Consider a spherical cell of radius 8 micrometers. The cell is suddenly placed in a solution of pure water. For simplicity, assume that the cell is a 0.15 M NaCl solution and the fluid density inside the cell is 1.005 g/ml. The density of pure water is 1g/ml.
a) Explain why the cell swells.
b) What is the concentration difference of water between inside and outside the cell.
c) The cell has extra membrane that enables the cell to swell. If the cell has 1 x 10^5 aquaporin channels and the water flow rate in each channel is 1 x 10^9 molecules/s, how long before the surface areas to 150% of the initial value and the cell bursts? Assume that the fluid density in the cell is 1g/cm^3 and the rate at which water molecules penter the cell is constant.