Question

Calculate the free energy change for glucose entry into cells when the extracellular concentration is 5 mM and the intracellular concentration is 3 mM.

Short answer

The free energy for glucose to enter into the cells at the given concentration is ${\text{- 1.27kJmol}}^{\text{- 1}}$.

Step-by-step solution

Free energy change

The amount of free energy required to move a substance through a membrane is determined by taking into account the concentrations on both sides of the membrane.

In the case of ions, the change in free energy is dependent on the kind of ion.

Calculating the free energy change

The extracellular concentration of glucose is$\text{5mM = 0.005M}$

The intracellular concentration of glucose is$\text{3mM = 0.003M}$

The free energy change is calculated using the formula: $△G=RT\ln \frac{{\left[Glu\cos e\right]}_{in}}{{\left[Glu\cos e\right]}_{out}}$

On substituting the values in the formula,

$$\begin{gathered} △G=(8.3145J{K}^{-1}mo{l}^{-1})\left(298K\right)\ln \frac{[0.003]}{[0.005]} \\ =(8.3145J{K}^{-1}mo{l}^{-1})\left(298K\right)(-0.51082) \\ =-1.27kJmo{l}^{-1} \end{gathered}$$

Thus, the free energy required for glucose to enter cells is ${\text{- 1.27kJmol}}^{\text{- 1}}$.

Conclusion

As a result, the free energy required for glucose to enter cells at a given concentration is $-1.27{\mathrm{KJmol}}^{-1}$.