7. Imagine you have 2 chambers connected by a flexible, semipermeable membrane and completely filled with solutions - one chamber contains 50ml of a 50mM NaCl solution (A), and the other (B) contains 100 ml of a 100mM NaCl solution? If the membrane permits both water and NaCl to cross:
a) describe and explain which way the water and the Na+ and Cl- ions would flow?
b) describe and explain what the volumes and concentrations of the two compartments would be at equilibrium?
c) Describe and explain how the result would differ if the opening were permeable to water only?
The concentration of NaCl in solution A is 50mL*(50mM)=250 moles of NaCl per mL
The concentration of NaCl in solution B is 100mL*(100mM)=1,000 moles of NaCl per mL
a) Describe and explain which way the water and the Na+ and Cl- ions would flow?
The ions would flow from solution B to solution A to establish an equal concentration gradient since the membrane is permeable to the ions. Since the membrane is also permeable to water, and there is more water on the B side, water would flow from B to A as well.
b) describe and explain what the volumes and concentrations of the two compartments would be at equilibrium?
The ions and the water concentrations would be equal on both sides of the membrane (i.e., the volumes would be the same as well as the concentrations of ions).
c) Describe and explain how the result would differ if the opening were permeable to water only?
Water would flow from the least concentrated side of the membrane (A) to more concentrated side (B) to establish an equal concentration gradient (i.e., equal mole to water ratios). This will result in A having a lesser volume then B to achieve an equal concentration gradient.
I hope this helps.
I have a typo
The concentration of NaCl in solution A is 50mL*(50mM)=250 moles of NaCl TOTAL not per mL
The concentration of NaCl in solution B is 100mL*(100mM)=1,000 moles of NaCl TOTAL not per mL
Also, the concentration of NaCl in solution B is 100mL*(100mM)=10,000 moles of NaCl TOTAL not 1,000 moles
I totally screwed up on the calculations.
The concentration of NaCl in solution A is 50 x 10^-3L*(50mM)=0.250 moles of NaCl
The concentration of NaCl in solution B is 100 x10^-3L*(100mM)=10 moles of NaCl
To analyze this scenario, we need to consider the principles of osmosis and diffusion. Here's how we can address each question:
a) The movement of water and ions (Na+ and Cl-) will be determined by the concentration gradient. Water molecules will move from an area of lower solute concentration to an area of higher solute concentration. Similarly, solute particles (Na+ and Cl-) will move from an area of higher concentration to an area of lower concentration.
In this case, the concentration of NaCl is higher in chamber B compared to chamber A. Consequently, water molecules will move from chamber A (50mM NaCl) to chamber B (100mM NaCl) through the semipermeable membrane, in an attempt to equalize the concentration on both sides.
b) At equilibrium, the movement of water will continue until the concentration of solutes (NaCl) is the same on both sides of the membrane. This means that, eventually, the movement of water will stop, resulting in equal volumes in both chambers.
The final concentration of the compartments will depend on the magnitude of the concentration gradient and the initial volumes. Since the initial volume is 50ml in chamber A and 100ml in chamber B, the water will continue to flow into chamber B until both chambers reach equal volumes (75ml each, assuming no volume changes due to ion movement).
Regarding the concentration of NaCl, it will also approach equilibrium. However, due to the different initial concentrations, the final concentration will not be the same in both chambers. The exact final concentration will depend on the net movement of ions during the process.
c) If the membrane is permeable to water only, but not to Na+ and Cl- ions, the movement of substances will be different. Water will still move from an area of lower solute concentration to higher solute concentration until equilibrium is reached, but the ions will not be able to pass through the membrane.
In this case, only water will move from chamber A to B until both chambers reach equal volumes. The concentrations of Na+ and Cl- ions will remain unchanged, as they cannot cross the membrane. Therefore, at equilibrium, the volume will be equal in both chambers, and the concentration of NaCl will remain the same as the initial concentrations (50mM in chamber A and 100mM in chamber B).
It's important to note that these explanations are based on the given scenario and assumptions. In practice, other factors such as pressure, temperature, and kinetics may affect the outcome.