A student is asked to find the free energy cost of moving one glucose molecule from a…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Physical foundations of the living cell · Physical foundations of the living cell

Life at Thermal Energy, Ch Entropy, free energy and the forces that counting produces

Problem

A student is asked to find the free energy cost of moving one glucose molecule from a region where the concentration is c1=2 mMc_1 = 2\,\mathrm{mM} to a region where it is c2=8 mMc_2 = 8\,\mathrm{mM}, at T=298 KT = 298\,\mathrm{K}. Their working is reproduced below. "The cost of building up a concentration difference should be proportional to how much bigger the difference is. The fractional increase is (c2−c1)/c1=(8−2)/2=3(c_2 - c_1)/c_1 = (8-2)/2 = 3. So the cost is ΔG=3 kBT=3×4.11 pN nm=12.3 pN nm\Delta G = 3\,k_BT = 3 \times 4.11\,\mathrm{pN\,nm} = 12.3\,\mathrm{pN\,nm} per molecule." ((a)) Identify the specific error in this reasoning, in words. ((b)) Give the correct value of ΔG\Delta G for moving the molecule from c1c_1 to c2c_2, in kBTk_BT and in pN nm\mathrm{pN\,nm}.

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