Question

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

Short answer

The gastric juice with a pH of 2.1 has a pOH of 11.9, a hydrogen ion concentration of approximately \(7.94 \times 10^{-3}\ \mathrm{M}\), and a hydroxide ion concentration of approximately \(1.26 \times 10^{-12}\ \mathrm{M}\). The gastric juice is acidic.

Step-by-step solution

Calculate pOH

Using the relationship between pH and pOH, we can calculate the pOH value: \(pH + pOH = 14\). Since we know the pH value (2.1), we can solve for pOH: \(pOH = 14 - pH = 14 - 2.1\)

Find pOH value

Calculate the pOH value: \(pOH = 14 - 2.1 = 11.9\)

Calculate H+ concentration

Use the definition of pH to find the concentration of hydrogen ions \([\mathrm{H}^+]\): \(pH = -\log\left[\mathrm{H}^{+}\right]\) Thus, we can solve for \([\mathrm{H}^+]\) using the given pH value (2.1) as follows: \[\left[\mathrm{H}^{+}\right] = 10^{-pH} = 10^{-2.1}\]

Find H+ concentration

Calculate the concentration of hydrogen ions: \[\left[\mathrm{H}^{+}\right] = 10^{-2.1} \approx 7.94 \times 10^{-3}\ \mathrm{M}\]

Calculate OH- concentration

Use the definition of pOH to find the concentration of hydroxide ions \([\mathrm{OH}^-]\): \(pOH = -\log\left[\mathrm{OH}^{-}\right]\) Thus, we can solve for \([\mathrm{OH}^-]\) using the calculated pOH value (11.9) as follows: \[\left[\mathrm{OH}^{-}\right] = 10^{-pOH} = 10^{-11.9}\]

Find OH- concentration

Calculate the concentration of hydroxide ions: \[\left[\mathrm{OH}^{-}\right] = 10^{-11.9} \approx 1.26 \times 10^{-12}\ \mathrm{M}\]

Determine if acidic or basic

Since the concentration of hydrogen ions \(\left[\mathrm{H}^{+}\right]\) is greater than the concentration of hydroxide ions \(\left[\mathrm{OH}^{-}\right]\), the gastric juice is considered acidic. In summary, the gastric juice with a pH of 2.1 has a pOH of 11.9, a hydrogen ion concentration of approximately \(7.94 \times 10^{-3}\) M, and a hydroxide ion concentration of approximately \(1.26 \times 10^{-12}\) M. The gastric juice is acidic.

Key concepts

pH and pOH Relationship

Understanding the relationship between pH and pOH is crucial for chemistry students. pH is a measure of the acidity or alkalinity of a solution, whereas pOH measures the concentration of hydroxide ions. The pH scale ranges from 0 to 14, with 0 being extremely acidic, 7 being neutral, and 14 being highly basic. The key to the pH-pOH connection lies in a simple equation:
\( pH + pOH = 14 \).
This equation is a cornerstone of acid-base chemistry and provides a straightforward method for finding one value when you have the other. For instance, with a gastric juice pH of 2.1, we can deduce that the pOH is 11.9, indicating a highly acidic solution. This balance ensures that by knowing one of these values, you can always find the other, which is essential in many chemical calculations.

Hydrogen Ion Concentration

The hydrogen ion concentration, denoted as \([H^+]\), is a measure of the number of hydrogen ions present in a solution. It's directly tied to pH, as the pH is the negative logarithm (base 10) of this concentration:
\( pH = -\log[H^+] \).
In practical terms, as the concentration of hydrogen ions in a solution increases, the pH value decreases, making the solution more acidic. For example, gastric juice with a pH of 2.1 corresponds to a hydrogen ion concentration of approximately \(7.94 \times 10^{-3}\) M. This is a key concept in acid-base chemistry because it allows us to quantify the acidity of a solution, which is essential in areas ranging from digestion to industrial processes.

Hydroxide Ion Concentration

Just as hydrogen ion concentration is crucial for understanding acidity, hydroxide ion concentration (\([OH^-]\)) is vital for examining basicity. The concentration of hydroxide ions is related to pOH, which is the negative base-10 logarithm of the hydroxide ion concentration:
\( pOH = -\log[OH^-] \).
In an aqueous solution, a low pOH corresponds to a high hydroxide ion concentration, indicating a more basic solution. Conversely, a higher pOH means a lower hydroxide ion concentration, suggesting acidity. For our gastric juice example, with a pOH of 11.9, the hydroxide ion concentration is found to be approximately \(1.26 \times 10^{-12}\) M, confirming the juice's acidic nature.

Acid and Base Characteristics

Acids and bases are two fundamental classes of compounds in chemistry, each with distinctive characteristics. Acids, such as the gastric juice in the exercise, increase the hydrogen ion concentration in a solution, leading to a low pH. They typically taste sour and can be corrosive. In contrast, bases decrease the number of hydrogen ions resulting in a higher pH, often taste bitter, and feel slippery. Each is important in various chemical reactions, such as neutralization, where an acid reacts with a base to form water and a salt. Gastric juice, with its high acidity indicated by a low pH and a high hydrogen ion concentration, is a good example of an acid at work, aiding in digestion by breaking down complex food molecules.