Question

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 p H of gastric juice is acidic, between 1–3. If the p H of gastric juice is 1.4 , what is the amount of energy ( Δ G ) required for the transport of hydrogen ions from a cell (internal p H 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 the cell is negative relative to the lumen of the stomach). Assume that the temperature is 37 °C. The Faraday constant is 96.5 kJ / ( V ⋅ mol ) and the gas constant is 8.314 × 10 − 3 kJ / ( mol ⋅ K ) . Express your answer in kilojoules per mole.

Answer 1

Amount of energy required foe transport of hydrogen ions from a cell into stomach lumen is given as follows:

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

H⁺_inside <===> H⁺_outside

equilibrium constant for the transport is given as follows:

K_eq = [H⁺]_outside / [H⁺]_inside

=   K_eq = [H⁺]_cell / [H⁺]_{stomach lumen}

[H⁺_cell] = 10^-7.4

= 3.98 X 10^-8 M

[H⁺]_{stomach lumen} = 10^-1.4

= 0.0398 M

thus,

K_eq = [H⁺]_cell / [H⁺]_{stomach lumen}

= 3.98 X 10^-8 / 0.0398

= 10^-6

for free energy change for this reaction is related to the equilibrium concentration as follows:

∆G₁ = -RT ln K_eq

given that temperature T is 37^o C and R is 8.314 Jmol^-1 K^-1

convert temperature to Kelvin = 37 + 273.15 = 310.15 K

Substitute the values in expression for ∆G₁ as shown below

calculate the amount of energy required in the process as follows:

∆G₁ = -RT ln( 10^-6)

= -(8.314 JK^-1 mol^-1)(310.15 K)(-13.81)

= 35.62 KJ mol^-1

Given that the potential difference across the cell membrane is 60.0 mV

energy required to cross cell membrane can be calculated as follows:

calculate the amount of energy required in the process as follows:

∆G₂ = -nFE^o_membrane

= -1 X (96.5 KJ mol^-1 V^-1)(60 X 10^-3 V)

= 5.79 KJ

thus for one mole of electron transfer across the membrane the energy required is 5.79 KJ/mol

total amount of energy required to transport H⁺ ions across the membrane is given as follows:

calculate the amount of energy required in the process as follows:

∆G_Total =  ∆G₁ + ∆G₂

= (35.62+ 5.79) KJ/mol

∆G_Total   = 41.41 KJ/mol

the amount of enegy required to transport ions from cell to stomach lumen is 41.41 KJ/mol

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