What is the volume of fluid that must flow through the semipermeable membrane?

[Andy Resnick]

I think this is a simple problem to solve, but I keep getting nonsense answers.

The question: two reserviors held at constant osmolarity (say 1000 mOsm/l) are connected by a semipermeable membrane. A current of 1 uA is measured across the membrane. What is the volume of fluid that must flow through the membrane?

So I have 1 uA = 1 umol/s ion flow, and 1000 mOsm/l means that 1 umol of osmolyte corresponds to 10^-7 liters of solution. So, 0.1 ul of solution is transported per second. Is this correct?

The reason I think I'm having trouble is that using my actual numbers (100 uA, 300 mOsm/l) I get very high fluid transport rates. Much higher than what is observed.

 

[Andy Resnick]

Never mind- I found the error. It was in converting Coulombs to moles- I was not using the correct conversion (Faraday's constant).

1 uA corresponds to 1.04 *10^-5 umol/s of charge flux, in case anyone is interested.

 

[ravenprp]

The volume of fluid that must flow through the semipermeable membrane can be calculated by using the formula Q = It, where Q is the charge transported (in coulombs), I is the current (in amperes) and t is the time (in seconds). In this case, the current is given as 1 uA, which is equivalent to 1x10^-6 amperes. The time is not specified, so we cannot calculate the exact volume of fluid that must flow through the membrane.

However, based on the information provided, we can make some assumptions. Since the reservoirs are held at a constant osmolarity of 1000 mOsm/l, we can assume that the concentration gradient is also constant. This means that the rate of osmosis (and therefore, the volume of fluid transported) will also be constant.

Using the given current of 1 uA, we can calculate the volume of fluid transported per second as follows:

Q = It
Q = (1x10^-6 A)(1 s)
Q = 1x10^-6 C

Since 1 mole of ions corresponds to 1 coulomb of charge, and 1 mole of osmolyte corresponds to 10^-7 liters of solution, we can calculate the volume of fluid transported as follows:

1x10^-6 C x (1 mol ions / 1 C) x (10^-7 L / 1 mol osmolyte) = 1x10^-13 L/s

Therefore, based on the given information, the volume of fluid that must flow through the semipermeable membrane is 1x10^-13 liters per second. This may seem like a small amount, but it is important to remember that this is only for 1 uA of current. If the current is increased to 100 uA as mentioned in the question, the volume of fluid transported would be 1x10^-11 liters per second, which is a much higher rate.

It is also worth noting that the actual volume of fluid transported may differ from these calculations due to factors such as membrane permeability and pressure differentials between the two reservoirs. However, the formula and calculations provided can give us a general idea of the volume of fluid that must flow through the semipermeable membrane.