What is the volume in milliliters of \(0.0150 \mathrm{M}\) \(\mathrm{NaOH}\) solution required to neutralize \(50.0 \mathrm{~mL}\) of \(0.0100 \mathrm{MHNO}_{3}(a q) ?\)

Imagine you have a glass of lemon juice, which is quite tart due to its acidic nature. To reduce that tartness (neutralize the acid), you might add a pinch of baking soda, which is a base. Neutralization reactions work on a similar principle but in a more controlled and measurable way. In chemistry, a neutralization reaction is where an acid and a base react to form water and a salt.

Take the classic reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH) for instance. The equation for their neutralization is: \[\text{HCl (aq) + NaOH (aq)} \rightarrow \text{NaCl (aq) + H}_2\text{O (l)}\]. Here, the hydrogen ion (H+) from the acid and the hydroxide ion (OH-) from the base combine to form water, while the sodium (Na+) and chloride (Cl-) ions pair up to form sodium chloride, a salt.

In the context of the exercise, the neutralization between sodium hydroxide (NaOH) and nitric acid (HNO3) can be expressed as \[\text{NaOH (aq) + HNO}_{3}\text{(aq)} \rightarrow \text{NaNO}_{3}\text{(aq) + H}_2\text{O (l)}\]. This reaction lays the foundation for understanding how we can calculate the precise amount of one reactant needed to completely react with a given amount of another reactant.

Stoichiometry is like the recipe for a chemical reaction. Just as a recipe dictates the precise amount of each ingredient needed to make a dish, stoichiometry gives us the proportions of reactants and products involved in a chemical reaction based on balanced chemical equations. The coefficients in a balanced equation tell us the ratio of moles of reactants and products.

For instance, in the balanced reaction \[\text{NaOH (aq) + HNO}_{3}\text{(aq)} \rightarrow \text{NaNO}_{3}\text{(aq) + H}_2\text{O (l)}\], we see a 1:1 ratio between NaOH and HNO3. This means one mole of NaOH will neutralize one mole of HNO3, which is crucial for calculations.

The exercise presents a situation to apply stoichiometry. We use the given volume and molarity (moles per liter) of nitric acid to find the moles needed for neutralization. Using the stoichiometric 1:1 ratio between HNO3 and NaOH, we can determine the required moles—and hence volume—of NaOH solution to complete the reaction. This precise calculation is fundamental in not just academic exercises, but in real-world applications such as pharmaceuticals, where dosages must be exact.

Molarity is a measure of concentration, specifically, it tells us how many moles of a solute are present in one liter of solution. The molarity (M) is crucial in chemistry for preparing solutions with precise concentrations and for performing calculations involving chemical reactions.

The formula for molarity is simple: \[\text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}}\]. To find out how much of a chemical is in a solution, simply multiply the volume of the solution by the molarity. Conversely, to find the volume of solution required for a certain number of moles, divide the moles by molarity.

In the given exercise, we were asked to determine the volume of a sodium hydroxide (NaOH) solution to neutralize a certain amount of nitric acid (HNO3). The initial step is to use the molarity and volume of HNO3 to calculate the moles present. Then, with our understanding of neutralization and stoichiometry, and knowing the molarity of the NaOH solution, we applied the molarity formula in reverse to find the needed volume of NaOH solution. Molarity, thus, is a versatile and fundamental concept in the realm of acid-base chemistry and titration analyses.