Question

How much energy does it take to transport an uncharged substrate into a cell if its starting inside concentration is 10-fold greater than outside at 37^oC ? (These values may be of use to you: R = 8.315 J/mol·K; 9(Faraday constant) = 96,480 J/V; N = 6.022x10²³/mol.) Show work.

Answer 1

The energy can be calculated in terms of amount of free energy released or consumed during transport of substrate through the membrane.

Let the outside concentration of the substrate = X
So, according to the given problem, inside concentration of the substrate = 10X
Temperature given = 37 ^$\degree$ C = (273+37)K = 310K

So,
ΔG = R*T*ln(10X/X) = 8.315 * 310 * 1 = 2577.65 J/mole

Now we need to find exactly how much energy it takes in the process.
For that we need to know how many moles have been involved in the transport. Since no such information is at hand, we can consider that the free energy change involved 10 times more number of moles than the usual.

So, answer = 2577.65 J/mole * 10moles = 257.765 Joules
This means 257.765 Joules more of energy is taken to transport an uncharged cell