(a) Sketch the titration curve for the titration of \(5.00 \mathrm{~mL}\) \(0.010 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) with \(0.005 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\), indicating the \(\mathrm{pH}\) of the initial and final solutions and the \(\mathrm{pH}\) at the stoichiometric point. What volume of \(\mathrm{HCl}\) has been added at (b) the stoichiometric point; (c) the halfway point of the titration?

Acid-base titration is a process used to determine the concentration of an unknown acid or base solution by adding a solution of known concentration until the reaction reaches neutralization. This is often visualized on a titration curve, a graph showing how the pH of the solution changes as the titrant is added.

Different points on the titration curve provide valuable information. The initial pH indicates the strength of the acid or base being titrated. As the titrant is added, the pH changes gradually until it reaches a point where the number of moles of acid equals the number of moles of base. This is known as the equivalence or stoichiometric point, and on the curve, it's often where the pH undergoes a sharp change. Finally, the pH will stabilize again as the addition of more titrant only slightly alters the pH of the excess strong acid or base in the solution.

Stoichiometry is the section of chemistry that involves using balanced chemical equations to calculate the quantities of reactants and products involved in chemical reactions. In the context of titration, stoichiometry allows us to predict the volume of titrant needed to reach the stoichiometric point, where the number of moles of acid equals the number of moles of base, indicating complete neutralization.

For instance, in a titration involving a strong base and a strong acid with a 1:1 mole ratio, stoichiometry indicates that equal amounts of acid and base (in moles) are needed to reach neutralization. By using the molarity (moles per liter) and the initial volume of the unknown solution, you can calculate how many moles you have and, hence, how much of the titrant you'll need to add to reach the equivalence point.

A neutralization reaction occurs when an acid and a base react together to form water and a salt. In the context of a strong acid and a strong base, the neutralization reaction is complete, meaning all the acid and base react fully to products. The general equation for such a reaction is: \[\text{Acid} + \text{Base} \rightarrow \text{Water} + \text{Salt}\]

In our example, the reaction is \(\mathrm{NaOH} + \mathrm{HCl} \rightarrow \mathrm{NaCl} + \mathrm{H_2O}\). Since NaOH and HCl are strong electrolytes, they dissociate completely in aqueous solutions, and the titration curve will show a sharp change in pH at the stoichiometric point.

Calculating the pH is crucial for plotting a titration curve and understanding the neutralization process. The pH scale measures how acidic or basic a solution is, ranging from 0 to 14. A pH of 7 is considered neutral, below 7 acidic, and above 7 basic. The initial pH of a solution can be found by determining the concentration of hydrogen ions (\(H^+\)) for an acid, or hydroxide ions (\(OH^-\)) for a base.

In a titration with a strong base like NaOH, its complete dissociation means the initial concentration of \(OH^-\) is the same as the concentration of NaOH. You calculate the pOH first, which is the negative logarithm of the \(OH^-\) ion concentration, and then use the relationship between pH and pOH (\(pH + pOH = 14\)) to find the pH. At the stoichiometric point, with complete neutralization, the pH is 7 in the titration of a strong acid with a strong base.