A saturated aqueous solution of sparingly soluble salt MX₂ is prepared at 298 K by adding excess crystalline MX₂ to 250 mL of distilled water in a closed flask. After vigorous stirring for 2 h, undissolved solid remains visible at the bottom of the flask. The concentration of M2+ ions in the solution is determined to be 1.3 × 10⁻³ mol L⁻¹.
A chemist then performs the following sequence of manipulations, allowing sufficient time for the system to respond after each step:
1. Adds a small amount of additional solid MX₂.
2. Withdraws 50 mL of the supernatant solution, filters it quickly, and measures the M2+ concentration.
3. Introduces a trace quantity of radioactive isotope ∗M2+ (having identical chemical behavior to M2+) into the remaining solution and continues stirring.
4. After 1 h, removes a sample of the undissolved solid and analyzes its isotopic composition.
a. For each of the four steps, predict whether the measured concentration of M2+ in the solution is expected to change from the initial value of 1.3 × 10⁻³ mol L⁻¹. Provide a concise justification for each prediction.
b. Explain how the results of the isotopic analysis in step 4 can be used to demonstrate that the dissolution–precipitation process is dynamic rather than static at equilibrium.
c. Design an additional experimental test (other than isotopic labeling) that could independently verify the dynamic nature of the equilibrium between solid MX₂ and its ions in solution. Outline the procedure and the expected observations that would support your conclusion.
d. If the entire experiment were repeated at 308 K, predict qualitatively how the solubility of MX₂ and the time required to reach equilibrium would change. Justify each prediction in terms of particle-level processes.