In addition, Einstein's equation tells us that the relative time it takes for an ion to diffuse increases as the square of the increase in distance. Through the membrane, via diffusion and protein mediated transport. Larger water-soluble molecules require the mediation of membrane transport proteins. These integral proteins act as pores or tunnels through the membrane, and employ various permeability controls. Water moves across semi-permeable membranes by osmosis .
Dissoved solutes reduce the chemical potential of a sample of water.
Thus, pure water will diffuse across a membrane into a cell containing a mixture of water and solutes. The amount of pressure necessary to stop the flow equals the osmotic pressure, which is calculated by the number of dissolved particles in solution. For example, a 1M solution of NaCl has an osmotic pressure of 2Os. In general, protein-mediated transport is faster than diffusion, shows chemical specificity, but saturates based on the number of carrier molecules. Facilitated transport can only transport a substance down its concentration gradient.