Question

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

Short answer

The limiting reactant in the given reaction is A, since we have a smaller amount of A based on the stoichiometric ratio (2:1). Therefore, using the mole ratio of A to \(A_2B\) (2:1), we can calculate that 0.5 moles of \(A_2B\) can be produced when mixing 1.0 mol of A and 1.0 mol of B.

Step-by-step solution

Identify the limiting reactant

In this reaction, we have 1.0 mole of A and 1.0 mole of B. To identify the limiting reactant, we need to compare the mole ratio of A and B according to the reaction equation. The mole ratio of A to B is 2:1 (from 2A and B in the equation). Now divide the available moles of each reactant by their respective mole ratio: - For A: \( \frac{1.0}{2} = 0.5 \) - For B: \( \frac{1.0}{1} = 1.0 \) The reactant with the smallest result is the limiting reactant. In this case, it is A with a result of 0.5.

Calculate the moles of \(A_2B\) produced

Now that we've identified A as the limiting reactant, we can calculate the moles of \(A_2B\) produced using the mole ratio. Since the mole ratio of A to \(A_2B\) is 2:1, we need to multiply the result obtained in step 1 (0.5) by the mole ratio of \(A_2B\) (1 mole) to find the number of moles produced: Moles of \(A_2B\) = 0.5 * 1 = 0.5 moles So, 0.5 moles of \(A_2B\) can be produced when 1.0 mol of A and 1.0 mol of B are mixed together.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry used to calculate the quantities of reactants and products involved in a chemical reaction. It allows us to predict how much product will form from given quantities of reactants. Stoichiometry is based on the balanced chemical equation, which shows the relationship between reactants and products. This relationship is represented by coefficients that denote the number of moles of each substance involved. To solve stoichiometry problems, such as the exercise provided, follow these general steps:

• Write and balance the chemical equation for the reaction.
• Convert the known quantities of reactants to moles.
• Use the mole ratios from the balanced equation to calculate the moles of the desired product.
• Convert the moles of product to the desired units if necessary.

By using stoichiometry, we ensure that calculations are consistent with the conservation of mass, maintaining an accurate representation of the chemical process.

Mole Ratio

Mole ratio is a key concept in assessing the proportions of reactants used and products formed in a chemical reaction. It is derived from the coefficients of a balanced chemical equation. In the equation given in the exercise, \[2A + B \longrightarrow A_2B\] Every 2 molecules of A react with 1 molecule of B to produce 1 molecule of \(A_2B\). This is indicated by the coefficients "2" for A and "1" for both B and \(A_2B\). Therefore, the mole ratio for A:B: \(A_2B\) is 2:1:1. Using this ratio, we can determine how the reactants will be consumed and the products will form. Applying the mole ratio, divide the number of moles of each reactant by its respective coefficient to identify the limiting reactant, as shown in the solution. The limiting reactant determines the maximum amount of product that can be formed.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions, displaying the substances involved as reactants and products. A balanced chemical equation ensures that the law of conservation of mass is followed, meaning the number of atoms for each element is the same on both sides of the equation. This is achieved by adjusting coefficients in front of chemical formulas, without altering the substances themselves.For example, consider the equation \[2A + B \longrightarrow A_2B\] In this equation, 2 moles of A react with 1 mole of B to produce 1 mole of \(A_2B\). Balancing equations accurately allows chemists to predict the outcomes of reactions, which is crucial in stoichiometric calculations.Balancing equations can be tricky but follows these general guidelines:

• Identify the reactants and products.
• Count the number of atoms of each element in both reactants and products.
• Adjust coefficients to balance the atoms in the equation.
• Check your work to ensure mass and charge (if applicable) are conserved.

Remember, understanding chemical equations is essential for performing accurate stoichiometry and predicting reactions.