Question

What will be the free energy change for moving an uncharged solute X against its concentration gradient from inside to outside?

[X] = 60 mM
[X] = 10 mM
For this problem, use
R= 8.314 x 10 kJ mol K
T= 298 degree Kelvin

Answer 1

The free energy change for moving an uncharged solute against its concentration gradient from inside (60 mM) to outside (10 mM) is approximately -4.42 kJ/mol, indicating the process requires energy.

Step-by-step explanation:

To calculate the free energy change (ΔG) for moving an uncharged solute X against its concentration gradient from a concentration of 60 mM inside to 10 mM outside, we can use the formula: ΔG = RTln([X]out/[X]in). Here, R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin (298 K), [X]out is the concentration outside (10 mM), and [X]in is the concentration inside (60 mM). We must also convert the concentration units from mM to M by dividing by 1000.

ΔG = (8.314 J/mol·K)(298 K)ln(10×10⁻³ M / 60×10⁻³ M)

ΔG = (8.314 J/mol·K)(298 K)ln(1/6) = (8.314 J/mol·K)(298 K)(-1.792) ≈ -4.42 kJ/mol

Thus, the free energy change for moving solute X against its concentration gradient is approximately -4.42 kJ/mol, indicating that work is required to move the solute in the direction specified.