The reaction of \(\mathrm{WCl}_{6}\) with \(\mathrm{Al}\) at \(\sim 400^{\circ} \mathrm{C}\) gives black crystals of a compound containing only tungsten and chlorine. A sample of this compound, when reduced with hydrogen, gives 0.2232 g of tungsten metal and hydrogen chloride, which is absorbed in water. Titration of the hydrochloric acid thus produced requires \(46.2 \mathrm{mL}\) of \(0.1051 \mathrm{M}\) NaOH to reach the end point. What is the empirical formula of the black tungsten chloride?

Stoichiometry is the section of chemistry that involves calculating the quantities of reactants and products in chemical reactions. Essential to understanding stoichiometry is the concept of the mole, which is the standard unit of measurement for the amount of substance. One mole corresponds to Avogadro's number (\(6.022 \times 10^{23}\) entities) of atoms, molecules, or ions.

For stoichiometric calculations, it’s crucial to balance the chemical equation, so that the number of atoms of each element is the same on both sides of the reaction. This reflects the conservation of mass and the stoichiometric proportions as dictated by the coefficients in the balanced equation. Once balanced, the mole ratio of reactants to products can be used to calculate the mass, moles, or volume of substances consumed or produced.

When working on the empirical formula determination, stoichiometry allows us to use the mass of each element in a compound to find the mole ratio of the elements. This ratio is then used to determine the simplest whole number ratio of atoms in the compound, which is the empirical formula. This principle is evident in the calculation of the empirical formula for the black tungsten chloride described in the exercise.

Titration is a common laboratory technique used to quantify the concentration of an unknown solution, involving a reaction where a solution of known concentration (titrant) is added to a volume of another solution of unknown concentration. In the exercise, titration is used to determine the concentration of hydrochloric acid produced by the reaction.

During a titration, the point at which the reactants have completely reacted is known as the endpoint, indicated by a color change or an electronic instrument. In acid-base titrations, a typical titration curve shows how the pH of the solution changes as the titrant is added.

In the provided example, sodium hydroxide (NaOH) is used to titrate the hydrochloric acid (HCl) produced by the compound's reduction. The concentration of NaOH is known, and through a stoichiometric 1:1 reaction with HCl, the moles of HCl can be determined. With this information, the moles of chlorine in the black tungsten chloride can also be found, ultimately contributing to the empirical formula determination.

Chemical reaction quantification is the process of determining how much of each substance is involved in a chemical reaction. This involves identifying the reactants and products along with their corresponding quantities, either in moles, mass, or volume. These quantities often come from experimental data, such as mass of a substance produced or volume of a reactant consumed.

For example, in the exercise regarding the black tungsten chloride, the quantity of tungsten is given by its mass after reduction, and the volume of HCl is determined through titration. From this data, the number of moles involved in the chemical reaction can be determined. The moles of each element, tungsten and chlorine in this case, are key factors in the empirical formula determination because they reveal the mole ratio of the elements in the compound.

By understanding the stoichiometry of the reaction, the titration calculations, and the techniques for quantifying chemical reactions, one can determine vital information about a compound, such as its empirical formula. These quantitative analyses are fundamental in chemistry, as they form the basis for creating and understanding chemical compounds and their reactions.