If it costs 10.5 kcal/mol to “run” a particular cation ATPase “pump”, then what is the minimum concentration of ATP required to provide just enough energy to run this ATPase? In other words, what does the concentration of ATP need to be so that the free energy of ATP hydrolysis is -10.5 kcal/mol. Report your answer to the nearest tenth of a mM, and assume that [\Delta] ΔG°' is -7.3 kcal/mol, the concentration of Pi is 3.4 mM, the concentration of ADP is 1 mM, the pH is 7.2, and that the temperature is 37 °C.
Therefore the free energy change is given by:
DG = DG0 + RTln([ADP][Pi]/[ATP])
DG= change in free energy
DG0= standard free energy change
R= 2=gas constant
T=temperature in kelvin=273 + t in celsius
pi= 3.4 mM
Therefore, putting all values in formula,
-10.5= (-7.3) + 2*310 ln (0.9*3.4 /x)
-10.5= -7.3 + 620 ln (3.06/x)
-10.5+7.3 = 620 ln (3.06/x)
Therefore, the minimum concentration of ATP required to provide just enough energy to run this ATPase is 3.07583 Kcal/mol.
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