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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?

Respuesta :

Answer:

(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:

[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]       .....(1)

For [tex]SiO_2[/tex]:

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

Molar mass = 60 g/mol

Putting values in equation 1:

[tex]\text{Moles of }SiO_2=\frac{155000g}{60g/mol}=2583.3mol[/tex]

For carbon:

Given mass = 78.2 kg = 78200 g

Molar mass = 12 g/mol

Putting values in equation 1:

[tex]\text{Moles of carbon}=\frac{78200g}{12g/mol}=6516.67mol[/tex]

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

[tex]SiO_2+2C\rightarrow Si+2CO[/tex]

By stoichiometry of the reaction:

1 mole of [tex]SiO_2[/tex] reacts with 2 moles of carbon

So, 2583.3 moles of [tex]SiO_2[/tex] will react with = [tex]\frac{2}{1}\times 2583.3=5166.4mol[/tex] 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, [tex]SiO_2[/tex] is considered a limiting reagent because it limits the formation of the product.

  • For (a):

By stoichiometry of the reaction:

1 mole of [tex]SiO_2[/tex] produces 1 mole of silicon

So, 2583.3 moles of [tex]SiO_2[/tex] will produce = [tex]\frac{1}{1}\times 2583.3=2583.3mol[/tex] of silicon

Since the molar mass of silicon = 28 g/mol

Putting values in equation 1:

[tex]\text{Mass of Si}=2583.3mol\times 28g/mol=72332.4g=72.33 kg[/tex]

Hence, the theoretical yield of silicon is 72.33 kg.

  • For (b):

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

[tex]\% \text{yield}=\frac{\text{Measured value}}{\text{Theoretical value}}\times 100[/tex]              ......(2)

Given values:

Measured value of silicon = 66.0 kg

Theoretical value of silicon  = 72.33 kg

Putting values in equation 1:

[tex]\% \text{yield}=\frac{66.0kg}{72.33kg}\times 100\\\\\% \text{yield}=91.25 \%[/tex]

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

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