P$6\mathrm{.}41$ High$-$purity silicon, used in making electronic devices and solar cells, is produced from two inexpensive raw materials, sand $(Si{O}_2)$ and coke $($C$).$ Typically, about $500kg$ sand and $200kg$ coke are placed in a retort. Sand and coke are then heated to about $400F,$ which produces solid silicon and carbon monoxide gas:

$Si{O}_2(s)+2C(s)Si(s)+2CO(g)$

$Si$ and $CO$ are easily separated into solid and gas phases. Because of impurities in the sand, the solid $Si$ phase is about $98\mathrm{.}5wt\%$ pure. This is not sufficiently pure, so two additional reactions are employed. First Si reacts with chlorine gas to make tetrachlorosilane:

$Si(s)+2C{l}_2(g)SiC{l}_4(g)$

Tetrachlorosilane reacts with magnesium:

$SiC{l}_4(g)+2Mg(s)MgC{l}_2(s)+Si(s)$

$MgC{l}_2$ is soluble in water $(54\mathrm{.}2g$ per $1000g$ water$),$ whereas $Si$ is not. Therefore, sufficient water is added to dissolve the $MgC{l}_2.$ Solid and liquid are separated by filtration. $Si$ is recovered as a filtrate cake along with some entrained liquid $(0\mathrm{.}1lb$ liquid per $lb$ solid$).$ The cake is sent to a dryer to remove the entrained liquid.

Draw and label a flow diagram. Assuming $100\%$ conversion of the Si$-$containing compounds in each of the reactions, calculate the quantities of all raw materials, the quantity of dried Si product, and the purity of the final product.