Question

Given the reaction of hydrogen and chlorine gases, calculate the moles of hydrogen that react to produce \(5.00 \mathrm{~mol}\) of \(\mathrm{HCl}\). $$\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g)$$

Short answer

2.50 moles of hydrogen are needed.

Step-by-step solution

Understand the Chemical Reaction

The balanced chemical equation for the reaction between hydrogen and chlorine is: \[ \mathrm{H}_{2}(g) + \mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g) \] This tells us that one mole of hydrogen reacts with one mole of chlorine to produce two moles of hydrogen chloride.

Use Stoichiometry to Set Up a Proportion

From the balanced equation, the stoichiometric ratio between \(\mathrm{H}_{2}\) and \(\mathrm{HCl}\) is 1:2. This means that for every 1 mole of \(\mathrm{H}_{2}\), 2 moles of \(\mathrm{HCl}\) are produced. This ratio can be written as: \[ \frac{\text{moles of } \mathrm{H}_2}{\text{moles of } \mathrm{HCl}} = \frac{1}{2} \]

Calculate Moles of Hydrogen Required

Using the stoichiometric ratio and the given amount of \(\mathrm{HCl}\), set up the equation: \[ \frac{x}{5.00} = \frac{1}{2} \] Solve for \(x\) to find the moles of \(\mathrm{H}_2\): \[ x = \frac{1}{2} \times 5.00 = 2.50 \]

Conclude the Calculation

The calculation shows that 2.50 moles of hydrogen \(\mathrm{H}_2\) are needed to produce 5.00 moles of \(\mathrm{HCl}\).

Key concepts

Understanding Chemical Reactions

Chemical reactions are transformations where substances, known as reactants, interact to form new substances called products. In this context, a chemical reaction involving hydrogen (\( \text{H}_2 \)) and chlorine (\( \text{Cl}_2 \)) gases produces hydrogen chloride (HCl).
When understanding this reaction, it's essential to look at the balanced chemical equation:\[ \text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g) \]

The reaction indicates the combination of hydrogen and chlorine gases to form hydrogen chloride.

Each molecule of hydrogen reacts with each molecule of chlorine.

The products form in a fixed ratio in relation to the amounts of reactants used.

This equation verifies that every molecule of hydrogen matches with chlorine to produce two molecules of hydrogen chloride. Understanding the nature of the substances and the transformations they undergo during the reaction helps in accurate stoichiometric calculations.

Calculating Moles in Stoichiometry

Stoichiometry is the calculation of reactants and products in a chemical reaction. A foundational aspect here is the concept of moles — allowing chemists to count particles by weighing them.
In the given exercise, hydrogen and chlorine react to form hydrogen chloride, and we need to calculate the moles of hydrogen (\( \text{H}_2 \)) required.

• We know from the balanced equation that 1 mole of hydrogen produces 2 moles of hydrogen chloride.
• The stoichiometric ratio is derived from the balanced equation: \[ \frac{\text{moles of } \text{H}_2}{\text{moles of } \text{HCl}} = \frac{1}{2} \] This ratio is fundamental in setting up our calculation.

Given 5.00 moles of hydrogen chloride, we apply the ratio:\[ \frac{x}{5.00} = \frac{1}{2} \]Solving for \( x \) involves simple rearrangement and multiplication, revealing that 2.50 moles of hydrogen are necessary to achieve the given product yield.

The Importance of Balanced Equations

A balanced chemical equation is crucial in chemical reactions to uphold the law of conservation of mass, ensuring the same number of each type of atom on both sides of the equation.
For the given reaction:\[ \text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g) \]

The equation is balanced because there are 2 hydrogen atoms and 2 chlorine atoms on both sides.

This balance ensures exact proportionate calculations of reactants and products.

In any stoichiometric calculation, achieving accuracy depends heavily on first balancing the equation. Balancing equations enables the clear identification of the mole ratios used in calculations. Thus, ensuring a balanced equation is the foundation for accurately predicting the result of the reaction, such as determining the exact amount of hydrogen required to produce a specific amount of hydrogen chloride in this example.