Question

Many cereals are made with high moisture content so that the cereal can be formed into various shapes before it is dried. A cereal product containing 58% ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$by mass is produced at the rateof$\mathbf{1000}\mathbf{}\raisebox{1ex}{$\mathbf{kg}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{h}$}\right.$. How much water must be evaporated per hour if the final product contains only20% water?

Short answer

Thewater must be evaporated per hour when the final product contains only20% water is$475\mathrm{g}$.

Step-by-step solution

Definition

The molar mass of a material is defined as the mass of the substance contained in one mole of the substance, and it isequal to the total massof the component atoms. It may be stated mathematically as follows:
$\mathrm{Molar}\mathrm{Mass}=\frac{\mathrm{Weight}\mathrm{in}\mathrm{g}}{\mathrm{Number}\mathrm{of}\mathrm{moles}}$

Determination of mass of Cereal

From the given, $1000\raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{h}$}\right.$product with 58% water produced.

Mass of water,

$\begin{array}{rcl}\mathrm{m}\left({\mathrm{H}}_2\mathrm{O}\right)& =& \frac{58}{100}\times 1000\\ & =& 580\mathrm{g}\end{array}$

$\begin{array}{rcl}\mathrm{m}\left(\mathrm{cereal}\right)& =& 1000\mathrm{g}-580\mathrm{g}\\ & =& 420\mathrm{g}\end{array}$

Thus thefinal product contains $20\mathrm{percent}$water.

Therefore the mass of cereal is constant, as ${\mathrm{H}}_2\mathrm{O}$evaporates.

Determination of percent of Cereal

Here, the percent of cereal in the final product is $100\mathrm{percent}-20\mathrm{percent}=80\mathrm{percent}$

$\begin{array}{rcl}0.8& =& \frac{420\mathrm{g}}{\mathrm{m}\left(\mathrm{final}\mathrm{product}\right)}\\ \mathrm{m}\left(\mathrm{final}\mathrm{product}\right)& =& 525\mathrm{g}\end{array}$

role="math" localid="1655213602917" $\begin{array}{rcl}\mathrm{m}{\left(\mathrm{Water}\right)}_{\mathrm{evaporated}}& =& 1000\mathrm{g}-525\mathrm{g}\\ & =& 475\mathrm{g}\end{array}$

Therefore water must be evaporated is $475\mathrm{g}$.