Question

The \(\mathrm{pH}\) of a sample of gastric juice in a person's stomach is \(2.1\). Calculate the \(\mathrm{pOH},\left[\mathrm{H}^{+}\right]\), and \(\left[\mathrm{OH}^{-}\right]\) for this sample. Is gastric juice acidic or basic?

Short answer

The gastric juice has a pOH of 11.9, a [H+] of approximately \(7.94 \times 10^{-3} \, \text{M}\), and a [OH-] of approximately \(1.26 \times 10^{-12} \, \text{M}\). The gastric juice is acidic.

Step-by-step solution

Calculate pOH from pH

Using the relationship between pH and pOH, we can calculate pOH as follows: pOH = 14 - pH Given pH = 2.1, we can determine pOH: pOH = 14 - 2.1 = 11.9

Calculate [H+] from pH

Using the definition of pH, we can calculate [H+] as follows: pH = -log[H+] To find [H+], we need to take the inverse logarithm or the 10 to the power of the negative pH: [H+] = 10^{-pH} Given pH = 2.1, we can determine [H+]: [H+] = 10^{-2.1} \approx 7.94 \times 10^{-3} \, \text{M}

Calculate [OH-] from pOH

Using the definition of pOH, we can calculate [OH-] as follows: pOH = -log[OH-] To find [OH-], we need to take the inverse logarithm or the 10 to the power of the negative pOH: [OH-] = 10^{-pOH} Given pOH = 11.9, we can determine [OH-]: [OH-] = 10^{-11.9} \approx 1.26 \times 10^{-12} \, \text{M}

Determine if the gastric juice is acidic or basic

To determine if the gastric juice is acidic or basic, we'd look at the pH value: - If pH < 7, the solution is acidic. - If pH > 7, the solution is basic. - If pH = 7, the solution is neutral. Since the given pH of gastric juice is 2.1, which is less than 7, it is acidic. In conclusion, the gastric juice has a pOH of 11.9, a [H+] of approximately \(7.94 \times 10^{-3} \, \text{M}\), and a [OH-] of approximately \(1.26 \times 10^{-12} \, \text{M}\). The gastric juice is acidic.

Key concepts

Gastric Juice Acidity

Gastric juice is a digestive fluid found in the stomach. It plays a crucial role in the digestion of food. One of the distinctive properties of gastric juice is its high acidity, primarily due to hydrochloric acid ( HCl ) present in it.
pH is a measure of how acidic or basic a solution is. It ranges from 0 to 14, with values less than 7 being acidic and values more than 7 being basic. A pH of 7 is considered neutral. The pH of gastric juice is typically around 2 or even lower, indicating a very acidic nature.
This acidity is important as it helps break down the food, activates digestive enzymes, and kills harmful bacteria and pathogens. However, having a pH too low can lead to conditions like gastroesophageal reflux disease (GERD).
If the pH is measured to be 2.1, as in this exercise, it confirms that gastric juice is indeed acidic. By understanding pH values and their impact on our body, we appreciate how our stomach functions optimally with highly acidic conditions.

Hydrogen Ion Concentration

The concentration of hydrogen ions (H^+), denoted as [H^+], determines how acidic a solution is. The more hydrogen ions present, the more acidic the solution. pH is related to hydrogen ion concentration as follows: \[ \text{pH} = -\log[H^+] \]
To find [H^+] given a pH, you calculate the antilog: \[ [H^+] = 10^{-\text{pH}} \]
In our exercise, where pH = 2.1, [H^+] becomes: \[ [H^+] = 10^{-2.1} \approx 7.94 \times 10^{-3} \, \text{M} \]
This shows that even small changes in pH reflect significant differences in [H^+], due to the logarithmic nature of the pH scale.
Understanding [H^+] is essential for chemistry and biology students and professionals, as it gives insight into the behavior of acids, their strengths, and their reactivity in various environments. The high concentration of hydrogen ions in gastric juice helps it perform its role quickly and effectively.

Hydroxide Ion Concentration

Hydroxide ions (OH^-), denoted as [OH^-], are the counterparts to hydrogen ions in determining the basicity of a solution. While [H^+] tells us about acidity, [OH^-] quantifies the basic side. The relation between pOH and [OH^-] is similar to that of pH and [H^+]: \[ \text{pOH} = -\log[OH^-] \]
To find [OH^-] from pOH, you perform an inverse logarithmic calculation: \[ [OH^-] = 10^{-\text{pOH}} \]
In the gastric juice scenario with a pOH of 11.9, [OH^-] is: \[ [OH^-] = 10^{-11.9} \approx 1.26 \times 10^{-12} \, \text{M} \]
This very low concentration is consistent with the high acidity of gastric juice. Since the pH and pOH are interconnected (\text{pH} + \text{pOH} = 14), knowing one value automatically gives you a pathway to calculate the other.
Grasping [OH^-] and its interactions with [H^+] is crucial for students, as it provides a complete picture of a substance's nature, helping predict reactions and changes in biological systems.