Problem 30 - Chemical Principles: The Quest for Insight

Question

A 1.331-g sample of impure barium hydroxide was dissolved in \(250 \mathrm{~mL}\) of aqueous solution. A \(35.0-\mathrm{mL}\). portion of this solution was titrated to the stoichiometric point with \(17.6 \mathrm{~mL}\) of \(0.0935 \mathrm{M} \mathrm{HCl}\) (aq). What is the percentage purity of the original sample?

Step-by-Step Solution

Answer

The percentage purity of the original sample is determined by calculating the moles of HCl used, finding the corresponding moles of Ba(OH)2, converting to the mass of Ba(OH)2, and then dividing by the mass of the impure sample.

Step 1: Calculate the moles of HCl used in the titration

Use the volume and concentration of the HCl solution to calculate the moles of HCl. The formula is: moles of HCl = volume of HCl (in liters) * concentration of HCl (in mol/L).

Step 2: Determine the moles of barium hydroxide that reacted

Since the reaction between barium hydroxide and hydrochloric acid is a 1:2 stoichiometry (Ba(OH)2 + 2HCl → BaCl2 + 2H2O), the moles of Ba(OH)2 will be half the moles of HCl.

Step 3: Calculate the total moles of barium hydroxide in the original sample

Calculate the moles of barium hydroxide in the entire 250 mL of solution by scaling up the moles found in the 35.0 mL aliquot. The total moles of barium hydroxide = moles in aliquot * (250/35).

Step 4: Find the mass of pure barium hydroxide in the sample

Using the molar mass of barium hydroxide (Ba(OH)2, 171.34 g/mol), convert the total moles to mass using the formula: mass = moles * molar mass.

Step 5: Calculate the percentage purity

The percentage purity is found by dividing the mass of pure barium hydroxide by the mass of the impure sample and then multiplying by 100. Percentage purity = (mass of pure Ba(OH)2 / mass of impure sample) * 100.

Key Concepts

Titration

Titration is an analytical technique commonly used in chemistry to determine the concentration or amount of a substance in a solution. During a titration, a solution of known concentration (titrant) is added to a measured volume of a solution of the unknown substance until the reaction between them is complete, which is often indicated by a color change known as the endpoint.

For the problem at hand, the titration involved hydrochloric acid (HCl) as the titrant and barium hydroxide (Ba(OH)₂) as the substance being evaluated. The process determines the purity of the barium hydroxide by calculating how much hydrochloric acid is required to neutralize a sample; this reflects the amount of actual barium hydroxide present in the impure sample.

Stoichiometry

Stoichiometry refers to the calculation of reactants and products in chemical reactions. It's a form of bookkeeping for chemistry where the balanced chemical equation offers the ratio of moles of reactants to products. In the provided exercise, the balanced equation (Ba(OH)₂ + 2HCl → BaCl₂ + 2H₂O) signifies that one mole of barium hydroxide reacts with two moles of hydrochloric acid.

Understanding the stoichiometric coefficients is vital because they tell you how to scale the quantities of substances involved in the reaction. This is essential when converting the moles of the titrant (HCl) to the moles of barium hydroxide to determine the sample's purity.

Molar Mass

The molar mass is the mass of one mole of a substance (typically in grams per mole) and it's a physical property unique to each substance. In stoichiometric calculations, molar mass bridges the gap between the mass of a substance and the number of moles. It allows chemists to convert between mass and moles of a substance, a critical step when calculating the purity of substances.

The molar mass of barium hydroxide is used in the final stages of the calculation in the problem provided, where the moles of barium hydroxide are converted into mass. Knowing that the molar mass of Ba(OH)₂ is 171.34 g/mol is essential for accurate purity calculation.

Acid-Base Reaction

An acid-base reaction is a chemical reaction that occurs between an acid and a base, which generally results in the formation of water and a salt. In the context of titration, an acid-base reaction provides the method for determining the amount of acid or base present in a sample.

The titration of a basic barium hydroxide solution with hydrochloric acid, an acid, is an example of an acid-base reaction. The reaction reaches completion at the stoichiometric point, where the amount of acid added neutralizes the base. This specific point in titration is crucial to finding out how much base was present in the solution, which subsequently is the basis to determine the sample's purity.