The intracellular \(\mathrm{pH}\) of human cells is approximately 7.4. Yet, the \(\mathrm{pH}\) within the lumen (inside) of the human stomach averages \(1.5 .\) Which of the following accurately describes the difference between the acidity of the cellular and gastric \(\mathrm{pH}\) ? (A) Gastric juices contain approximately 6 times more \(\mathrm{H}^{+}\) ions than the intracellular cytoplasm of cells and are more acidic. (B) Gastric juices contain approximately 1,000,000 -fold more \(\mathrm{H}^{+}\) ions than the intracellular cytoplasm of cells and are more acidic. (C) The intracellular cytoplasm of cells contain approximately 6 times more \(\mathrm{H}^{+}\) ions than gastric juices and is more acidic. (D) The intracellular cytoplasm of cells contains approximately 1,000,000 -fold more \(\mathrm{H}^{+}\) ions than gastric juices and is more acidic.

Step by step solution

01

Definition of pH

The pH is defined as the negative logarithm to the base 10 of the concentration of H⁺ ions (\([H^{+}]\)): \[pH = -\log_{10}([H^{+}])\] Here, we aim to find the fold difference in the concentration of H⁺ ions between the intracellular environment (pH = 7.4) and the gastric environment (pH = 1.5). In order to find this, first, we need to calculate the H⁺ concentrations for both environments using the given pH values.

02

Calculate H⁺ concentrations

Using the definition of pH, we can calculate the H⁺ concentrations for both environments: 1. Intracellular environment (pH = 7.4): \[ [H^{+}]_{intracellular} = 10^{-pH} = 10^{-7.4} \] 2. Gastric environment (pH = 1.5): \[ [H^{+}]_{gastric} = 10^{-pH} = 10^{-1.5} \]

03

Calculate fold difference

To understand the fold difference between the two H⁺ concentrations, we can take the ratio of gastric H⁺ concentration to intracellular H⁺ concentration: \[Fold \ Difference = \frac{[H^{+}]_{gastric}}{[H^{+}]_{intracellular}} = \frac{10^{-1.5}}{10^{-7.4}} = 10^{5.9} \approx 10^6 \] The fold difference in H⁺ concentrations is approximately 10⁶, which means the gastric environment contains about 1,000,000-fold more H⁺ ions than the intracellular environment.

04

Compare results to given options

Based on the calculations, the gastric juices have a 1,000,000-fold higher H⁺ concentration than the intracellular environment and are more acidic. This matches option (B): (B) Gastric juices contain approximately 1,000,000 -fold more \(\mathrm{H}^{+}\) ions than the intracellular cytoplasm of cells and are more acidic.

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