Question

Gastric juice (pH 1.5) is produced by pumping HClfrom blood plasma (pH 7.4) into the stomach. Calculate the amount of free energy required to move H+ at 37 °C under cellular conditions? How many moles of ATP must be hydrolyzed to provide this amount of free energy? How many molecules of ATP is that? he free energy change for ATP hydrolysis under cellular conditions is about -58 KJ/mol.

**Ignore the effects of the transmembrane electrical potential**

Answer 1

the amount of free energy required to move H+ at 37 0C under cellular condition can be calculated by the formula:

Free energy change = RTIn (Cin/Cout) where R is universal gas constant whose value is 8.314 J/mol and T is absolute temperature in Kelvin i.e. 310 in this case and C2/C1 is concentration inside the cell/concentration outside the cell. As we know pH = -log [H+ ] then [H+ ] = 10-pH

So at pH 1.5 (pH inside the gastric juice) [H+ ] = 10-pH i.e. 10-1.5 = 3.2 x 10-2 M

Similarly  at pH 7.4 (pH inside the blood) [H+ ] = 10-pH i.e. 10-7.4  = 4.0 x 10-8 M

so now putting all values in above formula we get: 8.314 x 310 x In (3.2 x 10-2/4.0 x 10-8) = 35 kJ/mol (i.e. Answer)

The number of moles of ATP hydrolyzed to provide 35 kJ/mol free energy is (35/58)= 0.60 moles

0.6 moles of ATP is 0.6 x N i.e. Avogadro number of molecules = 0.6 x 6.023 x 1023 = 3.6138 x 1023 molecules