Answer
-1265.66 J.K$^{-1}$.Mol$^{-1}$
Work Step by Step
The free energy $\Delta$G is calculated using the following formula:
$\Delta$G = RTIn $\frac{[Glucose]in}{[Glucose]out}$, where $\Delta$G is free energy.
R = 8.3145 J.K$^{-1}$.Mol$^{-1}$
T = 298K
There is a conversion factor of 1mM = 0.001M
Now, plug all of these elements into the original equation.
$\Delta$G = (8.3145J.K$^{-1}$.Mol$^{-1}$(298)In$\frac{0.003}{0.005}$
$\Delta$G = (8.3145J.K$^{-1}$.Mol$^{-1}$(298)In(0.6)
$\Delta$G = (8.3145J.K$^{-1}$.Mol$^{-1}$(298)(-0.51082)
= -1265.66 J.K$^{-1}$.Mol$^{-1}$
