Question

Silicon, which occurs in nature as SiO2, is the material from which most computer chips are made. If SiO2 is heated until it melts into a liquid, it reacts with solid carbon to form liquid silicon and carbon monoxide gas. In an industrial preparation of silicon, 63.8 kg of SiO2 reacted with 25.8 kg of carbon to produce 22.4 kg of silicon.

a. Determine limiting reactant
b. Determine theoretical yield
c. Determine % yield

Answer 1

The limiting reactant is SiO2

The theoretical yield is 29.82 Kg

The % yield is 75.1 %

Step-by-step explanation:

Step 1: Data given

Mass of SiO2 = 63.8 Kg

Mass of carbon = 25.8 Kg

Actual yield of silicon = 22.4 Kg

Molar mass of SiO2 = 60.085 g/mol

Molar mass of Carbon = 12g/mol

Molar mass of Si = 28.085 g/mol

Step 2: the balanced equation

SiO2 + 2C → Si + 2CO

This means for 1 mole of SiO2 consumed, we need 2 moles of Carbon to produce 1 mole of Silicon and 2 moles of CO

Step 3: Calculate moles of SiO2

Number of moles = mass of SiO2 / Molar mass of SiO2

Number of moles SiO2 = 638000 grams / 60.085 g/mol

Number of moles SiO2 = 1061.8 moles

Step 4: Calculate moles of Carbon

Number of moles = mass of C / Molar mass of C

Number of moles C = 258000 grams / 12 g/mol

Number of moles C = 2150 moles

Step 5: Calculate limiting reactant

SiO2 is the limiting reactant. It will completely react ( 1061.8 moles). Carbon is in excess. There will react 2*1061.8 = 2123.6 moles. There will remain 26.4 moles of Carbon.

Step 6: Calculate moles of Si produced

For 1 mole of SiO2 consumed, we need 2 moles of Carbon to produce 1 mole of Silicon

If there reacts 1061.8 moles of SiO2, there will be produced 1061.8 moles of Si

Step 7: Calculate mass of Si

Mass = numbers of moles Si* Molar mass Si

Mass = 1061.8 moles * 28.085 g/mol

mass = 29820.65 grams = 29.82 Kg

The theoretical yield is 29.82 Kg of silicon

Step 8: Calculate the percent yield

% yield = actual yield / theoretical yield = 22.4 kg /29.82 Kg * 100 % = 75.1 %

The % yield is 75.1 %