Calculate the \(\mathrm{pH}\) at each stage in the titration for the addition of \(0.150 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) to \(25.0 \mathrm{~mL}\) of \(0.110 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) : (a) initially; (b) after the addition of \(5.0 \mathrm{~mL}\) of acid; (c) after the addition of a further \(5.0 \mathrm{~mL}\); (d) at the stoichiometric point; (e) after the addition of \(5.0 \mathrm{~mL}\) of acid beyond the stoichiometric point; (f) after the addition of \(10.0 \mathrm{~mL}\) of acid beyond the stoichiometric point.

Understanding an acid-base titration is essential for comprehending the process of carefully adding one solution to another to form a neutral solution. During this process, an acid reacts with a base, typically involving an indicator that changes color at the endpoint, which is close to the stoichiometric point. In our example, we add hydrochloric acid (HCl) to sodium hydroxide (NaOH), which are both strong electrolytes.

Initially, we only have the strong base NaOH in water. As HCl is gradually added, it reacts with NaOH to produce water and sodium chloride (NaCl). The pH changes throughout this process and is measured at various stages: before any acid is added, after certain volumes of acid are introduced, at the stoichiometric point, and after adding an excess of acid. By carefully calculating the resulting pH at each step, we can monitor the titration progress.

The stoichiometric point, often referred to as the equivalence point, is a pivotal moment in a titration where the amount of added titrant exactly matches the quantity of the substance present in the solution. In the case of our titration, it is when the amount of HCl equals the amount of NaOH initially in the solution. At this juncture, all the OH⁻ ions from the NaOH have been neutralized by the H⁺ ions from the HCl, resulting in a neutral solution — assuming it's a strong acid with a strong base. Theoretically, the pH at the stoichiometric point should be 7, indicating a neutral solution; however, the actual pH can vary depending on the strengths of the acid and base involved.

When calculating pH changes in our exercise, the stoichiometric point is crucial because it determines the point of full neutralization before which the pH is calculated based on the concentration of OH⁻, and after which the pH depends on the concentration of excess H⁺.

The relationship between pOH and pH is straightforward yet crucial for understanding acid-base chemistry. The pH scale is used to determine how acidic or basic a solution is, while pOH provides the same information from the base's perspective. Mathematically, they are related through the equation pH + pOH = 14, which is accurate for aqueous solutions at 25°C.

When calculating pH, if you're given the concentration of hydroxide ions (OH⁻), you would first find pOH by taking the negative logarithm of the hydroxide ion concentration. Then, by subtracting the calculated pOH from 14, you get the pH. In our titration example, we calculate pH from pOH when dealing with a strong base. Conversely, if you're given the hydronium ion concentration (H⁺), you would calculate the pH directly and potentially derive the pOH if needed.

A neutralization reaction occurs when an acid and a base react to form water and a salt, and typically results in a change in the pH of the solution. In a typical acid-base titration, like the titration of HCl with NaOH, neutralization is the key chemical process taking place. This reaction is represented by the equation H⁺(aq) + OH⁻(aq) → H₂O(l).

Before reaching the stoichiometric point in our exercise, the neutralization reaction dictates the pH by the remaining hydroxide or hydronium ions. At the stoichiometric point, ideally, we achieve complete neutralization, which generally leads to a neutral pH of 7 for strong acids and bases. After this point, any additional titrant will no longer be neutralized, resulting in an acidic or basic solution depending on which component is in excess.

The behavior of strong acids and bases in water is an essential aspect of their characterization. Strong acids, such as HCl, dissociate completely in water, releasing all their hydrogen ions (H⁺) into the solution. Similarly, strong bases like NaOH dissociate fully to release hydroxide ions (OH⁻). This complete dissociation is crucial for accurate pH calculations during titrations since it ensures that the concentration of the respective ions in the solution reflects the initial concentration of the strong acid or base.

Our titration problem involves a strong acid and a strong base, allowing us to assume complete dissociation and straightforward stoichiometry to predict the outcomes at each step. Remember, the strong acid/base behavior leads to predictable pH changes during the titration: initially, the pH is high due to the strong base; as the strong acid is added, the pH decreases until the stoichiometric point is reached; and if the acid is in excess, the pH can become quite low, reflecting the strong acid's complete dissociation.