Many computer chips are manufactured from silicon , which occurs in nature as SiO2. WhenSiO 2 is heated to melting , it reacts with solid carbon to form liquid silicon and carbon monoxide gas. In an industrial preparation of silicon, 155.8 kg of SiO2 reacts with 78.3 kg of carbon to produce 66.1 kg of silicon. Determine the limiting reactant, theoretical yield, and percent yield for the reaction.

In the given case, SiO2 is the limiting reactant, 71.72 Kg is the theoretical yield, and 90.8 percent is the experimental yield.

Explanation:

A reactant that completely gets used up in a chemical reaction, and it limits the concentration of product, which can be produced is termed as a limiting reactant. The maximum concentration of product that can get generated from the limiting reactant is termed as the theoretical yield.  

Based on the given question, the balanced chemical reaction is:  

SiO₂ + 2C ⇒ Si + 2CO

Now the mole ratio of SiO₂: C = 1: 2

Based on the given information, the mass of SiO₂ is 155.8 Kg. The no. of moles can be calculated by using the formula, n = weight/molecular mass.  

The molecular mass of SiO₂ is 60.08 gram per mole. By putting the values we get,  

n = 155.8 × 10³ grams / 60.08 grams/mol

n = 2.59 × 10³ moles

The weight of Carbon given is 78.3 Kg or 78.3 × 10³ grams, the molecular mass of C is 12 gram per mole. Similarly, the moles of C will be,  

n = 78.3 × 10³ grams / 12 g/mol

n = 6.52 × 10³ moles

The experimental molar ratio of SiO₂: C is,  

= 2.59 × 10³: 6.52 × 10³

= 2.59: 6.52 = 1: 2.5

Hence, it is clear that carbon in the given case is present in excess amount, therefore, SiO₂ is a limiting reactant.  

With the help of the balanced equation, the molar ratio of SiO₂: Si is 1: 1. As SiO₂ is the limiting reactant, therefore, theoretical yield of the reaction will be determined by SiO₂.  

As calculated, the moles of SiO₂ used is 2.59 × 10³

Hence, the moles of Si produced in the given reaction is 2.59 × 10³.  

Now the mass of Si produced theoretically can be determined by using the formula, moles = weight/molar mass. The molar mass of Si is 28.08 gram per mole. Now putting the values we get,  

Weight = 2.59 × 10³ moles × 28.08 gram per mole

Weight = 72.72 × 10³ grams or 72.72 Kg

The theoretical yield of Si is 72.72 Kg, however, the experimental yield is 66.1 Kg. Therefore, the percent yield for the reaction will be,  

= Experimental yield / Theoretical yield × 100 %

= 66.1 Kg / 72.72 Kg × 100%

= 90.8 %

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