Question

The reaction of hydrogen with oxygen produces water. $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) $$ a. How many moles of \(\mathrm{O}_{2}\) are required to react with \(2.0\) moles of \(\mathrm{H}_{2}\) ? b. How many moles of \(\mathrm{H}_{2}\) are needed to react with \(5.0\) moles of \(\mathrm{O}_{2}\) ? c. How many moles of \(\mathrm{H}_{2} \mathrm{O}\) form when \(2.5\) moles of \(\mathrm{O}_{2}\) reacts?

Short answer

a. 1.0 mole of \( \mathrm{O}_2 \) b. 10.0 moles of \( \mathrm{H}_2 \) c. 5.0 moles of \( \mathrm{H}_2 \mathrm{O} \)

Step-by-step solution

Analyze the balanced chemical equation

The balanced chemical equation is: \[ 2 \mathrm{H}_2(g) + \mathrm{O}_2(g) \longrightarrow 2 \mathrm{H}_2 \mathrm{O}(g) \] From the equation, 2 moles of hydrogen gas (\( \mathrm{H}_2 \)) react with 1 mole of oxygen gas (\( \mathrm{O}_2 \)) to produce 2 moles of water (\( \mathrm{H}_2 \mathrm{O} \)).

Solve Part (a) - Moles of \( \mathrm{O}_2 \) reacting with 2.0 moles of \( \mathrm{H}_2 \)

Using the stoichiometric relationship from the balanced equation: \[ \frac{2 \; \text{moles of} \; \mathrm{H}_2}{1 \; \text{mole of} \; \mathrm{O}_2} = 2 \] Given 2.0 moles of hydrogen gas: \[ \mathrm{O}_2 = \frac{2.0 \; \text{moles} \; \mathrm{H}_2}{2} = 1.0 \; \text{mole of} \; \mathrm{O}_2 \]

Solve Part (b) - Moles of \( \mathrm{H}_2 \) needed for 5.0 moles of \( \mathrm{O}_2 \)

Using the same stoichiometric relationship: \[ \frac{2 \; \text{moles of} \; \mathrm{H}_2}{1 \; \text{mole of} \; \mathrm{O}_2} = 2 \] Given 5.0 moles of oxygen gas: \[ \mathrm{H}_2 = 2 \times 5.0 \; \text{moles} \; \mathrm{O}_2 = 10.0 \; \text{moles of} \; \mathrm{H}_2 \]

Solve Part (c) - Moles of \( \mathrm{H}_2 \mathrm{O} \) formed from 2.5 moles of \( \mathrm{O}_2 \)

Using the stoichiometric relationship: \[ 1 \; \text{mole of} \; \mathrm{O}_2 \longrightarrow 2 \; \text{moles of} \; \mathrm{H}_2 \mathrm{O} \] Given 2.5 moles of oxygen gas: \[ \mathrm{H}_2 \mathrm{O} = 2 \times 2.5 \; \text{moles} \; \mathrm{O}_2 = 5.0 \; \text{moles of} \; \mathrm{H}_2 \mathrm{O} \]

Key concepts

balanced chemical equation

A balanced chemical equation is vital in understanding chemical reactions. It represents the exact quantities of reactants and products involved. For example, in the hydrogen-oxygen reaction, the balanced equation is:

\[ 2\ \text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(g) \]

This implies that 2 molecules of hydrogen react with 1 molecule of oxygen to produce 2 molecules of water. Each side of the equation has equal numbers of each type of atom, which shows that mass is conserved. When balancing equations, we adjust coefficients, not subscripts, to ensure the same number of each atom on both sides.

mole ratio

The mole ratio comes from the coefficients in a balanced chemical equation. It helps us understand the proportions between different reactants and products. For example, the hydrogen and oxygen reaction has a mole ratio of:

\[ \frac{2\text{moles of} \text{H}_2}{1\text{mole of} \text{O}_2} \]

This ratio means that for every 2 moles of hydrogen, we need 1 mole of oxygen. The mole ratio is essential for stoichiometry calculations, allowing us to convert moles of one substance to moles of another. This is critical for predicting the amounts of products formed or reactants needed.

chemical reaction calculations

Chemical reaction calculations involve using stoichiometry to determine the amounts of reactants or products. Let's solve some typical problems:

Example 1: How many moles of \( \text{O}_2 \) are required to react with \( 2.0 \) moles of \( \text{H}_2 \)?
From our balanced equation and mole ratio, we need: \[ \frac{2.0 \text{moles of} \text{H}_2}{2\ \text{moles of} \text{H}_2/\text{1 mole of} \text{O}_2} = 1.0\ \text{mole of} \text{O}_2 \]

Example 2: How many moles of\ \text{H}_2 \ are needed to react with \ 5.0 moles of \text{O}_2?
Using the mole ratio: \[ 2 \times 5.0\ \text{moles of} \ \text{O}_2 = 10.0 \ \text{moles of} \ \text{H}_2 \]

Example 3: How many moles of \ \text{H}_2 \text{O} \ form when \ 2.5 moles of \ \text{O}_2 \ react?
According to the balanced equation, we get: \[ 2 \times 2.5 \ moles of \ \text{O}_2 = 5.0 \ moles of \ \text{H}_2 \text{O} \]

mole concept

The mole concept is fundamental in chemistry for counting atoms, molecules, or ions. One mole equals \( 6.022 \times 10^{23} \) entities (Avogadro's number). It helps bridge the gap between the atomic scale and the macroscopic scale we can measure.

For example, in the hydrogen-oxygen reaction, knowing the moles of each gas lets us predict how much water forms. The balanced equation shows that 2 moles of \ \text{H}_2 \ react with 1 mole of\ \text{O}_2 \ to create 2 moles of \ \text{H}_2 \text{O}. By converting grams to moles, we can solve real-world problems, such as:

• Determining reactant quantities
• Calculating product amounts
• Balancing equations and conserving mass

The mole concept connects mass to formula units, making stoichiometric calculations possible and practical in various scientific fields.