Question

Consider the equation \(2 A+B \longrightarrow A_{2} B\). If you mix 1.0 mole of \(A\) with 1.0 mole of \(B\), what amount (moles) of \(A_{2} B\) can be produced?

Short answer

0.5 moles of A2B can be produced when 1.0 mole of A and 1.0 mole of B are mixed, as A is the limiting reactant.

Step-by-step solution

Balance the chemical equation

The given chemical equation is already balanced: \(2A + B \rightarrow A2B\). This means 2 moles of A react with 1 mole of B to produce 1 mole of A2B.

Identify the initial moles of reactants

We are given the initial amounts of reactants A and B: - 1.0 mole of A - 1.0 mole of B

Determine the limiting reactant

To determine the limiting reactant, we need to check which reactant runs out first as the reaction progresses. We can do this by comparing the mole ratio of reactants to the balanced chemical equation. For A: \( \frac{1.0\, \text{moles}}{2\, \text{moles}} = 0.5 \) For B: \( \frac{1.0\, \text{moles}}{1\, \text{mole}} = 1.0 \) Since the value (0.5) for A is lower than B (1.0), reactant A is the limiting reactant.

Calculate the amount of A2B produced

Following the stoichiometry of the balanced equation, we can calculate the amount of A2B produced using the limiting reactant, A: Amount of A2B = (Initial amount of A / stoichiometric ratio of A) x stoichiometric ratio of A2B Amount of A2B = \( \frac{1.0\, \text{mole}}{2} \cdot 1 = 0.5\, \text{mole} \) So, 0.5 moles of A2B can be produced.

Key concepts

Limiting Reactant

Understanding the concept of a limiting reactant is essential for mastering stoichiometry, the area of chemistry that concerns the relative quantities of reactants and products in chemical reactions. In a chemical reaction, the limiting reactant is the substance that is completely consumed first, stopping the reaction from proceeding because there's no more of it left to react. It's akin to running out of bricks when building a wall; no matter how much mortar you have, without bricks, you cannot continue building.

In our exercise, we have 1.0 mole of reactant A and 1.0 mole of reactant B mixing together to potentially form A2B. By comparing the mole ratios, we identify that A is the limiting reactant. This means A will be used up first in the reaction, and it determines the maximum amount of A2B that can be produced. Knowing the limiting reactant prevents you from overestimating the amount of product formed, allowing for more precise calculations and predictions in chemical manufacturing and laboratory settings.

Mole Ratio

The mole ratio is a critical component in stoichiometry that comes from the coefficients of a balanced chemical equation. It tells us the proportions of reactants that react and the proportions of products formed. Think of it as a recipe for the chemical reaction - for example, the balanced equation from our exercise (\(2A + B \rightarrow A2B\) ) indicates that for every 2 moles of A, you need 1 mole of B to make 1 mole of A2B.

In practice, this means if you were to have, for instance, 4 moles of A, you would need 2 moles of B to fully consume A according to the equation. Utilizing mole ratios effectively allows us to predict the outcome of a reaction and is the key to converting from moles of one substance to moles of another.

Chemical Equation Balancing

Balancing chemical equations is a fundamental skill in chemistry that ensures the law of conservation of mass is satisfied. This principle states that mass cannot be created or destroyed in a chemical reaction. To balance a chemical equation, we adjust the coefficients in front of the molecular formulas to make sure the same number of atoms of each element exists on both the reactant and product sides of the equation.

Hence, in our example (\(2A + B \rightarrow A2B\) ), the coefficients tell us that two atoms of A combine with one atom of B to form one molecule of A2B. Not balancing equations correctly will lead to incorrect stoichiometric calculations, which may result in misjudged amounts of reactants needed or products that can be formed.

Theoretical Yield

Theoretical yield is the maximum amount of product that can be generated from a given amount of reactants under ideal conditions, based on the balanced chemical equation. It's the predicted quantity of product, assuming complete conversion of the limiting reactant into the product, with no losses during the process.

In the context of our exercise, the theoretical yield of A2B is 0.5 moles. This value is found by applying the mole ratio derived from the balanced equation to the amount of the limiting reactant, which in this case is A. Knowing the theoretical yield is crucial for chemists as it serves as a benchmark for the efficiency of the reaction. In industrial settings, actual yield (the amount actually obtained from a reaction) is compared to the theoretical yield to calculate percent yield, a measure of the reaction's efficiency.