Question

The molecular-level diagram shows a mixture of reactant molecules (three \(\mathrm{O}_{2}\) molecules and eight \(\mathrm{H}_{2}\) molecules) for the following reaction: $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) $$ (a) Draw what the mixture should look like when the reaction is complete. (b) What is the limiting reactant? (c) Which reactant is left over?

Short answer

When the reaction is complete, the mixture will contain 6 water molecules and 2 unreacted hydrogen molecules. The limiting reactant is oxygen, while the reactant left over is hydrogen.

Step-by-step solution

Analyzing the Reaction

Looking at the reaction equation, it can be seen that 2 molecules of hydrogen (\( \mathrm{H}_{2} \)) react with 1 molecule of oxygen (\( \mathrm{O}_{2} \)) to form 2 molecules of water (\( \mathrm{H}_{2}\mathrm{O} \)). The stoichiometric ratios we can derive from this are: 2:1:2 for \( \mathrm{H}_{2} : \mathrm{O}_{2} : \mathrm{H}_{2}\mathrm{O} \) respectively.

Identifying the Limiting Reactant

Comparing the initial number of molecules with the stoichiometric ratios, we have 4 times the required amount of hydrogen (\( \mathrm{H}_{2} \)) molecules (8 as against 2), and the required amount of oxygen (\( \mathrm{O}_{2} \)) molecules (3 as against 1). Since the reaction consumes hydrogen and oxygen in a ratio of 2:1, the amount of hydrogen is ample, but the amount of oxygen will only permit 3 of the reactions to occur. As such, oxygen (\( \mathrm{O}_{2} \)) is the limiting reactant.

Identifying the system state after the reaction

Based on the 2:1:2 ratio and knowing that oxygen is the limiting reactant, when 3 molecules of oxygen complete the reaction, 6 molecules of hydrogen will be consumed and 6 molecules of water will be produced. Given we initially had 8 molecules of hydrogen, there will remain 2 molecules unreacted. Thus, hydrogen (\( \mathrm{H}_{2} \)) is the reactant left over.

Drawing the final state

When complete, the mixture will contain 6 water (\( \mathrm{H}_{2}\mathrm{O} \)) molecules (product), 2 hydrogen (\( \mathrm{H}_{2} \)) molecules (excess reactant), and no oxygen (\( \mathrm{O}_{2} \)) molecules (limiting reactant).

Key concepts

Limiting Reactant

Understanding the concept of a limiting reactant is crucial for mastering chemical reactions. When chemicals react, they do so in a defined proportion known as stoichiometry. However, in the real world, reactants are not always present in these perfect proportions, and so one reactant will be used up first, thus limiting the extent of the reaction.

This 'limiting reactant' determines the maximum amount of product that can be formed from the reactants; once it is consumed, the reaction stops, even if the other reactant is still available. For example, when you make a sandwich, if you have only three slices of bread but plenty of cheese, the bread would be your limiting reactant - you can only make one and a half sandwiches, no matter how much cheese you have.

In the exercise given, the molecular-level diagram hints at this concept by showing a mixture of reactants wherein the oxygen molecules are fewer in ratio compared to the hydrogen molecules. By identifying the limiting reactant, students can predict the quantity of product yielded and determine the amount of excess reactants left. This fundamental stoichiometric insight reveals that every molecule matters in chemical reaction patterns.

Stoichiometric Ratios

Stoichiometric ratios are the heart of chemical equations, revealing how reactants combine and how products form. These ratios, derived directly from the balanced chemical equation, tell us in precise terms the proportion of reactants that react together to produce the desired products.

For instance, in the reaction between hydrogen and oxygen to make water (\(2 \text{H}_2 + 1 \text{O}_2 \rightarrow 2 \text{H}_2\text{O}\)), the stoichiometric ratio of hydrogen to oxygen to water is 2:1:2. This means that two molecules of hydrogen react with one molecule of oxygen to produce two molecules of water.

Importance of Stoichiometric Ratios

These ratios are invaluable for scientists as they provide the basis for calculations in various chemical processes, from industrial synthesis to biochemical reactions. Knowing the stoichiometric ratios allows the users to calculate how much reactant is needed to produce a certain amount of product, or how much product to expect from given quantities of reactants. This makes stoichiometric calculations an essential part of chemical literacy.

Chemical Reaction Completion

Chemical reaction completion is a key consideration in both academic problems and real-world applications because it helps us understand when a reaction has gone to its full extent. A reaction is considered complete when the limiting reactant is completely consumed, leaving no further possibility for the formation of additional product.

Upon completion of a reaction, there may still be excess reactants present, just like our exercise where hydrogen molecules are left over after all the oxygen is used up. Recognizing the completion state is not only about seeing no more reactants disappear, but also about the ability to predict and calculate the amounts of products and remaining reactants accurately.

Chemists use the concept of reaction completion to optimize reactions, minimize waste, and ensure the desired products are obtained efficiently. In industrial processes, incomplete reactions can lead to costs and environmental concerns, while in a laboratory setting, they can affect the accuracy of experiments. Teaching students about reaction completion empowers them with the knowledge to approach chemical reactions with an understanding of the underlying principles that dictate when and how reactions occur.