Question

Consider the reaction: $$2 \mathrm{NO}(g)+5 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$ A reaction mixture initially contains 5 moles of \(\mathrm{NO}\) and 10 moles of \(\mathrm{H}_{2} .\) Without doing any calculations, determine which set of amounts best represents the mixture after the reactants have reacted as completely as possible. Explain your reasoning. \(\begin{equation}\begin{array}{l}{\text { a. } 1 \mathrm{mol} \mathrm{NO}, 0 \mathrm{mol} \mathrm{H}_{2}, 4 \mathrm{mol} \mathrm{NH}_{3}, 4 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}} \\ {\text { b. } 0 \mathrm{mol} \mathrm{NO}, 1 \mathrm{mol} \mathrm{H}_{2}, 5 \mathrm{mol} \mathrm{NH}_{3}, 5 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}}\end{array} \end{equation} \begin{equation}\begin{array}{l}{\text { c. } 3 \text { mol } \mathrm{NO}, 5 \mathrm{mol} \mathrm{H}_{2}, 2 \mathrm{mol} \mathrm{NH}_{3}, 2 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}} \\ {\text { d. } 0 \text { mol } \mathrm{NO}, 0 \mathrm{mol} \mathrm{H}_{2}, 4 \mathrm{mol} \mathrm{NH}_{3}, 4 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}}\end{array} \end{equation}\)

Short answer

Option b: 0 mol NO, 1 mol H2, 5 mol NH3, 5 mol H2O are the correct amounts after the reaction.

Step-by-step solution

Analyze the Initial Amounts of Reactants

Determine the initial number of moles of each reactant. In this case, there are initially 5 moles of NO and 10 moles of H2.

Understand the Stoichiometry of the Reaction

The balanced chemical equation shows that 2 moles of NO react with 5 moles of H2 to produce 2 moles of NH3 and 2 moles of H2O.

Identify the Limiting Reactant

Compare the mole ratios of the reactants to those required by the stoichiometry. Since 2 moles of NO react with 5 moles of H2, and we have a greater amount of H2 initially (10 moles as compared to 5 moles of NO), NO is the limiting reactant.

Calculate the Amounts of Products Formed

As NO is the limiting reactant, all 5 moles will be used up. For each mole of NO, 1 mole of NH3 and 1 mole of H2O are produced, so 5 x 1 = 5 moles of NH3 and H2O are formed.

Calculate the Remaining Amount of Excess Reactant

With every 2 moles of NO that react, 5 moles of H2 are consumed. So 5/2 moles of H2 are used for each mole of NO. For 5 moles of NO, 5/2 x 5 = 12.5 moles of H2 would be needed. Since we only started with 10 moles, all the H2 will be consumed.

Determine the Final Mixture

The reactants have reacted as completely as possible, leaving 0 moles of NO and 0 moles of H2. We are left with 5 moles of NH3 and 5 moles of H2O.

Key concepts

Limiting Reactant

In chemistry, stoichiometry deals with the quantitative relationships between the amounts of reactants and products in a chemical reaction. An essential part of stoichiometry is understanding the concept of the limiting reactant (or limiting reagent). This is the substance that dictates the extent of the reaction; it's completely consumed first, hence preventing further reaction and determining the amount of product formed.

Visualize a simple analogy: if you're making sandwiches with one slice of cheese per two slices of bread, running out of cheese will stop your sandwich production, no matter how much bread remains. That's exactly how a limiting reactant works in a chemical equation.

Identifying the limiting reactant requires comparing the mole ratios of the reactants in the initial mixture to the mole ratios dictated by the balanced chemical equation. In case of the given exercise, the ratio is 2 moles of NO to 5 moles of H2. With 5 moles of NO and 10 moles of H2 available, NO will limit the reaction since it will be consumed before H2, just like cheese in the sandwich analogy. Therefore, option b, with 0 moles of NO and 1 mole of H2 remaining, represents the best set of amounts after the reaction.

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, transform into different substances called products. Reactions are governed by laws of conservation, including the conservation of mass and conservation of charge. These laws state that in a closed system, mass and charge cannot be created or destroyed, only converted from one form to another.

Chemical reactions are represented by balanced equations, which reflect the conservation laws and help us understand the stoichiometry of the reaction. Such equations show how many moles of each reactant and product participate in the reaction. For instance, the equation from our exercise, \[2 \text{NO}(g) + 5 \text{H}_2(g) \rightarrow 2 \text{NH}_3(g) + 2 \text{H}_2\text{O}(g)\]indicates that 2 moles of nitric oxide (NO) react with 5 moles of hydrogen gas (H2) to produce 2 moles of ammonia (NH3) and 2 moles of water vapor (H2O). Such balanced equations are fundamental tools for determining the limiting reactant and predicting the quantities of products formed.

Mole Concept

The mole concept is a cornerstone of stoichiometry in chemistry. The mole provides a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure. A mole is defined as the quantity of a substance that contains the same number of particles as there are atoms in 12 grams of carbon-12. This number is known as Avogadro's number, which is approximately \(6.022 \times 10^{23}\)particles per mole.

One can think of a mole similarly to a dozen in that it is a count of units. Just as a dozen signifies 12 of any items, a mole signifies \(6.022 \times 10^{23}\)of any chemical entities. This concept allows chemists to count atoms, ions, or molecules by weighing, thus linking the mass of a substance to the number of particles it contains. The mole concept is crucial for calculating how much reactants are required or products formed in a chemical reaction, which ultimately leads to understanding the composition of the reaction mixture at any stage, as showcased in our exercise problem.