Problem 31 - Chemical Principles

Question

Suppose that \(1.436 \mathrm{~g}\) of impure sodium hydroxide is dissolved in \(300 . \mathrm{mL}\) of aqueous solution and that \(25.00 \mathrm{~mL}\) of this solution is titrated to the stoichiometric point with \(34.20 \mathrm{~mL}\) of \(0.0695 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\). What is the percentage purity of the original sample?

Step-by-Step Solution

Answer

The percentage purity of the original NaOH sample is calculated by dividing the mass of pure NaOH by the mass of the impure sample and multiplying by 100.

Step 1: Calculate moles of HCl

First, calculate the number of moles of HCl used in the titration. Use the formula: moles of HCl = molarity of HCl * volume of HCl in liters. Since the volume of HCl is given in milliliters, convert it to liters by dividing by 1000.

Step 2: Calculate moles of NaOH

According to the stoichiometry of the neutralization reaction between NaOH and HCl, which is 1:1, the moles of NaOH is equal to the moles of HCl.

Step 3: Calculate moles of NaOH in impure sample

The 25.00 mL of solution titrated is a portion of the original 300 mL solution prepared. So, the total moles of NaOH in the original 300 mL are 12 times the moles titrated (since 300 mL / 25 mL = 12).

Step 4: Calculate the mass of pure NaOH in the impure sample

Use the molar mass of NaOH to convert the total moles of NaOH to grams. The molar mass of NaOH is approximately 40.00 g/mol.

Step 5: Calculate percentage purity of sample

To find the percentage purity, divide the mass of pure NaOH by the mass of the impure sample and multiply by 100 to convert to a percentage.

Key Concepts

Titration

Titration is an analytical technique used to determine the concentration of a solute in a solution by reacting it with a standard solution of known concentration. In a typical titration setup, a solution called the titrant is gradually added to the analyte until the reaction reaches the end point, which is often indicated by a color change with the help of an indicator or by measuring a physical property of the solution, such as pH.

For instance, if we're investigating an acid-base titration, the process includes delivering a base (the titrant) into an acid (the analyte) until neutralization occurs. In the exercise given, we specifically look at the neutralization of sodium hydroxide (NaOH) with hydrochloric acid (HCl), which requires precise measurement of the volume of titrant used to reach the stoichiometric point (the point where the amount of titrant is stoichiometrically equivalent to the amount of substance in the sample).

• To calculate the amount of titrant used, we take the volume of the titrant delivered and multiply it by its concentration (molarity).

Stoichiometry

Stoichiometry is the study of the quantitative relationships, or ratios, between reactants and products in chemical reactions. Using the balanced chemical equation, we can determine how much of one reactant is needed to react completely with a given amount of another reactant. In the context of our exercise, the stoichiometry of the neutralization reaction between NaOH and HCl is a simple 1:1 ratio.

This means that one mole of NaOH will react with one mole of HCl.

• When we know the number of moles of one reactant that reacted, we can use stoichiometry to find the number of moles of the other reactant.
• This is crucial for purity calculations, as we need to know the actual amount of the substance of interest (in this case, NaOH) present in the sample.

Molarity

Molarity, denoted as M, is a unit of concentration representing the number of moles of a solute per liter of solution. It's widely used in chemistry because it directly relates the volume of the solution to the amount of the substance it contains.

For example, a 0.0695 M HCl solution contains 0.0695 moles of hydrochloric acid per liter of solution. To find the amount of HCl used in a titration, we multiply the molarity by the volume of the solution in liters.

• If the volume is given in milliliters, we convert it to liters by dividing by 1000 before multiplying by the molarity.

The moles of acid or base calculated from molarity are essential in determining the stoichiometry of the reaction and thus aid in further calculations regarding the purity of a substance.

Percentage Purity

The percentage purity of a substance indicates the proportion of a specified pure chemical compound within a mixture. In the analysis of an impure sample, determining its purity level is a frequent necessity. For the given exercise, percentage purity is calculated by comparing the mass of pure NaOH calculated from titration to the mass of the original impure sample.

• After finding the mass of pure NaOH that reacts, we can calculate the percentage purity by dividing this mass by the total mass of the impure sample and then multiplying by 100 to convert the fraction to a percentage.

This value is vital in quality control and commercial transactions, as it quantifies the actual usable amount of a chemical in a given sample.

Neutralization Reaction

A neutralization reaction is a type of chemical reaction in which an acid and a base react to form water and a salt. These reactions are central to acid-base titrations as they allow us to calculate concentrations of acid or base solutions. In the exercise, the neutralization reaction between NaOH and HCl is represented by the equation: NaOH + HCl → NaCl + H₂O.

The reaction proceeds until the acid and base neutralize each other, which is indicated by reaching the stoichiometric point in a titration process. The mole-to-mole relationships in a neutralization reaction are instrumental in solving for the purity of the sample since they tell us exactly how much of each reactant is needed to complete the reaction without any excess of either.