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, 155.0 kg of SiO2 is allowed to react with 78.2 kg of carbon to produce 66.0 kg of silicon. Required:
a. What is the theoretical yield for the reaction in Kg Si?
b. What is the percent yield for the reaction?

(a): The theoretical yield of silicon is 72.33 kg.

(b): The percent yield of the reaction is 91.25 %.

Explanation:

Limiting reagent is defined as the reagent which is completely consumed in the reaction and limits the formation of the product.

Excess reagent is defined as the reagent which is left behind after the completion of the reaction.

The number of moles is defined as the ratio of the mass of a substance to its molar mass. The equation used is:

      .....(1)

For :

Given mass = 155.0 kg = 155000 g          (Conversion factor: 1 kg = 1000 g)

Molar mass = 60 g/mol

Putting values in equation 1:

For carbon:

Given mass = 78.2 kg = 78200 g

Molar mass = 12 g/mol

Putting values in equation 1:

The chemical equation for the reaction of silicon dioxide and carbon follows:

By stoichiometry of the reaction:

1 mole of reacts with 2 moles of carbon

So, 2583.3 moles of will react with = of carbon

As the given amount of carbon is more than the required amount. Thus, it is present in excess and is considered as an excess reagent.

Thus, is considered a limiting reagent because it limits the formation of the product.

By stoichiometry of the reaction:

1 mole of produces 1 mole of silicon

So, 2583.3 moles of will produce = of silicon

Since the molar mass of silicon = 28 g/mol

Putting values in equation 1:

Hence, the theoretical yield of silicon is 72.33 kg.

The percent yield of a reaction is calculated by using an equation:

             ......(2)

Given values:

Measured value of silicon = 66.0 kg

Theoretical value of silicon  = 72.33 kg

Putting values in equation 1:

Hence, the percent yield of the reaction is 91.25 %.