Question

The pH of a sample of gastric juice in a person's stomach is 2.1. Calculate the pOH, [H'l, and [OH- ] for this sample. Is gastric juice acidic or basic?

Short answer

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

Step-by-step solution

Calculate pOH

We are given the pH value, which is 2.1. To find the pOH value, we use the relationship between pH and pOH: pH + pOH = 14 Now, we can substitute the given pH value and solve for pOH: 2.1 + pOH = 14 pOH = 14 - 2.1 pOH = 11.9

Calculate [H'] concentration

Now, we'll find the [H+] concentration using the given pH value and the formula for pH: pH = -log[H+] We can rearrange the formula to find [H+]: [H+] = 10^(-pH) Substitute the given pH value and solve for [H+]: [H+] = 10^(-2.1) [H+] ≈ 7.94 × 10^(-3) M

Calculate [OH-] concentration

Next, we will find the [OH-] concentration using the calculated pOH value and the formula for pOH: pOH = -log[OH-] We can rearrange the formula to find [OH-]: [OH-] = 10^(-pOH) Substitute the calculated pOH value and solve for [OH-]: [OH-] = 10^(-11.9) [OH-] ≈ 1.26 × 10^(-12) M

Determine if gastric juice is acidic or basic

Finally, we'll determine whether the gastric juice is acidic or basic by comparing the concentrations of [H+] and [OH-]. Remember that: - If [H+] > [OH-], then the solution is acidic. - If [H+] < [OH-], then the solution is basic. - If [H+] = [OH-], then the solution is neutral. In our case, the [H+] concentration is 7.94 × 10^(-3) M, and the [OH-] concentration is 1.26 × 10^(-12) M. Since [H+] > [OH-], gastric juice is acidic.

Key concepts

pOH calculation

To calculate the pOH of a solution, we first need to understand its connection to pH. The pH and pOH are related through a simple equation:
\[ \text{pH} + \text{pOH} = 14 \]
This equation implies that the sum of pH and pOH in any solution at 25°C always equals 14.Knowing this, if we have the pH value, we can easily find the pOH by subtracting the pH from 14.For instance, if the pH is 2.1, the calculation goes as follows:

• pOH = 14 - pH = 14 - 2.1 = 11.9

This indicates the basic nature of a solution, as a lower pOH corresponds to a higher concentration of OH- ions.

acidic vs. basic solutions

Identifying whether a solution is acidic or basic depends on the concentration of hydrogen ions ([H+]) compared to hydroxide ions ([OH-]).
Here are the key points:

• If [H+] > [OH-], the solution is acidic.
• If [H+] < [OH-], the solution is basic.
• If [H+] = [OH-], the solution is neutral.

For the gastric juice example, we computed the [H+] as approximately\( 7.94 \times 10^{-3} \) M and [OH-] as approximately \( 1.26 \times 10^{-12} \) M.Since [H+] is greater than [OH-], the gastric juice is acidic, which aligns with its typical characteristics, as our stomach's environment favors digestion with acidity.

H+ concentration

The concentration of hydrogen ions in a solution, denoted as [H+], is a key determinant of its acidity. The pH value is a logarithmic measure of [H+] concentration and is calculated using:
\[ \text{pH} = -\log[H^+] \]
To find [H+], the formula can be rearranged:

• [H+] = 10^{-\text{pH}}

For a pH of 2.1:

• [H+] = 10^{-2.1} \approx 7.94 \times 10^{-3} \text{ M}

This high concentration of hydrogen ions is typical in acidic solutions, like gastric juice,helping with the breakdown of food during digestion.

OH- concentration

The concentration of hydroxide ions, [OH-], is another critical measure in determining a solution's basicity.
Like pH, pOH provides insight into these concentrations and is logarithmically related to [OH-]:
\[ \text{pOH} = -\log[OH^-] \]
We can derive [OH-] using:

• [OH-] = 10^{-\text{pOH}}

In the gastric juice scenario with a pOH of 11.9:

• [OH-] = 10^{-11.9} \approx 1.26 \times 10^{-12} \text{ M}

With such a low concentration of OH- ions, along with the higher concentration of H+, it's clear why gastric juice is classified as acidic.