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 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. a. \(1 \mathrm{~mol} \mathrm{NO}, 0 \mathrm{~mol} \mathrm{H}_{2}, 4 \mathrm{~mol} \mathrm{NH}_{3}, 4 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) b. \(0 \mathrm{~mol} \mathrm{NO}, 1 \mathrm{~mol} \mathrm{H}_{2}, 5 \mathrm{~mol} \mathrm{NH}_{3}, 5 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) c. \(3 \mathrm{~mol} \mathrm{NO}, 5 \mathrm{~mol} \mathrm{H}_{2}, 2 \mathrm{~mol} \mathrm{NH}_{3}, 2 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) d. \(0 \mathrm{~mol} \mathrm{NO}, 0 \mathrm{~mol} \mathrm{H}_{2}, 4 \mathrm{~mol} \mathrm{NH}_{3}, 4 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\)

Understanding the concept of the limiting reactant is crucial for predicting the amounts of products formed in a chemical reaction. In any reaction, the limiting reactant is the substance that is completely consumed first, and as a result, it determines when the reaction stops. To identify the limiting reactant, we compare the mole amounts of each reactant to the mole ratios required by the balanced chemical equation.

For instance, in the exercise provided, we see that 2 moles of NO react with 5 moles of H2, according to the balanced equation. When we start with 5 moles of NO and 10 moles of H2, we must determine which reactant will run out first. By comparing the initial moles to the required mole ratio, we see that NO is the limiting reactant because its available amount is less than what is needed to fully react with the available H2. This concept is key to predicting the composition of the reaction mixture after the reaction has occurred to the greatest extent possible.

The mole ratio is a fixed proportion of reactants and products represented in a balanced chemical equation. It serves as a conversion factor that enables us to predict how moles of one substance relate to moles of another during the reaction. In chemical stoichiometry, using the mole ratio allows us to calculate how much product will form from a given quantity of reactants or how much of one reactant is needed to react with a certain amount of another reactant.

In our example, the balanced equation indicates a mole ratio of NO to H2 of 2:5. This means that for every 2 moles of NO that react, 5 moles of H2 are required. We can use these ratios to calculate the expected outcomes of the reaction when given the starting quantities of reactants. So, by knowing the initial moles and the mole ratio, we can easily determine which reactant is the limiting one, and hence, calculate the amount of products formed.

Chemical equilibrium is a state in a chemical reaction where the rates of the forward and reverse reactions are equal, leading to no net change in the concentrations of reactants and products over time. While not directly referenced in the exercise, understanding equilibrium is important for explaining why a reaction mixture may still contain both reactants and products even when the reaction has gone to completion.

In a scenario where chemical equilibrium is achieved, changing the amounts of reactants or products, or altering conditions such as temperature or pressure, can shift the equilibrium position, thus changing the concentrations of reactants and products according to Le Chatelier's Principle. However, the problem provided illustrates a situation where the reaction proceeds until one of the reactants is totally used up - a condition that is typically separate from the concept of equilibrium. Nevertheless, being familiar with equilibrium can enrich a student's comprehension of chemical reactions and their dynamics.