Gastric juice is made up of substances secreted from parietal cells, chief cells, and mucous-secreting cells. the cells secrete hcl, proteolytic enzyme zymogens, mucin, and intrinsic factor. the ph of gastric juice is acidic, between 1-3. if the ph of gastric juice is 2.1, what is the amount of energy (? g) required for the transport of hydrogen ions from a cell (internal ph of 7.4) into the stomach lumen? assume that the potential difference across the membrane separating the cell and the interior of the stomach is �60.0 mv (inside of cells negative relative to the lumen of the stomach).

assume that the temperature is 37 �c.

the faraday constant is 96.5 kj�v�1�mol�1 and the gas constant is 8.314� 10�3 kj�mol�1�k�1. express your answer in kj/mol.

The amount of energy required to transport hydrogen ions from a cell into the stomach is 37.26KJ/mol.

Explanation:

The free change for the process can be written in terms of its equilibrium constant as:

ΔG° =

where:

R= universal gas constant

T= temperature

= equilibrum constant for the process

Similarly, free energy change and cell potentia; are related to each other as follows;

ΔG= -nFE°

from above;

F = faraday's constant

n = number of electrons exchanged in the process; and  

E = standard cell potential

∴ The amount of energy required for transport of hydrogen ions from a cell into stomach lumen can be calculated as:

ΔG° =

where;

[texK_eq[/tex]=

For transport of ions to an internal pH of 7.4, the transport taking place can be given as:

⇒

Equilibrum constant for the transport is given as:

= 10⁻⁷⁴

=3.98 * 10⁻⁸M

= 10⁻²¹

=7.94 * 10⁻³M

Hence;

=

= 5.012 × 10⁻⁶

Furthermore, free energy change for this reaction is related to the equilibrium concentration given as:

ΔG° =

If temperature T= 37° C ; in kelvin

=37° C + 273.15K

=310.15K; and

R-= 8.314 j/mol/k

substituting the values into the equation we have;

ΔG₁ =

= 31467.93Jmol⁻¹

≅ 31.47KJmol⁻¹

If the potential difference across the cell membrane= 60.0mV.

Energy required to cross the cell membrane will be:

ΔG₂ =

ΔG₂ =

= 5.79KJ

Therefore, for one mole of electron transfer across the membrane; the energy required is 5.79KJmol⁻¹

Now, we  can calculate the total amount of energyy required to transport H⁺ ions across the membrane:

Δ

= (31.47+5.79) KJmol⁻¹

= 37.26KJmol⁻¹

We can therefore conclude that;

   The amount of energy required to transport ions from cell to stomach lumen is 37.26KJmol⁻¹

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