Question

Which of the following reaction mixtures would produce the greatest amount of product, assuming all went to completion? Justify your choice. Each involves the reaction symbolized by the equation \\[ 2 \mathrm{H}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O} \\] a. 2 moles of \(\mathrm{H}_{2}\) and 2 moles of \(\mathrm{O}_{2}\) b. 2 moles of \(\mathrm{H}_{2}\) and 3 moles of \(\mathrm{O}_{2}\) c. 2 moles of \(\mathrm{H}_{2}\) and 1 mole of \(\mathrm{O}_{2}\) d. 3 moles of \(\mathrm{H}_{2}\) and 1 mole of \(\mathrm{O}_{2}\) e. Each would produce the same amount of product.

Short answer

The correct answer is (e): Each would produce the same amount of product. All the options generate 2 moles of \(H_{2}O\), as the limiting reagent dictates the amount of product formed in each case.

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation for the reaction is given as: \[2 H_{2} + O_{2} \rightarrow 2 H_{2}O\]

Calculate the limiting reactant and amount of product formed for each option

According to the balanced equation, we need 2 moles of hydrogen and 1 mole of oxygen to produce 2 moles of water. We will now calculate the limiting reactant and the amount of product formed for each option: a. 2 moles of \(H_{2}\) and 2 moles of \(O_{2}\) b. 2 moles of \(H_{2}\) and 3 moles of \(O_{2}\) c. 2 moles of \(H_{2}\) and 1 mole of \(O_{2}\) d. 3 moles of \(H_{2}\) and 1 mole of \(O_{2}\)

Compare the amount of product formed for each option

Now we need to compare the amount of product formed for each option and choose the one that has the greatest amount of product: a. Since there are equal amounts of hydrogen and oxygen, one mole of \(O_{2}\) will react with 2 moles of \(H_{2}\) to form 2 moles of water. Total: 2 moles of \(H_{2}O\) b. Oxygen is in excess here. Only 1 mole of \(O_{2}\) can react with 2 moles of \(H_{2}\) to form 2 moles of water. Total: 2 moles of \(H_{2}O\) c. It's perfectly balanced: 2 moles of \(H_{2}\) will react with 1 mole of \(O_{2}\) to form 2 moles of water. Total: 2 moles of \(H_{2}O\) d. Hydrogen is in excess here. One mole of \(O_{2}\) will react with 2 moles of \(H_{2}\) to form 2 moles of water. Hydrogen remains unreacted. Total: 2 moles of \(H_{2}O\)

Conclude

All the options produce the same amount of product: 2 moles of \(H_{2}O\). Therefore, the correct answer is (e): Each would produce the same amount of product.

Key concepts

Balanced Chemical Equation

A balanced chemical equation is crucial when studying a chemical reaction. It represents the reactants and products, and ensures that the same number of each type of atom appears on both sides of the equation. This balancing allows for the conservation of mass, aligning with the law of conservation of matter.
For instance, in the reaction \(2 \mathrm{H}_{2} + \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}\), two molecules of hydrogen combine with one molecule of oxygen to form two molecules of water.
Maintaining a balanced equation helps chemists understand the proportions of reactants and products involved, ensuring accurate predictions about the outcome of the reaction.

Mole Concept

The mole is a fundamental concept in chemistry, acting as a bridge between the atomic scale and the macroscopic world. One mole is equivalent to Avogadro's number, approximately \(6.022 \times 10^{23}\) entities, typically atoms or molecules.
This concept helps in quantifying substances in chemical reactions. For example, in the balanced chemical equation \(2 \mathrm{H}_{2} + \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}\), it indicates the ratio of molecules reacting.

• 2 moles of \(\mathrm{H}_{2}\) reacts with 1 mole of \(\mathrm{O}_{2}\).
• Producing 2 moles of \(\mathrm{H}_{2} \mathrm{O}\).

This proportionality underscores the importance of moles in predicting yields and the amount of products formed.

Product Formation

Product formation in a chemical reaction denotes the output resulting from the transformation of reactants. It's determined by the reactants' stoichiometry as expressed in a balanced equation.
In our example, the reaction \(2 \mathrm{H}_{2} + \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}\) produces water:

• Every time 2 moles of \(\mathrm{H}_{2}\) and 1 mole of \(\mathrm{O}_{2}\) react, 2 moles of \(\mathrm{H}_{2} \mathrm{O}\) are formed.

If the reactants are provided in these exact proportions or if there’s a limiting reactant,then the maximum possible product is formed. Therefore no reactant is wasted.

Chemical Reaction Completeness

Chemical reaction completeness examines whether a reaction goes to completion, meaning all the reactants are consumed to form products without any leftover.
To achieve this, we must identify the limiting reactant. The limiting reactant is the substance that runs out first, ceasing the reaction.

• In the exercise, each scenario provided different initial amounts of hydrogen and oxygen.
• Yet in every case, it turned out that the limiting reactant combination formed the same amount of water: 2 moles.

This means each chemical reaction went to completion as dictated by the balanced chemical equation. Understanding this concept aids in predicting how much product will form in industrial or laboratory settings, ensuring efficiency.