Salty Cell

A cell is surrounded by a porous semipermeable membrane that allows passage of small ions but not large ones. We can model ion movement across the cell membrane using physics.

a. A semipermeable membrane contains an aqueous solution of 0.1M of NaCl inside and outside. What are the final concentrations a long time later of sodium and chlorine ions and the voltage across the membrane if a concentration of 0.05 M NaQ is suddenly added to the the inside of the membrane? Assume that NaQ dissociates completely into Na+ and Q- ions, NaCl likewise, and assume the system reaches thermal and diffusive equilibrium (this condition would not be true in a living cell). The membrane is permeable to all ions except Q-, which is too large to fit through the pores. Assume all ions in solution are non-interacting and behave like ideal gases. The final temperature is 300 K.

b. A semipermeable membrane contains an aqueous solution of 0.1 M of CuCl₂ inside and outside. What are the final concentrations a long time later of copper and chlorine ions and the voltage across the membrane if 0.2 mol of CuQ is suddenly added to 1 L of solution inside the membrane? Neglect the volume change when the CuQ is added. Assume that CuQ is a weakly soluble salt which dissociates into Cu⁺² and Q^-2 ions with a solubility product constant of 0.01 M², which means that [Cu⁺²][Q^-2] = 0.01. The membrane is permeable to all ions except Q^-2. The final temperature is 300 K.