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, 155.8 kg of SiO2 reacts with 78.3 kg of carbon to produce 66.1 kg of silicon. Determine the limiting reactant and the theoretical yield.

Verified step by step guidance

1. Write the balanced chemical equation for the reaction: \[ \text{SiO}_2 (s) + 2\text{C} (s) \rightarrow \text{Si} (l) + 2\text{CO} (g) \]
2. Convert the masses of \( \text{SiO}_2 \) and \( \text{C} \) to moles using their molar masses: \( \text{Molar mass of SiO}_2 = 60.08 \, \text{g/mol} \) and \( \text{Molar mass of C} = 12.01 \, \text{g/mol} \).
3. Calculate the moles of \( \text{SiO}_2 \) and \( \text{C} \) using the formula: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \).
4. Determine the limiting reactant by comparing the mole ratio of \( \text{SiO}_2 \) to \( \text{C} \) from the balanced equation with the calculated moles.
5. Calculate the theoretical yield of silicon by using the moles of the limiting reactant and the stoichiometry of the balanced equation.

Key Concepts

Limiting Reactant

The limiting reactant is the substance that is completely consumed first in a chemical reaction, thus determining the maximum amount of product that can be formed. To identify it, one must compare the mole ratios of the reactants based on the balanced chemical equation. The reactant that produces the least amount of product is the limiting reactant.

Theoretical Yield

The theoretical yield is the maximum amount of product that can be generated from a given amount of reactants, calculated using stoichiometry based on the balanced chemical equation. It assumes complete conversion of the limiting reactant into product without any losses. The theoretical yield is expressed in grams or moles and is essential for evaluating the efficiency of a reaction.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves using balanced chemical equations to calculate the amounts of substances consumed and produced. Understanding stoichiometry is crucial for determining limiting reactants and theoretical yields in chemical processes.