Q12. What thickness (in cm) is the silicon block (density = 2.13 g/cm3) that is 2.65 cm wide and long necessary to react with 88.3 g of Cr2O3 by the reaction:
Si (s) + Cr203 (s) → SiO2 (s) + Cr (1)

1.63cm

Explanation:

Given parameters:

Density of silicon = 2.13g/cm³

Mass of Cr₂O₃ = 88.3g

Width of the block = 2.65cm

Length of the block  = 2.65cm

Unknown:

Thickness of the block  = ?

Solution:

Reaction equation:

          3Si   +   2Cr₂O₃   →  3SiO₂ + 4Cr

Let us find the mass of Si,

   So,

    Number of moles  =

  we find the number of moles of Cr₂O₃ ;

Molar mass of Cr₂O₃ = 2(52) + 3(16) = 152g/mol

  Number of moles of Cr₂O₃ =   = 0.58mole

Then;

  we know that;

              2 moles of Cr₂O₃ reacted with 3 moles of Cr₂O₃

              0.58moles of Cr₂O₃ will react with   = 0.87mole

So,

    Mass of Si  = number of moles x molar mass

          molar mass of Si = 28g/mol

   Mass of Si  = 0.87 x 28  = 24.4g

Since density is the mass per unit volume of a compound;

     Mass of Si  = density of Si x volume of Si block

  Volume of Si block  = length x width x thickness = 2.65 x 2.65 x thickness

   Volume of Si block = 7.02 x thickness

Mass of Si  = 2.13 x 7.02 x thickness

    24.4  = 15 x thickness

         thickness = = 1.63cm