm{L}\end{array}$