(c) If 25.8 mL of an AgNO₃ solution is needed to precipitate all the Cl^- ions in a 785-mg sample of KCl (forming AgCl), what is the molarity of the AgNO₃ solution?

Verified step by step guidance

1. Determine the moles of Cl- ions in the KCl sample. Start by calculating the moles of KCl using its molar mass. The molar mass of KCl is approximately 74.55 g/mol. Convert the mass of KCl from mg to g (785 mg = 0.785 g) and use the formula: \( \text{moles of KCl} = \frac{\text{mass of KCl (g)}}{\text{molar mass of KCl (g/mol)}} \).
2. Since KCl dissociates completely in solution, the moles of Cl- ions will be equal to the moles of KCl. Therefore, the moles of Cl- ions are the same as the moles of KCl calculated in the previous step.
3. Write the balanced chemical equation for the reaction: \( \text{AgNO}_3 + \text{Cl}^- \rightarrow \text{AgCl} + \text{NO}_3^- \). This shows that one mole of AgNO3 reacts with one mole of Cl- ions to form one mole of AgCl.
4. Use the stoichiometry of the reaction to determine the moles of AgNO3 needed. Since the reaction is a 1:1 ratio, the moles of AgNO3 required will be equal to the moles of Cl- ions.
5. Calculate the molarity of the AgNO3 solution using the formula: \( \text{Molarity (M)} = \frac{\text{moles of AgNO}_3}{\text{volume of solution in liters}} \). Convert the volume from mL to L (25.8 mL = 0.0258 L) and use the moles of AgNO3 from the previous step to find the molarity.

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. In this context, it helps determine how many moles of AgNO3 are required to react with the moles of Cl- ions from KCl to form AgCl, based on the balanced chemical equation.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. To find the molarity of the AgNO3 solution, one must calculate the moles of AgNO3 used in the reaction and divide that by the volume of the solution in liters, which is essential for understanding the concentration of the reactant.

Precipitation Reaction

A precipitation reaction occurs when two soluble salts react in solution to form an insoluble product, known as a precipitate. In this case, AgNO3 reacts with Cl- ions from KCl to form AgCl, which precipitates out of the solution. Understanding this concept is crucial for determining the amount of AgNO3 needed to completely react with the Cl- ions.