A 20-mL sample of \(0.020 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) was titrated with \(0.035 \mathrm{M} \mathrm{KOH}(\mathrm{aq})\). Calculate the \(\mathrm{pH}\) at the following points in the titration and sketch the \(\mathrm{pH}\) curve: (a) no \(\mathrm{KOH}\) added; (b) \(5.00 \mathrm{~mL}\) of \(\mathrm{KOH}\) (aq) added; (c) an additional \(5.00 \mathrm{~mL}\) of \(\mathrm{KOH}\) (aq) (for a total of \(10.0 \mathrm{~mL}\).) added; (d) another \(5.0 \mathrm{~mL}\) of \(\mathrm{KOH}(\mathrm{aq})\) added; (e) another \(5.00 \mathrm{~mL}\). \(\mathrm{KOH}(\mathrm{aq})\) added. (f) Determine the volume of \(\mathrm{KOH}\) (aq) required to reach the stoichiometric point.

Understanding how to calculate pH is fundamental in acid-base chemistry. pH stands for the 'potential of Hydrogen' or 'power of Hydrogen' and is a measure of the acidity or alkalinity of a solution. It is calculated on a logarithmic scale, where a lower pH value indicates a higher concentration of hydrogen ions (), making the solution more acidic. Conversely, a higher pH value signifies lower concentration and a more alkaline solution.

The formula to calculate pH is given by pH = -log(). For a strong acid like HCl, which dissociates completely in water, the pH can be directly calculated from its concentration. For example, if the concentration of HCl is 0.020 M, then the pH is -log(0.020 M). At each point in the titration with a base such as KOH, the pH can change depending on the amounts of acid and base present.

Stoichiometry is the section of chemistry that involves calculating the quantities of reactants and products in chemical reactions. When performing an acid-base titration, stoichiometry allows us to understand the mole relationship between the acid and the base involved. In a titration, the goal is often to determine the unknown concentration of a substance using a reaction for which the stoichiometry is known.

For the reaction between HCl and KOH, the stoichiometry is 1:1, meaning that one mole of HCl reacts with one mole of KOH. We use this information to help find the equivalence point of a titration, where the number of moles of acid equals the number of moles of base added. To calculate moles, we multiply the volume of the solution by its molarity. Stoichiometry is crucial for determining the amount of reactant remaining at different points during the titration, which in turn allows us to calculate pH.

A neutralization reaction is a type of chemical reaction in which an acid and a base react quantitatively with each other. In a simple acid-base neutralization, the protons from the acid combine with the hydroxide ions from the base to form water. This reaction can be represented by the general equation: Acid + Base → Salt + Water.

During an acid-base titration, the neutralization reaction occurs incrementally as the titrant is added to the analyte. In the case of HCl being titrated with KOH, the neutralization reaction produces KCl (a salt) and H2O. The process continues until all the available H+ ions from the acid have been consumed by OH- ions to form water, marking the end of the neutralization reaction.

A titration curve is a graph that displays the change in pH as a function of the amount of titrant added during a titration. The curve typically starts with the initial pH of the solution being titrated and changes as the titrant is added.

In the titration of a strong acid with a strong base, the curve starts at a low pH due to the acidic solution. As base is added, the pH increases gradually until it reaches the equivalence point, where the amount of acid equals the amount of base added. At this point, the curve shows a steep rise in pH. Beyond the equivalence point, the solution becomes increasingly basic, and the pH rises more slowly. By analyzing the titration curve, one can determine the equivalence point and other significant data regarding the reaction.

In a strong acid and base titration, both the acid and base fully dissociate in water, releasing their respective ions. When titrating a strong acid like HCl with a strong base such as KOH, the titration shows a clear and sharp equivalence point on the titration curve.

Since the stoichiometry is 1:1, the volume of KOH needed to reach the equivalence point can be found by equating the moles of KOH added to the initial moles of HCl. This type of titration allows for precise calculations of concentration and is frequently used in standardizing solutions and determining unknown concentrations. The clear end point, marked by a sharp pH change, is a characteristic feature of titrations involving strong acids and bases, making the analysis relatively straightforward.