Passage
Gastric acid is one of many acids important to biological function in the human body. Production of the main component of gastric acid, hydrochloric acid (HCl) , is accomplished in the stomach by the parietal cells, as shown in Figure 1.
Figure 1 Formation of gastric acid in the stomachFacilitated by the carbonate dehydratase enzyme (1) , the parietal cells utilize the interaction between aqueous carbon dioxide and water in the blood as a source of bicarbonate ions and acidic H⁺ ions (protons) . The H⁺ ions produced in this process are then exchanged for potassium ions through the cell membrane by a proton pump, the H⁺/K⁺-ATPase (2) . In conjunction with this proton exchange, bicarbonate ions are also exchanged for chloride ions from the interstitial fluid. As a result, H⁺ and Cl⁻ ions are concentrated in the lumen of the stomach to form aqueous hydrochloric acid.Because the production of the acid proceeds with a drop in pH from 7.0 in the cell cytosol to 1.0 in the stomach lumen, the process occurs against a concentration gradient and is endergonic, requiring the input of energy supplied by the hydrolysis of ATP. Ignoring effects from ion charge, the free energy change for ion transport across the cell membrane (ΔG_t) can be estimated by Equation 1:
∆Gt=kRT logCfCiEquation 1where R is the gas constant (8.32 J/mol·K) , k is a logarithm conversion constant, T is the absolute temperature, and C_i and C_f are the initial and final molar concentrations across the gradient, respectively.Although dilute, the gastric (hydrochloric) acid released into the lumen yields a strongly acidic environment crucial to protein digestion and the destruction of harmful micro-organisms. A comparison of its acid dissociation constant (K_a) to those of other biologically relevant organic acids is given in Table 1.Table 1 Comparison of Strengths of Selected 0.10 M Acids at 25°C
Adapted from Koolman J, Roehm KH. Color Atlas of Biochemistry. Thieme; 2011: 268-271; and Lehninger AL, Nelson DL, Cox MM. Lehninger Principles of Biochemistry. Macmillan; 2005: 397-398, 419, 520.
-What is the estimated free energy change to transport H⁺ ions across the cell membrane from the parietal cell cytosol to the stomach lumen at a physiological temperature?

Question

Passage
Gastric acid is one of many acids important to biological function in the human body. Production of the main component of gastric acid, hydrochloric acid (HCl) , is accomplished in the stomach by the parietal cells, as shown in Figure 1.

Figure 1 Formation of gastric acid in the stomachFacilitated by the carbonate dehydratase enzyme (1) , the parietal cells utilize the interaction between aqueous carbon dioxide and water in the blood as a source of bicarbonate ions and acidic H⁺ ions (protons) . The H⁺ ions produced in this process are then exchanged for potassium ions through the cell membrane by a proton pump, the H⁺/K⁺-ATPase (2) . In conjunction with this proton exchange, bicarbonate ions are also exchanged for chloride ions from the interstitial fluid. As a result, H⁺ and Cl⁻ ions are concentrated in the lumen of the stomach to form aqueous hydrochloric acid.Because the production of the acid proceeds with a drop in pH from 7.0 in the cell cytosol to 1.0 in the stomach lumen, the process occurs against a concentration gradient and is endergonic, requiring the input of energy supplied by the hydrolysis of ATP. Ignoring effects from ion charge, the free energy change for ion transport across the cell membrane (ΔG_t) can be estimated by Equation 1:

∆Gt=kRT logCfCiEquation 1where R is the gas constant (8.32 J/mol·K) , k is a logarithm conversion constant, T is the absolute temperature, and C_i and C_f are the initial and final molar concentrations across the gradient, respectively.Although dilute, the gastric (hydrochloric) acid released into the lumen yields a strongly acidic environment crucial to protein digestion and the destruction of harmful micro-organisms. A comparison of its acid dissociation constant (K_a) to those of other biologically relevant organic acids is given in Table 1.Table 1 Comparison of Strengths of Selected 0.10 M Acids at 25°C

Adapted from Koolman J, Roehm KH. Color Atlas of Biochemistry. Thieme; 2011: 268-271; and Lehninger AL, Nelson DL, Cox MM. Lehninger Principles of Biochemistry. Macmillan; 2005: 397-398, 419, 520.
-What is the estimated free energy change to transport H⁺ ions across the cell membrane from the parietal cell cytosol to the stomach lumen at a physiological temperature?

Quizplus · Accepted Answer

11ecba2d_11d5_03cd_a3bf_33a827810180_MD0008_00 The free energy (ΔG) of the system can be generally described by the equation ΔG= −kRTlog(Q), where R is the gas constant, T is the absolute temperature, and Q is the reaction quotient (concentration ratio) for the system. Therefore, Equation 1 represents a specific case of this relationship where Q= C_f/C_i (the ratio of the hydrogen ion concentrations [H⁺] on each side of the membrane). Because [H⁺] correlates directly to pH (as given by [H⁺] = 10^−pH), the pH values of the cell cytosol (7.0) and the stomach lumen (1.0) can be used to calculate [H⁺] for each. The hydrogen ions are being concentrated from the cell to the lumen, so the final concentration C_f pertains to the stomach (C_f = 10^−1.0 = 1.0 × 10⁻¹ M) whereas the initial concentration C_i pertains to the cell (C_i = 10^−7.0 = 1.0 × 10⁻⁷ M). Accordingly, the free energy required to transport H⁺ ions is proportional to the change in the pH across the membrane and can be estimated by Equation 1: ΔG_t = kRT log(C_f/C_i) ΔG_t = kRT log(10⁻¹/10⁻⁷) ΔG_t = kRTlog(10⁶) = 6kRT (Choice A) When dividing exponential expressions of the same base (in this case, 10), exponents are subtracted (numerator minus denominator); they are not added together. Elimination of the negative signs from the exponents must also result from the exponent subtraction operation, not by direct cancellation as is performed in a ratio. (Choices B and D) When dividing exponential expressions, the exponents are subtracted (not divided). Dividing the exponential concentration expressions does not produce values of either 10^(7/1) or 10^(1/7), which would be required to yield results of 7 or 1/7 from the logarithmic term of the equation. Educational objective: The equation ΔG = −kRT log(Q) describes the free energy (ΔG) of a system, where R is the gas constant, T is the absolute temperature, and Q is the reaction quotient (concentration ratio) related to the system. For systems involving hydrogen ion concentrations, the pH correlates directly to [H⁺] by the relationship pH = −log[H⁺] (or [H⁺] = 10^−pH), and ΔG for H⁺ transport is related to differences in pH.

Passage Gastric Acid Is One of Many Acids Important to Biological