Ignoring protolysis reactions, indicate the concentration of each ion or molecule present in the following solutions: (d) a mixture of 45.0 mL of 0.272 M NaCl and 65.0 mL of 0.0247 M (NH₄)₂CO₃. Assume that the volumes are additive.

Verified step by step guidance

1. Calculate the total volume of the solution by adding the volumes of the NaCl and (NH₄)₂CO₃ solutions. This is done by adding 45.0 mL and 65.0 mL.
2. Calculate the moles of NaCl initially present using its concentration and the volume of the NaCl solution. Use the formula: moles = concentration (M) imes volume (L).
3. Calculate the moles of (NH₄)₂CO₃ initially present using its concentration and the volume of the (NH₄)₂CO₃ solution. Use the same formula as in step 2.
4. Determine the concentration of each ion in the final solution. For NaCl, which dissociates into Na⁺ and Cl^-, the concentration of each ion is equal to the total moles of NaCl divided by the total volume of the solution. For (NH₄)₂CO₃, which dissociates into 2NH₄⁺ and CO₃^2-, the concentration of NH₄⁺ is twice the moles of (NH₄)₂CO₃ divided by the total volume, and the concentration of CO₃^2- is equal to the moles of (NH₄)₂CO₃ divided by the total volume.
5. Summarize the concentrations of Na⁺, Cl^-, NH₄⁺, and CO₃^2- in the final solution.

Key Concepts

Concentration and Molarity

Concentration refers to the amount of solute present in a given volume of solution, commonly expressed in molarity (M), which is moles of solute per liter of solution. Understanding how to calculate molarity is essential for determining the concentration of ions or molecules in a mixture.

Dilution and Mixing Solutions

When two solutions are mixed, the total volume increases, and the concentrations of the solutes change. The final concentration can be calculated using the formula C1V1 + C2V2 = CfinalVfinal, where C is concentration and V is volume. This principle is crucial for accurately determining the concentrations of ions in the resulting solution.

Ionic Dissociation

Ionic compounds, such as NaCl, dissociate into their constituent ions when dissolved in water. For example, NaCl dissociates into Na⁺ and Cl⁻ ions. Understanding how different compounds dissociate is vital for calculating the concentrations of individual ions in a mixed solution.