Question

Consider the following reaction: $$4{\mathrm{NH}}_3(g)+5{\mathrm{O}}_2(g)⟶4\mathrm{NO}(g)+6{\mathrm{H}}_2\mathrm{O}(g)$$ If a container were to have 10 molecules of ${\mathrm{O}}_2$ and 10 molecules of ${\mathrm{NH}}_3$ initially, how many total molecules (reactants plus products) would be present in the container after this reaction goes to completion?

Short answer

After the given reaction reaches completion, there will be 22 total molecules present in the container, consisting of 8 NO molecules, 12 H2O molecules, and 2 leftover NH3 molecules.

Step-by-step solution

Identify the Limiting Reactant

To find the limiting reactant, we need to compare the number of molecules of each reactant with their respective stoichiometric coefficients. Since we have 10 molecules of each to begin with: Ratio for $N{H}_3=\frac{10}{4}$ Ratio for $O_2=\frac{10}{5}$ Comparing the two ratios, the ratio for $N{H}_3$ is higher, meaning we will run out of $O_2$ first. Therefore, $O_2$ is the limiting reactant.

Determine the Number of Molecules of Products Formed

Using stoichiometry, knowing $O_2$ is the limiting reactant, we can find out how many molecules of each product are formed. For NO molecules formed: $5O_2⟶4NO$ $1O_2⟶\frac{4}{5}NO$ $10O_2⟶8NO$ For H2O molecules formed: $5O_2⟶6H_{2}O$ $1O_2⟶\frac{6}{5}{H}_{2}O$ $10O_2⟶12H_{2}O$

Determine the Number of Leftover Reactants

Now, let's find the number of leftover $N{H}_3$ molecules. Initially, there are 10 $N{H}_3$ molecules available. Since we react 10 $O_2$ molecules: $5O_2⟶4N{H}_3$ $1O_2⟶\frac{4}{5}N{H}_3$ $10O_2⟶8N{H}_3$ Number of leftover $N{H}_3$ molecules = 10 - 8 = 2

Calculate the Total Number of Molecules in the Container

To find the total number of molecules present in the container after the reaction goes to completion, sum the leftover reactants and product molecules. Total number of molecules = 8 NO + 12 H2O + 2 NH3 = 8 + 12 + 2 = 22 So there are 22 total molecules present in the container after the reaction goes to completion.

Key concepts

Limiting Reactant

The concept of a limiting reactant is a foundational principle in stoichiometry, a field within chemistry that focuses on the quantitative relationships between the amounts of reactants and products in a chemical reaction.

In every chemical reaction, the reactants combine in a specific ratio to form products. When quantities of the reactants are not in this precise ratio, one reactant will be completely used up before the others. This reactant, which determines how much product can be formed and thus 'limits' the reaction, is known as the limiting reactant. Identifying the limiting reactant is crucial because it allows chemists to calculate theoretical yields, optimize reactions, and reduce waste.

Using a simple analogy, imagine making sandwiches with bread and cheese. If you have 10 slices of bread and 5 slices of cheese, you can only make 5 sandwiches. In this scenario, cheese is the limiting reactant.

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, transform into different substances called products. It involves breaking of bonds in reactants and the formation of new bonds in products. The way reactants combine to form products is depicted by a chemical equation, which shows the reactants on the left side and the products on the right, separated by an arrow indicating the direction of the reaction.

Each reaction is governed by specific stoichiometric coefficients, which are numbers that balance the equation to respect the Law of Conservation of Mass. This law states that in a closed system, mass is conserved; it cannot be created or destroyed. Thus, in a balanced chemical equation, the number of atoms of each element in the reactants must equal the number of atoms of that element in the products.

Molecular Stoichiometry

Molecular stoichiometry refers to the numerical relationship between the amounts of reactants and products at the molecular level in a chemical reaction. It is a key tool in chemistry for calculating precise amounts of substances needed for reactions to proceed efficiently with minimal waste.

Understanding Ratios

Molecular stoichiometry involves understanding the ratios in which molecules react with one another. These ratios are derived from the coefficients found in the balanced chemical equation. For example, the reaction between hydrogen and oxygen to form water has a stoichiometry of 2:1:2 because the balanced chemical equation is $2H_2+O_2\to 2H_{2}O$.

Calculations

Stoichiometric calculations often involve converting mass to moles or calculating the number of molecules involved in a reaction. These calculations allow chemists to predict the amount of product produced and determine the amount of each reactant needed.

Molecular stoichiometry is the basis for theoretical predictions in chemistry, guiding both industrial processes and laboratory experiments. By using stoichiometry, the practical aspects of conducting a chemical reaction, such as yield and purity, can be optimized.