Answer:
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]=![\frac{[H^+]_(cell)}{[H^+(stomach lumen)]}](https://tex.z-dn.net/?f=%5Cfrac%7B%5BH%5E%2B%5D_%28cell%29%7D%7B%5BH%5E%2B%28stomach%20lumen%29%5D%7D)
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:
![K_{eq}=\frac{[H^+]_{outside}}{[H^+]_{inside}}](https://tex.z-dn.net/?f=K_%7Beq%7D%3D%5Cfrac%7B%5BH%5E%2B%5D_%7Boutside%7D%7D%7B%5BH%5E%2B%5D_%7Binside%7D%7D)
![=\frac{[H^+]_{cell}}{[H^+]_{stomach lumen}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5BH%5E%2B%5D_%7Bcell%7D%7D%7B%5BH%5E%2B%5D_%7Bstomach%20lumen%7D%7D)
![[H^+]_{cell}](https://tex.z-dn.net/?f=%5BH%5E%2B%5D_%7Bcell%7D)
= 10⁻⁷⁴
=3.98 * 10⁻⁸M
![[H^+]_{stomach lumen}](https://tex.z-dn.net/?f=%5BH%5E%2B%5D_%7Bstomach%20lumen%7D)
= 10⁻²¹
=7.94 * 10⁻³M
Hence;
![K_{eq}=\frac{[H^+]_{cell}}{[H^+]_{stomachlumen}}](https://tex.z-dn.net/?f=K_%7Beq%7D%3D%5Cfrac%7B%5BH%5E%2B%5D_%7Bcell%7D%7D%7B%5BH%5E%2B%5D_%7Bstomachlumen%7D%7D)
=
= 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
