Question

What is the theoretical yield for a reaction, and how does this quantity depend on the limiting reactant?

Short answer

The theoretical yield in a reaction is the maximum amount of product that can be formed, based on the balanced chemical equation and initial amounts of reactants. It depends on the limiting reactant, which is the reactant that is completely consumed during the reaction and determines the maximum amount of product that can be formed. In the example of the reaction \(2H_2 + O_2 \rightarrow 2H_2O\), where we have 4 moles of H2 and 2 moles of O2, both reactants are limiting, and the theoretical yield of water is 4 moles.

Step-by-step solution

1. Defining Theoretical Yield

Theoretical yield is the maximum amount of product that can be formed in a chemical reaction, based on the balanced chemical equation and the initial amounts of the reactants. In any reaction, the theoretical yield is calculated by considering the stoichiometric ratio or mole-to-mole ratio between the reactants and products.

2. Understanding Limiting Reactant

The limiting reactant is the reactant that is completely consumed during a chemical reaction and determines the maximum amount of product that can be formed. It limits the reaction progress because once it is fully consumed, the reaction cannot proceed further, even if there are still other reactants available.

3. Choosing a Sample Reaction

Let's use the reaction between hydrogen gas (H2) and oxygen gas (O2) to form water (H2O) as an example: \[ 2H_2 + O_2 \rightarrow 2H_2O \]

4. Calculating Mole-to-Mole Ratio

From the balanced chemical equation, we can see that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. This gives us a mole-to-mole ratio of 2:1:2 for H2:O2:H2O.

5. Identifying Limiting Reactant

Suppose we have 4 moles of H2 and 2 moles of O2, we need to determine the limiting reactant by comparing the relative amounts of each reactant to the mole-to-mole ratio. Divide the moles of each reactant by their respective coefficients in the balanced equation: - For H2: 4 moles H2 / 2 = 2 - For O2: 2 moles O2 / 1 = 2 Both values are equal, indicating that both reactants are present in the correct stoichiometric ratio and both are limiting reactants.

6. Calculating Theoretical Yield

To calculate the theoretical yield, use the limiting reactant value and the mole-to-mole ratio between the limiting reactant and the product. In this case, since both reactants are limiting, either can be used. We'll choose H2 for our calculation: - Theoretical Yield (H2O) = 2 (moles of H2) × (2 moles of H2O / 2 moles of H2) - Theoretical Yield (H2O) = 4 moles of H2O The theoretical yield of water in this reaction is 4 moles. This yield depends on the limiting reactant, which in this case was determined to be both H2 and O2.