Calculate the volume of \(0.150 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) required to neutralize (a) one-half and (b) all the hydroxide ions in \(25.0 \mathrm{~mL}\) of \(0.110 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\). (c) What is the molarity of \(\mathrm{Na}^{+}\)ions at the stoichiometric point? (d) Calculate the \(\mathrm{pH}\) of the solution after the addition of \(20.0 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) to \(25.0 \mathrm{~mL}\) of \(0.110 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq})\).

Stoichiometry is akin to a recipe for chemical reactions. It provides the proportions of reactants and products involved, based on the balanced chemical equation. This balance ensures that matter is conserved, reflecting the fact that atoms are neither created nor destroyed in chemical reactions.

For example, in the neutralization reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH), the stoichiometry is 1:1, meaning one mole of HCl reacts with one mole of NaOH to produce one mole of water (H₂O) and one mole of sodium chloride (NaCl).

This is expressed by the balanced equation: \[\mathrm{HCl(aq)} + \mathrm{NaOH(aq)} \rightarrow \mathrm{NaCl(aq)} + \mathrm{H_2O(l)}\].

Understanding stoichiometry allows us to predict the outcomes of reactions, such as how much of each reactant is needed or how much of a product is produced.

Molarity (M) is a measurement of the concentration of a solution, defined as the number of moles of solute dissolved in one liter of solution. It is a key concept when preparing solutions in chemistry and is fundamental for reactions that occur in solution, like acid-base reactions.

The formula for molarity is: \[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}\].

In our exercise, molarity helps determine the required volume of HCl to neutralize a given amount of NaOH. For instance, to find the volume of a 0.150 M HCl solution required to react with a certain number of moles of NaOH, the formula is rearranged to solve for volume: \[\text{Volume (L)} = \frac{\text{moles of solute}}{\text{Molarity (M)}}\].

Thus, with the stoichiometry and molarity at hand, one can calculate how much of one reactant is needed to completely react with a known quantity of another.

The pH scale is a measure of the acidity or basicity of an aqueous solution. It ranges from 0 to 14, with 7 being neutral, values less than 7 representing acidic solutions, and values greater than 7 representing basic solutions.

The pH is calculated by taking the negative logarithm (base 10) of the hydrogen ion concentration: \[\text{pH} = -\log_{10}[\mathrm{H}^+]\].

In our exercise, after the addition of HCl to the NaOH solution, some NaOH remains unreacted. This leftover NaOH determines the basicity of the solution. The pH can be determined by first calculating the hydroxide ion (OH^-) concentration, converting it to pOH, and then using the relationship that \(\text{pH} + \text{pOH} = 14\) to find the pH.

Acid-base titration is a laboratory method used to determine the concentration of an unknown solution by reacting it with a solution of known concentration, called the titrant. Titrations are based on neutralization reactions, where an acid and a base react to form water and a salt.

The point at which the number of moles of hydrogen ions (H⁺) equals the number of moles of hydroxide ions (OH^-) is known as the equivalence or stoichiometric point. At this stage, the number of moles of acid equals the moles of base originally in solution. In a titration curve, this point is typically indicated by a sharp change in pH.

In the exercise, we effectively conduct a titration to find the volume of HCl needed to react with NaOH. One can also deduce the molarity of sodium ions at the stoichiometric point, which reflects the complete reaction of the initial NaOH.