CHEMISTRY · Subjective · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures
Problem
Two classmates, Alex and Jordan, each draw a particulate-level diagram of what they believe is the more concentrated of two CaCl2(aq) solutions: one labeled 0.10 M and one labeled 0.50 M. Both diagrams are described below and are intended to show the same fixed microscopic volume of solution (the box dimensions are identical). Assume all CaCl2 present has dissolved completely.
Diagram A (Alex’s drawing):
• 6 Ca²⁺ ions (orange spheres) and 12 Cl⁻ ions (green spheres) are present, dispersed among 26 water molecules.
• Around every Ca²⁺ ion, exactly two water molecules are depicted, with the oxygen atoms pointing toward the Ca²⁺ center.
• Around every Cl⁻ ion, exactly four water molecules are depicted, with the hydrogen atoms pointing toward the Cl⁻ center.
Diagram B (Jordan’s drawing):
• 3 Ca²⁺ ions and 6 Cl⁻ ions are present among 60 water molecules.
• Water molecules surrounding the ions are shown with random orientations (no consistent alignment of dipoles).
• In addition, 2 intact CaCl2 formula units are drifting in the box, each surrounded by water molecules that are not oriented in any particular way.
(a) Based solely on relative numbers of solute and solvent particles, determine which diagram—A or B—better represents the more concentrated CaCl2 solution. Justify your answer quantitatively by comparing appropriate ratios.
(b) In Diagram A, evaluate whether the number of water molecules drawn in each first-shell solvation cage for Ca²⁺ and for Cl⁻ is realistic. Explain your reasoning with reference to ion-dipole interactions.
(c) Diagram B contains multiple representational errors. Identify TWO different errors other than the overall concentration mismatch you discussed in part (a). For each error, explain why it violates accepted conventions for depicting ionic solutions.
(d) Choose one of the two diagrams and describe precisely how you would revise it so that it correctly depicts a 0.50 M CaCl2 solution at the particulate level. Your description should specify the correct numbers of each ion type relative to water molecules in the fixed volume and the proper orientation of water molecules around BOTH cations and anions.