A limiting reactant is the substance in a chemical reaction that is completely consumed first. This reactant determines the maximum amount of product that can be formed from the reaction mixture. Once the limiting reactant is used up, the chemical process stops, making any other reactants present irrelevant to the final product quantity. Therefore, all calculations regarding the maximum product yield must be based on this reactant.
Laying the Groundwork: The Balanced Chemical Equation
The process of determining the limiting reactant must always begin with the balanced chemical equation for the reaction. A balanced equation ensures that the number of atoms for every element is equal on both the reactant and product sides, which aligns with the law of conservation of mass. Without a properly balanced equation, subsequent calculations about the amounts of materials involved will be fundamentally incorrect.
The numbers written in front of each chemical formula are known as stoichiometric coefficients. These coefficients represent the precise molar ratios required for the reaction to occur completely. For example, in a generic reaction such as \(2A + B \rightarrow C\), the coefficients indicate that two moles of A must combine with exactly one mole of B to produce one mole of C. These whole-number ratios act as conversion factors, linking the quantities of all substances in the reaction.
The Core Comparison Method: Calculating Required vs. Available Moles
Once the equation is balanced, the next step involves converting all known quantities of reactants into moles. This conversion is necessary because the stoichiometric ratios only apply to mole amounts. If a problem provides mass in grams, the molar mass of each substance must be used to perform this conversion before any comparison can be made. This step establishes the actual number of moles available for each reactant in the system.
The most direct method for identifying the limiting reactant is to compare the available moles of one reactant against the required moles of the other reactant. To illustrate, imagine a reaction where the balanced equation is \(2A + B \rightarrow C\), and we have 5.0 moles of A and 2.0 moles of B available. We can choose one reactant, say A, and use its available amount to calculate how many moles of B would be perfectly consumed by it.
Using the mole ratio from the balanced equation, we determine the theoretical requirement for B. Since the ratio is 2 moles of A to 1 mole of B, the calculation is: \(5.0 \text{ moles } A \times (1 \text{ mole } B / 2 \text{ moles } A) = 2.5 \text{ moles } B\). This result represents the exact amount of reactant B needed to consume all \(5.0 \text{ moles } A\) completely.
The final step is to compare the calculated requirement to the amount of B actually available. We found that \(2.5 \text{ moles } B\) are required, but only \(2.0 \text{ moles } B\) are available. Since the required amount is greater than the available amount, B will run out first, identifying it as the limiting reactant.
Identifying the Limiting Reactant
The comparison calculation directly leads to the identification of the limiting reactant by revealing the supply shortage. In the example, we determined that \(2.5 \text{ moles } B\) were necessary to react with all of A, but only \(2.0 \text{ moles } B\) were present. Because the available amount of B is less than the amount required, reactant B must be the limiting reactant.
The reactant that is not completely consumed is designated the excess reactant. In our scenario, reactant A is the excess reactant because the limiting reactant dictates the end of the reaction and determines the scale of the product formation.
Practical Application: Determining Theoretical Yield
Once the limiting reactant is identified, the calculation of the theoretical yield can proceed. The theoretical yield is the maximum amount of product that can possibly be formed from the initial quantities of reactants. Only the moles of the limiting reactant can be used for this calculation, as the excess reactant will remain partially unreacted when the process stops.
To find the theoretical yield, the moles of the limiting reactant are converted into moles of the desired product using the appropriate mole ratio from the balanced equation. In the \(2A + B \rightarrow C\) example, with \(2.0 \text{ moles } B\) as the limiting reactant, we use the ratio of \(B\) to \(C\) (which is 1:1). The calculation is: \(2.0 \text{ moles } B \times (1 \text{ mole } C / 1 \text{ mole } B) = 2.0 \text{ moles } C\). This result is the theoretical yield in moles.
Calculating Excess Reactant Remaining
A secondary calculation involves determining the amount of the excess reactant that remains after the reaction is complete. To do this, the moles of the limiting reactant are used to calculate the moles of the excess reactant that were actually consumed. For our example, \(2.0 \text{ moles } B\) react with \(A\) using the 1:2 ratio: \(2.0 \text{ moles } B \times (2 \text{ moles } A / 1 \text{ mole } B) = 4.0 \text{ moles } A \text{ consumed}\).
The amount of excess reactant left over is found by subtracting the consumed amount from the initial available amount. With \(5.0 \text{ moles } A\) initially available and \(4.0 \text{ moles } A\) consumed, \(1.0 \text{ mole } A\) remains unreacted in the final mixture. This final accounting confirms that the limiting reactant was entirely used up.