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Chapter 14: Problem 51

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

Expert verified
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

01

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
02

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}
03

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}
04

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.

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