What volume of \(0.350 \mathrm{M} \mathrm{BaCl}_{2}\) solution is required to obtain \(0.500 \mathrm{~mole}\) of \(\mathrm{Cl}^{-}(a q) ?\)

The mole concept is a fundamental principle in chemistry that allows scientists to count the number of particles in a substance. A mole (abbreviated as mol) is defined as the amount of any substance that contains the same number of particles as there are atoms in exactly 12 grams of carbon-12. This number is known as Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles.

The mole concept is integral to understanding chemical reactions and stoichiometry because it provides a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure in the laboratory. For instance, saying we have \(1\) mole of \( Cl^- \) ions means we have \(6.022 \times 10^{23}\) chloride ions.

One challenge that students often face is relating moles to mass and volume. The molar mass (mass per mole of a substance) helps translate between mass and moles. However, when dealing with solutions, the concept is extended to include concentration measures such as molarity, which involves volume.

Solution concentration describes how much of a given substance is contained within a certain volume of solvent. There are various ways to express concentration, but one of the most commonly used in chemistry is molarity. Molarity (M) is defined as the number of moles of solute (the substance being dissolved) per liter of solution.

Understanding molarity is crucial when preparing solutions for experiments or when performing titrations. In the given exercise, the molarity of the \( BaCl_2 \) solution is \(0.350\ M\), meaning that each liter of the solution contains \(0.350\) moles of \( BaCl_2 \). To find out how much volume is needed to obtain a specific amount of solute, you can reorganize the basic molarity equation \( M = \frac{n}{V} \) to solve for \(V\), giving you \(V = \frac{n}{M}\).

In practice, this means that if a student knows the number of moles of solute they need and the molarity of the solution, they can easily calculate the volume required. The process of calculating the volume is crucial in laboratory settings where precision is key.

Stoichiometry is the section of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It is based on the conservation of mass and the concept of the mole. In a balanced chemical equation, the coefficients represent the stoichiometric ratios, indicating how many moles of each substance are involved in the reaction.

In the context of the exercise, stoichiometry is applied to understand the dissociation of \( BaCl_2 \) in water. The compound \( BaCl_2 \) will dissociate into \( Ba^{2+} \) and \(2 Cl^-\) ions. Therefore, for each mole of \( BaCl_2 \), there are two moles of \( Cl^- \) ions. This stoichiometric ratio is crucial for determining the volume of solution needed to obtain a desired amount of reactant or product.

Breaking down reactions into their stoichiometric parts can make it easier for students to comprehend complex reactions by focusing on the individual components and their relationships. Recognizing these ratios allows for the precise calculation of reactants or products in a chemical reaction, thereby reinforcing the connection between theoretical stoichiometry and practical laboratory work.