A student reads that ATP hydrolysis under cellular conditions releases about

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Physical foundations of the living cell · Molecular machines, transport and bioenergetics

Life at Thermal Energy, Ch The scales of life and the thermal energy

Problem

A student reads that ATP hydrolysis under cellular conditions releases about 50 kJ mol−150\,\mathrm{kJ\,mol^{-1}}, and separately knows that kBT=4.11×10−21 Jk_BT = 4.11\times10^{-21}\,\mathrm{J} at 298 K298\,\mathrm{K}. They argue: "4.11×10−21 J4.11\times10^{-21}\,\mathrm{J} is minute compared with 50 000 J50\,000\,\mathrm{J}, a factor of about 102510^{25}. So thermal motion could never supply the energy of one ATP hydrolysis, and the textbook's claim that this reaction releases only about 20kBT20k_BT per molecule must be a mistake." ((a)) Identify the error in this reasoning. ((b)) Carry out the correct conversion and state the energy of one ATP hydrolysis in units of kBTk_BT at 298 K298\,\mathrm{K}.

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