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Stoichiometry is the study of the quantitative relationships between reactants and products in a chemical reaction. It allows chemists to predict how much product will be formed from a given amount of reactants, and vice versa. One important application of stoichiometry is determining the limiting reactant in a chemical reaction. The limiting reactant is the reactant that is completely consumed in a reaction, limiting the amount of product that can be formed.

To determine the limiting reactant, we need to compare the amount of each reactant present to the stoichiometric ratio of the reaction. The stoichiometric ratio is the ratio of the coefficients of the reactants and products in a balanced chemical equation. For example, consider the reaction:

2 H2 + O2 → 2 H2O

The stoichiometric ratio of this reaction is 2:1 for H2 to O2, meaning that 2 moles of H2 react with 1 mole of O2 to produce 2 moles of H2O. If we have 4 moles of H2 and 2 moles of O2, we can use stoichiometry to determine which reactant is limiting.

First, we need to convert the amounts of each reactant to moles. We can use the molar mass of each substance to convert from mass to moles. For example, if we have 4 grams of H2 and the molar mass of H2 is 2 g/mol, then we have:

4 g H2 × (1 mol H2 / 2 g H2) = 2 mol H2

Similarly, if we have 2 grams of O2 and the molar mass of O2 is 32 g/mol, then we have:

2 g O2 × (1 mol O2 / 32 g O2) = 0.0625 mol O2

Now we can compare the amount of each reactant to the stoichiometric ratio. For H2, we have 2 mol, which is exactly the amount needed to react with 1 mole of O2. For O2, we have 0.0625 mol, which is less than the amount needed to react with 2 moles of H2. Therefore, O2 is the limiting reactant and H2 is in excess.

To determine the amount of product that will be formed, we need to use the stoichiometric ratio to calculate the theoretical yield. The theoretical yield is the maximum amount of product that can be formed from the limiting reactant. In this case, the stoichiometric ratio tells us that 1 mole of O2 reacts with 2 moles of H2 to produce 2 moles of H2O. Therefore, the theoretical yield of H2O is:

0.0625 mol O2 × (2 mol H2O / 1 mol O2) = 0.125 mol H2O

This means that if we had exactly 0.0625 mol of O2 and unlimited H2, we could produce a maximum of 0.125 mol of H2O. However, since we have excess H2, we will not actually produce this much H2O. The actual yield will be determined by the amount of limiting reactant present.

To calculate the actual yield, we need to determine how much of the limiting reactant is consumed in the reaction. In this case, we know that 1 mole of O2 reacts with 2 moles of H2 to produce 2 moles of H2O. Therefore, for every mole of O2 consumed, 2 moles of H2 are also consumed. Since we have 0.0625 mol of O2, we can calculate the amount of H2 consumed as:

0.0625 mol O2 × (2 mol H2 / 1 mol O2) = 0.125 mol H2

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This is exactly the amount of H2 we have, so all of the H2 will be consumed and there will be no excess H2 left over. Therefore, the actual yield of H2O will be:

0.125 mol H2O

This is the same as the theoretical yield, since we had exactly the right amount of limiting reactant to produce the maximum amount of product.

Stoichiometry can be used to determine the limiting reactant in a chemical reaction by comparing the amounts of each reactant to the stoichiometric ratio. The limiting reactant is the reactant that is completely consumed in the reaction, limiting the amount of product that can be formed. The theoretical yield of the product can be calculated using the stoichiometric ratio, and the actual yield depends on the amount of limiting reactant present. By using stoichiometry to determine the limiting reactant and theoretical yield, chemists can optimize reactions to produce the maximum amount of product and minimize waste.