Use the equation provided to answer the questions that follow. $$2 \mathrm{NO}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{2}$$ \begin{equation}\begin{array}{l}{\text { a. How many molecules of } \mathrm{NO}_{2} \text { can form }} \\ {\text { from } 1.11 \mathrm{mol} \mathrm{O}_{2} \text { and excess } \mathrm{NO} \text { ? }} \\ {\text { b. How many molecules of NO will react }} \\ {\text { with } 25.7 \mathrm{g} \mathrm{O}_{2} ?} \\ {\text { c. How many molecules of } \mathrm{O}_{2} \text { are needed to }} \\ {\text { make } 3.76 \times 10^{22} \text { molecules } \mathrm{NO}_{2} ?}\end{array}\end{equation}

Balancing a chemical equation is a foundational skill in chemistry that ensures the law of conservation of mass is obeyed in a chemical reaction. Essentially, it requires that the number of atoms for each element is the same on both the reactant and product sides of the equation.

For instance, in the reaction provided, the balanced equation is:
\[2 \mathrm{NO} + \mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{2}\]
This indicates that 2 molecules of nitrogen monoxide (NO) react with 1 molecule of oxygen (O2) to form 2 molecules of nitrogen dioxide (NO2). The coefficients—2 for NO and NO2, and 1 for O2—reflect the stoichiometric ratios and are crucial for solving quantitative problems in stoichiometry. Balancing equations gives us the roadmap for predicting the quantities of reactants needed and products formed.

The mole concept is a central theme in chemical stoichiometry, providing a link between the microscopic world of atoms and molecules and the macroscopic world we can measure. One mole represents \(6.022 \times 10^{23}\) entities, known as Avogadro's number. It's essentially the chemist's dozen, and just as a dozen eggs means 12 eggs, a mole of any substance means \(6.022 \times 10^{23}\) of its elementary entities.

The exercise solutions use this concept to convert between masses, moles, and the number of molecules. For example, to find out how many NO molecules react with a given mass of O2, we start by converting the mass of O2 to moles, and then use the mole ratio from the balanced chemical equation to find the corresponding number of moles—and thus molecules—of NO.

Avogadro's number, \(6.022 \times 10^{23}\), is a cornerstone of chemistry as it allows us to count particles by weighing them. This large number is the bridge between the atom and the practical units of grams and moles, defining how many atoms or molecules are in one mole of a substance.

When solving the provided exercises, we apply Avogadro's number to translate the moles calculated into the tangible number of molecules involved in the reactions. For example, once we've determined the moles of NO2 that can form from 1.11 moles of O2, we multiply by Avogadro's number to find the actual number of NO2 molecules produced, yielding a clear and quantifiable sense of the scale of the reaction.