Consider the reaction for the synthesis of nitric acid: $$ 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g) $$ (a) If \(12.8 \mathrm{~L}\) of \(\mathrm{NO}_{2}(g)\), measured at \(\mathrm{STP}\), is allowed to react with \(14.9 \mathrm{~g}\) of water, find the limiting reagent and the theoretical yield of \(\mathrm{HNO}_{3}\) in grams. (b) If \(14.8 \mathrm{~g}\) of \(\mathrm{HNO}_{3}\) forms, what is the percent yield?

Understanding the limiting reagent concept is pivotal in any stoichiometric calculation. This concept refers to the reactant that will be consumed first during a chemical reaction, thus preventing more of the product from forming. Think of it as ingredients in a recipe - if you run out of one ingredient, you can't make more of the final dish, no matter how much of the other ingredients you have left.

To determine the limiting reagent, we compare the amount of reactants using the mole ratio set by the balanced chemical equation. In the problem given, the equation requires a 3:1 ratio of NO₂ to H₂O. By calculating the moles of each reactant and comparing them to this ratio, one can identify which reactant is the limiting reagent. Remember, the limiting reagent determines the theoretical yield of the product.

The theoretical yield is the maximum amount of product that can be produced in a chemical reaction based on the amount of the limiting reagent. It is a crucial part of any stoichiometric calculation, representing the ideal scenario, under perfect conditions, where every single reactant particle reacts.

To calculate the theoretical yield, start with the moles of the limiting reagent. Then, use the mole ratio from the balanced chemical equation to find out how many moles of product can theoretically be formed. Finally, convert these moles to grams using the molar mass of the product. In the given exercise, you would use the molar mass of HNO₃ to convert from moles to grams.

The percent yield shows how efficient a chemical reaction is by comparing the actual yield (the amount of product actually obtained) to the theoretical yield. It's given by the formula:
\[ \text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100 \% \].

This measure is important for evaluating the practicality of a chemical process in real-world applications. Percent yield can be affected by factors such as incomplete reactions, side reactions, and loss of product during recovery. In our example, the percent yield calculation helps to assess the efficiency of the reaction in converting NO₂ and H₂O into HNO₃.

Chemical reactions involve the transformation of reactants into products. They are governed by the laws of conservation of mass and energy, which state that matter and energy cannot be created or destroyed, only transformed. Reactions are described using balanced chemical equations, which show the corresponding quantities of reactants and products, maintaining the balance of atoms on both sides.

For example, the given synthesis of nitric acid is expressed with a balanced chemical equation that shows the stoichiometric conversion of gaseous nitrogen dioxide and liquid water into aqueous nitric acid and gaseous nitrogen monoxide. Understanding chemical reactions is foundational to mastering stoichiometry, as they provide the framework for which mole ratios are used to quantify reactants and products.

The mole concept is a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure and observe. One mole of any substance contains \(6.022 \times 10^{23}\) entities (Avogadro's number) of that substance. This allows chemists to count atoms and molecules by weighing them. The molar mass, which is the mass of one mole of a substance, is used to convert between grams and moles.

In the context of the provided exercise, moles are used to quantify the amounts of NO₂ and H₂O based on the volumes and weights provided. With the moles of each reactant calculated, we can proceed with stoichiometry to predict the behavior of the chemical reaction, including the identification of the limiting reagent, calculation of theoretical yield, and determination of percent yield.