Many computer chips are manufactured from silicon, which occurs in nature as sio2 . when sio2 is heated to melting, it reacts with solid carbon to form liquid silicon and carbon monoxide gas. in an industrial preparation of silicon, 155.3kg of sio2 of is allowed to react with 79.3kg of carbon to produce 66.2kg of silicon. a. what is the theoretical yield for the reaction in kg si? b. what is the percent yield for the reaction?

a. Theoretical yield of Si = 72.58 kg

b. Percent Yield = 91.2 %

Explanation:

The chemical reaction involved is:  SiO₂ (l) + 2C (s) → Si (l) + 2CO (g)

The stoichiometric ratio = 1 mol SiO₂ ÷ 2 mol C = 0.5 mol SiO₂ ÷ 1 mol C

Given: mass of SiO₂: w₁ = 155.3kg = 155.3 × 10³g,  mass of C: w₂ = 79.3kg = 79.3 × 10³g,  mass of Si: w₃ = 66.2kg = 66.2 × 10³g                  (∵ 1 kg =1000g)

Molar mass of SiO₂: m₁ = 60.08 g/mol, atomic mass of C: m₂ = 12.01 g/mol, atomic mass of Si: m₃ = 28.08 g/mol

Number of moles of SiO₂ taken: n₁ = w₁ ÷ m₁ = 155300 g ÷ 60.08 g/mol = 2584.88 mol

Number of moles of C taken: n₂ = w₂ ÷ m₂ = 79300 g ÷ 12.01 g/mol = 6602.83 mol

Actual ratio = n₁ ÷ n₂ = 2584.88 mol SiO₂ ÷ 6602.83 mol C = 0.39 mol SiO₂ ÷ 1 mol C

Since the stoichiometric ratio > actual ratio

Therefore, SiO₂ is the limiting reagent.

Now, the mass of SiO₂ in 1 mol = number of moles × molar mass = 1 mol × 60.08 g/mol = 60.08 g

the mass of Si in 1 mol = number of moles × molar mass = 1 mol × 28.08 g/mol = 28.08 g

So 28.08 g of Si is produced from 60.08 g SiO₂

Therefore, the amount of Si produced from 155300 g SiO₂ = 155300 g × 28.08 g ÷ 60.08 g = 72583.62 g = 72.58 kg

Therefore, the theoretical yield of Si = 72.58 kg

Actual yield of Si = 66.2 kg

Therefore, Percent Yield  = Actual yield ÷ Theoretical yield × 100 = 66.2 kg ÷ 72.58 kg × 100 = 91.2 %

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