A 0.968-g sample of impure sodium hydroxide was dissolved in \(200 \mathrm{ml}\). of aqueous solution. A \(20.0-\mathrm{mL}\). portion of this solution was titrated to the stoichiometric point with \(15.8 \mathrm{~mL}\) of \(0.107 \mathrm{M} \mathrm{HCl}\) (aq). What is the percentage purity of the original sample?

When it comes to understanding the purity of a sample in chemistry, titration becomes an indispensable technique. This analytical method involves the gradual addition of a known concentration solution, termed the titrant, to a solution with an unknown concentration. The goal is to reach the stoichiometric point, where the amount of titrant added is just enough to completely react with the analyte (substance being analyzed) in the solution.

The point at which this occurs is often indicated by a color change with the help of an indicator or by reaching a particular pH level. In the problem, the analysis of sodium hydroxide (NaOH) purity via titration is conducted using hydrochloric acid (HCl) as the titrant. This procedure allows the precise determination of the amount of NaOH in the impure sample, crucial for calculating the sample's percentage purity.

Stoichiometry lies at the heart of chemical reactions, essentially acting as the recipe that dictates the proportions of reactants and products. Understanding stoichiometry is crucial for quantitatively analyzing chemical reactions, like the one in our example involving NaOH and HCl.

The reaction between NaOH and HCl is a simple one-to-one relationship, meaning one mole of NaOH reacts with one mole of HCl. Utilizing this stoichiometric ratio, we can directly relate the moles of HCl used in the titration to the moles of NaOH present in the solution. This relationship becomes the foundation for subsequent calculations in determining the purity of the NaOH sample.

The molar mass is a pivotal factor in converting moles, a unit of measurement for quantity in chemistry, to grams which is a practical unit of mass. It represents the weight of one mole of a substance and is expressed in grams per mole (g/mol).

The pure substance molar mass calculation is critical when converting the measured moles of a substance, derived from stoichiometric relationships, into a physical mass that can be compared against the impure sample's mass. In our example, the molar mass of NaOH (approximately 40.00 g/mol) is used to find the actual mass of NaOH that reacted, which is key to determining the percentage purity of the compound.

Chemical principles govern the behavior of substances and their interactions. These principles include the laws of conservation of mass and energy, the understanding of chemical equilibrium, and the concept of mole ratios in reactions.

These foundational concepts are implicitly applied when solving for the purity of a compound. For instance, the conservation of mass is assumed when we equate the moles of HCl used to the moles of NaOH that reacted—the substances change form but are not lost or gained. The equilibrium assumption underlies the titration process. When the stoichiometric point is reached, it is assumed that the reaction has gone to completion. Additionally, the understanding of mole ratios is what allows us to perform stoichiometry-based calculations confidently. By grasping these chemical principles, students can understand not just how to perform the calculations but also the reasons behind each step.