70. The pH of gastric juice in the stomach is 2.0. However the pH inside the cells that line the stomach is 7.0. For transport of protons from inside the cell to the stomach, the free energy change (∆G) in kJmol–1at 37oC is

[Assume Universal Gas constant R = 8.314 Jmol–1K–1]

How to Calculate the Free Energy Required for Proton Transport Across the Stomach Membrane?

Correct Answer

ΔG = +29.7 kJ mol⁻¹

Introduction

The movement of ions across biological membranes is one of the most important processes in cellular physiology. Cells maintain concentration gradients of ions such as H⁺, Na⁺, K⁺, Ca²⁺, and Cl⁻, which are essential for nutrient transport, nerve impulse conduction, ATP synthesis, and maintenance of intracellular pH. Whenever an ion moves against its concentration gradient, energy must be supplied, making the process an example of active transport. The gastric epithelial cells of the stomach provide an excellent biological example of this principle because they continuously secrete large quantities of protons into the stomach lumen, producing highly acidic gastric juice.

The stomach lumen has a pH of approximately 2, whereas the cytoplasm of gastric epithelial cells maintains a nearly neutral pH of 7. Therefore, protons are transported from a region of low proton concentration inside the cell to a region of high proton concentration outside the cell. This energetically unfavorable process is driven by the H⁺/K⁺-ATPase proton pump, which utilizes energy derived from ATP hydrolysis.

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Understanding the Concept Behind the Question

Since only a proton concentration gradient is given and no membrane potential is mentioned, the free energy is calculated using the chemical gradient equation:

ΔG = 2.303 RT ΔpH

where:

• ΔG = Free energy change
• R = Universal gas constant = 8.314 J mol⁻¹ K⁻¹
• T = Absolute temperature = 37°C = 310 K
• ΔpH = pHoutside − pHinside

Given:

pH inside cell = 7

pH stomach lumen = 2

Because protons move from the cell to the stomach,

ΔpH = 7 − 2 = 5

The movement is against the proton concentration gradient, so the free energy will be positive.

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Step 1. Write the Formula

ΔG = 2.303 RT ΔpH

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Step 2. Substitute the Given Values

ΔG = 2.303 × 8.314 × 310 × 5

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Step 3. Calculate RT

8.314 × 310 = 2577.34 J mol⁻¹

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Step 4. Multiply by 2.303

2.303 × 2577.34 = 5934.8 J mol⁻¹

This value represents the free energy required for transporting one mole of protons across a one-unit pH difference.

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Step 5. Multiply by the pH Difference

5934.8 × 5 = 29674 J mol⁻¹

Convert joules into kilojoules:

29674 J mol⁻¹ = 29.67 kJ mol⁻¹

Rounded:

ΔG ≈ +29.7 kJ mol⁻¹

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Final Calculation

ΔG = +29.7 kJ mol⁻¹

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Why Is the Free Energy Positive?

The proton concentration inside the gastric epithelial cell is much lower than in the stomach lumen.

Transporting protons from pH 7 to pH 2 means moving them from a region of low H⁺ concentration to a region of high H⁺ concentration.

Such movement occurs against the concentration gradient and therefore requires an external energy source.

Consequently, the free energy change is positive, indicating that the process is non-spontaneous.

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Formula Used

Proton Transport Across a pH Gradient

ΔG = 2.303 RT ΔpH

where:

• R = 8.314 J mol⁻¹ K⁻¹
• T = Temperature in Kelvin
• ΔpH = Difference in pH across the membrane

If membrane potential is included, the complete equation becomes:

ΔG = RT ln(C₂/C₁) + zFΔΨ

However, because no electrical potential is provided in this question, only the chemical gradient term is used.

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Biological Importance

The secretion of hydrochloric acid by the stomach depends on the H⁺/K⁺-ATPase, a primary active transporter located in the apical membrane of gastric parietal cells. This enzyme hydrolyzes ATP to pump protons into the stomach lumen, maintaining the acidic environment required for protein digestion, activation of pepsinogen, destruction of ingested microorganisms, and nutrient absorption. The large positive free energy associated with proton transport illustrates why ATP hydrolysis is essential for gastric acid secretion. Drugs such as omeprazole, pantoprazole, and other proton pump inhibitors reduce gastric acidity by inhibiting this ATP-dependent transporter.

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High-Yield Points

• Gastric lumen pH ≈ 2.
• Cytoplasmic pH ≈ 7.
• Gastric acid secretion is mediated by H⁺/K⁺-ATPase.
• Proton transport from pH 7 to pH 2 is active transport.
• ΔG = 2.303 RT ΔpH when only the concentration gradient is considered.
• Positive ΔG indicates energy-requiring (non-spontaneous) transport.
• Proton pump inhibitors block gastric proton secretion.

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Frequently Asked Questions

Why is proton transport into the stomach an active process?

The stomach lumen contains a much higher proton concentration than the cytoplasm. Therefore, protons must move against their concentration gradient, requiring ATP.

Why is ΔG positive?

A positive ΔG indicates that energy must be supplied for the process to occur because the transport is thermodynamically unfavorable.

Which enzyme pumps protons into the stomach?

The H⁺/K⁺-ATPase, commonly known as the gastric proton pump, transports protons into the stomach lumen using energy released from ATP hydrolysis.

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Key Takeaways

The stomach maintains a highly acidic lumen (pH 2) while gastric epithelial cells maintain a nearly neutral cytoplasm (pH 7). Transporting protons from the cytoplasm into the stomach therefore requires movement against a five-unit pH gradient. Using the equation ΔG = 2.303 RT ΔpH, with R = 8.314 J mol⁻¹ K⁻¹, T = 310 K, and ΔpH = 5, the calculated free energy is 29.67 kJ mol⁻¹. Because the transport occurs against the proton concentration gradient, the free energy is positive, indicating that ATP is required to drive the process.

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Final Answer

ΔG = +29.7 kJ mol⁻¹

Explanation

The free energy required to transport protons across a pH gradient is calculated using:

ΔG = 2.303 RT ΔpH

where R = 8.314 J mol⁻¹ K⁻¹, T = 310 K, and ΔpH = 7 − 2 = 5.

Substituting the values:

ΔG = 2.303 × 8.314 × 310 × 5

= 29674 J mol⁻¹

= 29.67 kJ mol⁻¹

Since protons are transported from the neutral cytoplasm into the highly acidic stomach lumen against their concentration gradient, the process is non-spontaneous and the free energy change is positive.

Therefore, the required free energy is:

+29.7 kJ mol⁻¹.