Question

If \(5.00 \mathrm{~mol}\) of hydrogen gas and \(5.00 \mathrm{~mol}\) of oxygen gas react, what is the limiting reactant and how many moles of water are produced from the reaction? $$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)$$

Short answer

Oxygen is the limiting reactant, producing 10.00 moles of water.

Step-by-step solution

Understand the chemical equation

The given chemical equation is \(2 \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)\). This means that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water.

Identify the mole ratio between reactants

According to the balanced equation, 2 moles of hydrogen (H₂) are needed for every 1 mole of oxygen (O₂). Thus, the ratio of hydrogen to oxygen should be 2:1.

Calculate the required moles of oxygen

Since we have 5.00 moles of hydrogen, determine how many moles of oxygen are needed: \( \frac{5.00 \text{ moles H}_2}{2} = 2.50 \text{ moles O}_2 \).

Determine the limiting reactant

We have 5.00 moles of oxygen available, but only 2.50 moles are needed according to the ratio from Step 3. Therefore, hydrogen is in excess, and oxygen is the limiting reactant.

Calculate moles of water produced

Using the initial amount of the limiting reactant (oxygen), calculate the moles of water produced. Since 1 mole of O₂ produces 2 moles of H₂O, if 5.00 moles of O₂ react, they will produce \(5.00 \text{ mol O}_2 \times 2 = 10.00 \text{ moles H}_2\text{O}\).

Key concepts

Chemical Equations

A chemical equation represents the substances involved in a chemical reaction. It shows the reactants (substances that start the reaction) and the products (substances produced by the reaction). In the given equation, \(2 \text{H}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{H}_{2}\text{O}(l)\), the reactants are hydrogen gas (\(\text{H}_2\)) and oxygen gas (\(\text{O}_2\)), while the product is water (\(\text{H}_2\text{O}\)).
Understanding chemical equations involves knowing how each substance is represented with chemical symbols and numbers, showing the number of molecules or moles. The equation must be balanced, meaning the number of atoms of each element must be the same on both sides.
This principle is based on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. It merely changes forms.

Mole Ratios

Mole ratios are derived from the coefficients of the substances in a balanced chemical equation. They indicate the proportions in which the reactants combine and the products form.
In the water formation reaction, \(2 \text{H}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{H}_{2}\text{O}(l)\), the mole ratio reflects that 2 moles of \(\text{H}_2\) react with 1 mole of \(\text{O}_2\) to form 2 moles of \(\text{H}_2\text{O}\).
Here's how we use mole ratios:

• The ratio helps determine how much of one reactant is needed to react with a certain amount of another reactant.
• Mole ratios can be used to find out how much product can be formed from given amounts of reactants.

For example, understanding that 2 moles of \(\text{H}_2\) are required for every 1 mole of \(\text{O}_2\) helps identify the limiting reactant.

Stoichiometry

Stoichiometry involves making quantitative predictions about chemical reactions using mole ratios and balanced equations. It is a calculation process that determines the amount of reactants needed and products formed in a reaction.
To solve a stoichiometry problem, one must:

• Ensure the chemical equation is balanced.
• Convert all given information (like mass or volume) into moles.
• Use mole ratios from the balanced equation to relate different substances.
• Calculate the desired quantity, often using the limiting reactant.

Using stoichiometry, we calculate that if all available oxygen reacts, 10 moles of water can be produced in the given exercise.
This is done by using the ratio of 1:2 from the balanced equation (1 mole of \(\text{O}_2\) produces 2 moles of \(\text{H}_2\text{O}\)).

Reaction Yield

Reaction yield refers to the actual amount of product obtained from a chemical reaction. It's an essential concept in chemistry to assess the effectiveness of a reaction.
The theoretical yield is the maximum amount of product that could be formed from the reactants as calculated from the stoichiometry of the balanced equation. However, in practice, the actual yield, which is the amount actually produced, is often less due to various factors like experimental conditions or side reactions.
Percent yield is a comparison between the actual yield and the theoretical yield, often expressed as:
\[ \text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100 \% \]
In this exercise, if everything proceeds perfectly with no losses, we expect to generate 10 moles of water as the theoretical yield. However, any practical experiment might result in less than this amount.