The concentration of sulfate in water can be determined by adding a solution of barium chloride to precipitate the sulfate ion. Write the net ionic equation for this reaction. Treating a 145-mL sample of water with excess \(\mathrm{BaCl}_{2}(a q)\) precipitated \(0.330 \mathrm{~g}\) of \(\mathrm{BaSO}_{4} .\) Determine the concentration of sulfate in the original water sample.

Net ionic equations are vital in chemistry as they help us understand reactions at the ionic level, which is useful when observing precipitation reactions like the determination of sulfate concentration in water. In simple terms, a net ionic equation strips a chemical equation down to only the particles that participate in the reaction. It omits the spectator ions, which are present in the reaction mixture but do not take part in the reaction itself.

In the given exercise, the net ionic equation is used to describe the reaction between sulfate ions (\(SO_{4}^{2-}\)) and barium ions (\(Ba^{2+}\)), which combine to form an insoluble solid, barium sulfate (\(BaSO_{4}\)). This precipitate is a clue that a chemical reaction has occurred, specifically, a double displacement reaction.

Understanding the molar mass of a substance is essential for quantifying the amount of material involved in a chemical reaction. The molar mass, expressed in grams per mole (g/mol), is the mass of one mole of a substance. It is found by summing the atomic masses of all the atoms in a molecule.

For example, barium sulfate (\(BaSO_{4}\)) has a molar mass calculated by adding the masses of one barium atom, one sulfur atom, and four oxygen atoms. Accurate molar mass calculations are fundamental in converting between mass and moles of a substance, a step that is critical for stoichiometry and molarity calculations. In our exercise, determining the molar mass of barium sulfate allowed us to find the number of moles from the given mass, which in turn is used to calculate the concentration of sulfate in the sample.

Stoichiometry lies at the heart of chemical reactions. It is the quantitative relationship between reactants and products in a chemical reaction, and it allows chemists to predict the quantities of substances consumed and produced in a given reaction.

Using the coefficients from the balanced chemical equation, we can determine the ratio of the number of moles of each reactant and product involved in the reaction. In the context of our exercise, stoichiometry is applied by understanding that one mole of barium ions reacts with one mole of sulfate ions to produce one mole of barium sulfate. Hence, the number of moles of barium sulfate precipitated gives us a direct measure of the number of moles of sulfate ions originally present in the water sample.

Molarity, a measure of the concentration of a solute in a solution, is defined as moles of solute per liter of solution (mol/L). It's a key concept in chemistry because it links the amount of substance to the volume of the solution, which is crucial for a variety of applications like dilutions, reaction yields, and titrations.

In the step-by-step solution, molarity calculations come into play after determining the number of moles of sulfate ions. With both the number of moles and the volume of the solution in liters, the molarity formula (\(Molarity = \frac{moles}{liters}\)) assists in finding the sulfate concentration in the water sample. This value gives actionable information regarding the quality of the water and if it's suitable for its intended use.