Final answer:
When the concentration of urea in Solution A doubles, while Solution B's concentration remains the same, the gradient across the membrane increases and so does the flux of urea, assumably doubling it under ideal, linear conditions.
Step-by-step explanation:
If Solution A, which initially has a concentration of 10 mM urea, has its concentration doubled, it will then have a concentration of 20 mM urea. This change increases the concentration gradient across the membrane since Solution B remains at 5 mM urea. According to the principles of osmosis, the flux of urea across a semipermeable membrane is driven by the concentration gradient. Therefore, when the concentration gradient is increased, the flux of urea will also increase.
However, the exact change in flux depends on the system's characteristics and whether the transfer process remains within the proportional limit described by Fick's law of diffusion. Assuming linearity, if we double the concentration difference between Solution A and Solution B, the resultant flux should also double under ideal conditions. Consequently, when Solution A's concentration is doubled from 10 mM to 20 mM, the flux of urea across the membrane will also double.