An HNO \(_{3}\) solution has a pH of \(3.06 .\) What volume of 0.015 \(\mathrm{M}\) LiOH will be required to titrate 65.0 \(\mathrm{mL}\) of the HNO \(_{3}\) solution to reach the equivalence point?

Understanding the pH calculation is essential in acid-base chemistry, especially in titration exercises. pH is a measure of how acidic or basic a solution is, on a scale of 0 to 14, with 7 being neutral, lower values acidic, and higher values basic. To calculate the pH of a solution, you use the formula \( pH = -\text{log}[H_3O^+] \). In practice, if you know the pH, you can find the concentration of hydronium ions \( [H_3O^+] \) by reversing the formula: \( [H_3O^+] = 10^{-pH} \).
In our exercise, the pH of an HNO3 solution was given as 3.06, implying a hydronium concentration of \( 10^{-3.06} \) or 0.000873 M. This calculation is the starting point for the rest of the titration process, offering a bridge between the qualitative nature of pH and quantitative chemical calculations.

Molarity, often represented by the symbol M, is a measurement of the concentration of a solute in a solution. It is defined as the number of moles of solute divided by the volume of the solution in liters. The formula is \( M = \frac{moles}{volume (L)} \).
Measurement of molarity is a critical step in quantitative chemistry, including titration. In our example, we use molarity to determine the amount of HNO3 and find out how much LiOH is needed to neutralize it. For a clear understanding during homework or lab sessions, remember molarity gives you the 'strength' of the solution in terms of solute quantity per liter of solution.

Stoichiometry lies at the heart of chemical reactions, allowing chemists to predict the proportions of reactants and products. It involves applying the laws of conservation of mass and fixed proportions, often using a balanced chemical equation as a guide.
When calculating amounts of substances required in reactions, the stoichiometric coefficients from the balanced chemical equation tell us in what ratio the substances react. In a titration, it helps in determining the volume of titrant (in this case, LiOH) needed. As our exercise presents a 1:1 molar ratio between HNO3 and LiOH, stoichiometry becomes straightforward. One mole of acid reacts with one mole of base, a concept crucial for accurately finding the equivalence point in titration.

The equivalence point of a titration is the point at which the added titrant has completely reacted with the analyte, meaning the moles of acid equal the moles of base. It is a central concept in titration because it signifies the completion of the reaction.
For a strong acid-strong base titration, the equivalence point typically occurs at pH 7, but this varies with the acid and base's strengths involved. In our example, calculating the volume of LiOH needed to reach the equivalence point required knowing the number of moles of HNO3 and the molarity of the LiOH solution. Carefully determining the equivalence point is essential for successful titration, whether it's for an academic exercise or in practical applications like medicine or environmental science.