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

When 1.0 mole of A and 1.0 mole of B are mixed, the limiting reactant is A. Using stoichiometry, 0.5 moles of A2B can be produced from the given amounts of reactants.

Step-by-step solution

Identify the limiting reactant

Given the balanced equation: \[ 2A + B \longrightarrow A_{2}B \] We have to identify the limiting reactant, which is the reactant that will run out first during the reaction and determine the amount of product formed. First, let's calculate the mole ratios of reactants A and B. In the balanced equation, for every 2 moles of A, 1 mole of B is consumed. Mole ratio A:B = 2:1

Calculate the moles of reactant required based on the balanced equation

We have 1.0 mole of A and 1.0 mole of B, let's calculate how much of each reactant required based on mole ratios: Moles of A required for 1 mole of B = (2 moles of A)/(1 mole of B) * (1 mole of B) = 2 moles of A Since, we only have 1.0 mole of A (which is less than the required 2 moles), A is the limiting reactant.

Use stoichiometry of limiting reactant to calculate the moles of A2B

Using stoichiometry, we can find out the amount of A2B that can be produced. From the balanced equation, when 2 moles of A reacts with 1 mole of B, 1 mole of A2B is produced. Moles of A2B formed = (1 mole of A2B)/(2 moles of A) * (1.0 mole of A) = 0.5 mole of A2B So, 0.5 moles of A2B can be produced from the given amounts of reactants A and B.

Key concepts

Stoichiometry

Stoichiometry is a core concept in chemistry that involves using a balanced chemical equation to calculate the quantities of reactants and products in a chemical reaction. When we talk about stoichiometry, we deal with the quantitative relationships based on the chemical equation. In simple terms, it allows us to know how much of one substance will react with another, or how much product is formed.

In the provided exercise, stoichiometry helps us determine how much of the product, which is \(A_2B\), can be formed from given amounts of reactants \(A\) and \(B\). We begin by analyzing the balanced chemical equation, \(2A + B \rightarrow A_2B\). The coefficients tell us the ratio in which reactants combine to form products. Using this ratio, which in our equation is 2 moles of \(A\) to 1 mole of \(B\), we decide how much product can be formed based on the available moles of each reactant.

In essence, stoichiometry is a tool to predict outcomes of reactions and to ensure that we have the correct proportions of reactants. It plays a vital role in planning practical chemical reactions in a lab or industry by ensuring efficient and cost-effective use of materials.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They consist of reactants, the starting substances, and products, the substances formed after the reaction. In our example, the chemical equation is \(2A + B \rightarrow A_2B\). This equation provides a clear picture of the transformation from reactants \(A\) and \(B\) into product \(A_2B\).

A chemical equation must be balanced, meaning the number of atoms of each element on the reactant's side must equal the number on the product's side. This balance ensures the conservation of mass—an essential principle in chemistry. To balance a chemical equation, we adjust the coefficients, which are the numbers placed before the chemical formulas. In the equation \(2A + B \rightarrow A_2B\), it's balanced because two atoms of \(A\) and one atom of \(B\) react to form the product \(A_2B\), mirroring the composition on both sides.

Understanding and writing balanced chemical equations is a fundamental skill in chemistry. They tell us not just what is reacting and what's formed, but also the quantitative aspect needed for applications such as determining the amount of substances required.

Mole Ratios

Mole ratios are derived from the coefficients of a balanced chemical equation, providing a bridge between the moles of one substance and another in a chemical reaction. They are essential for solving stoichiometric problems because they help convert moles of reactants to moles of products.

In the given reaction \(2A + B \rightarrow A_2B\), the mole ratio between \(A\) and \(B\) is 2:1. This means that for every 2 moles of \(A\), 1 mole of \(B\) is needed. Using these ratios, we can determine how much of one reactant we need, or how much product we can expect to form.

• If we start with 1 mole of \(B\), based on the mole ratio, we should ideally have 2 moles of \(A\).
• However, if only 1 mole of \(A\) is available, then \(A\) becomes the limiting reactant.
• The concept of limiting reactant is crucial as it limits the amount of product that can be formed, which in this case is 0.5 mole of \(A_2B\).

Mole ratios thus guide us in calculating and predicting the outcomes of chemical reactions in a precise and systematic manner, ensuring successful experimental or industrial chemical transformations.