Question

For the reaction \(\mathrm{A}+2 \mathrm{~B} \longrightarrow \mathrm{C}, 5\) moles of \(\mathrm{A}\) and 8 moles of B will produce (1) 5 moles of \(\mathrm{C}\) (2) 4 moles of \(\mathrm{C}\) (3) 8 moles of \(\mathrm{C}\) (4) 13 moles of \(\mathrm{C}\)

Short answer

4 moles of C will be produced.

Step-by-step solution

Write the balanced chemical equation

The given reaction is \[ \text{A} + 2 \text{B} \rightarrow \text{C} \]. This equation is already balanced.

Identify the limiting reactant

We need to find which reactant will be completely used up first. This is the limiting reactant. We start with 5 moles of A and 8 moles of B. According to the balanced equation, 1 mole of A reacts with 2 moles of B. Therefore, 5 moles of A would require \[ 5 \text{ moles of A} \times \frac{2 \text{ moles of B}}{1 \text{ mole of A}} = 10 \text{ moles of B} \]. However, we only have 8 moles of B, so B will be the limiting reactant.

Calculate the moles of product formed

Since B is the limiting reactant, the amount of product (C) formed will be determined by the moles of B. From the balanced equation, 2 moles of B produce 1 mole of C. Therefore, 8 moles of B will produce \[ 8 \text{ moles of B} \times \frac{1 \text{ mole of C}}{2 \text{ moles of B}} = 4 \text{ moles of C} \].

Key concepts

stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It's fundamental to understanding how much of each substance is involved and produced in a reaction.
In the given exercise, stoichiometry helps us determine the amount of product formed from given amounts of reactants.
Here's a step-by-step breakdown:

• First, we used the balanced chemical equation to see how the reactants and products relate to each other in a ratio.
• We then identified the limiting reactant, which is the reactant that gets completely used up first, limiting the amount of product formed.
• Finally, using the moles of the limiting reactant, we calculated the moles of the product formed using stoichiometric coefficients from the balanced chemical equation.

Doing stoichiometric calculations requires a good grasp of the mole concept and balanced equations.

balanced chemical equation

A balanced chemical equation is crucial for solving stoichiometry problems. It shows the exact ratios in which reactants combine and products form.
In the exercise, the balanced equation is \(\text{A} + 2 \text{B} \rightarrow \text{C}\). This tells us that:

• 1 mole of A reacts with 2 moles of B to form 1 mole of C.

Having a balanced equation ensures that the law of conservation of mass is followed. This law states that mass in a closed system must remain constant over time.
To balance equations:

• Ensure the same number of each type of atom on both sides of the equation.
• Use coefficients to adjust the amounts of reactants and products.
• Recheck that all elements are balanced.

In our problem, since the equation was already balanced, we directly used it to determine the limiting reactant and the amount of product formed.

mole concept

The mole concept is a way to quantify atoms, molecules, or ions in a given substance. One mole equals \(6.022 \times 10^{23}\) entities (Avogadro's number).
In chemical reactions, using moles allows us to compare how much of one substance reacts with another. This is essential to perform accurate stoichiometric calculations.
For the exercise, we first identified the amounts of reactants in moles: 5 moles of A and 8 moles of B.

• We used the mole concept to find how many moles of B react with A.
• This told us if B or A would limit the reaction's progress (limiting reactant).
• Then, using B as the limiting reactant, we computed the moles of C produced.

The mole concept simplifies dealing with large quantities in reaction calculations, making it easier to predict and measure chemical reactions' outcomes.