Pennies minted after 1982 are mostly zinc (97.5%) with a copper cover. If a post-1982 penny is dissolved in a small amount of nitric acid, the copper coating reacts as in Problem 4.52, and the exposed zinc reacts according to the following equation: For a penny that weighs 2.482 g, what is the molarity of the Zn(NO3)2 if the resultant solution is diluted to 250.0 mL with water?

Verified step by step guidance

1. Determine the mass of zinc in the penny by calculating 97.5% of the total mass of the penny (2.482 g).
2. Convert the mass of zinc to moles using the molar mass of zinc (65.38 g/mol).
3. Write the balanced chemical equation for the reaction of zinc with nitric acid: \( \text{Zn} + 2\text{HNO}_3 \rightarrow \text{Zn(NO}_3\text{)}_2 + \text{H}_2 \).
4. Use stoichiometry to determine the moles of \( \text{Zn(NO}_3\text{)}_2 \) produced, which is equal to the moles of zinc reacted.
5. Calculate the molarity of the \( \text{Zn(NO}_3\text{)}_2 \) solution by dividing the moles of \( \text{Zn(NO}_3\text{)}_2 \) by the volume of the solution in liters (0.250 L).

Key Concepts

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L) and is crucial for understanding how much of a substance is present in a given volume of solution. In this problem, calculating the molarity of Zn(NO3)2 requires knowing the moles of zinc produced from the penny's reaction with nitric acid and the final volume of the solution.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced chemical equations. It allows us to determine the amount of product formed from a given amount of reactant. In this case, understanding the stoichiometry of the reaction between zinc and nitric acid is essential to find out how many moles of Zn(NO3)2 are produced from the zinc in the penny.

Dilution

Dilution is the process of reducing the concentration of a solute in a solution, typically by adding more solvent. The dilution equation, C1V1 = C2V2, relates the concentrations and volumes before and after dilution. In this scenario, after calculating the moles of Zn(NO3)2, the final molarity must be determined after the solution is diluted to a total volume of 250.0 mL.