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Chapter 14: Problem 53

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

Expert verified
The pOH of the gastric juice is 11.9, the \(\left[\mathrm{H}^{+}\right]\) concentration is approximately \(7.94 \times 10^{-3}\: \mathrm{M}\), and the \(\left[\mathrm{OH}^{-}\right]\) concentration is approximately \(1.26 \times 10^{-12}\: \mathrm{M}\). Since the \(\left[\mathrm{H}^{+}\right]\) concentration is greater than the \(\left[\mathrm{OH}^{-}\right]\) concentration, the gastric juice is acidic.

Step by step solution

01

Calculate pOH

To calculate the pOH, we use the formula: pH + pOH = 14 We know that the pH = 2.1, so we can find the pOH by rewriting the formula: pOH = 14 - pH pOH = 14 - 2.1 pOH = 11.9
02

Calculate \(\left[\mathrm{H}^{+}\right]\) concentration

To determine the \(\left[\mathrm{H}^{+}\right]\) concentration, we use the formula: \(\left[\mathrm{H}^{+}\right] = 10^{-\mathrm{pH}}\) \(\left[\mathrm{H}^{+}\right] = 10^{-2.1}\) \(\left[\mathrm{H}^{+}\right] \approx 7.94 \times 10^{-3}\: \mathrm{M}\)
03

Calculate \(\left[\mathrm{OH}^{-}\right]\) concentration

To determine the \(\left[\mathrm{OH}^{-}\right]\) concentration, we use the formula: \(\left[\mathrm{OH}^{-}\right] = 10^{-\mathrm{pOH}}\) \(\left[\mathrm{OH}^{-}\right] = 10^{-11.9}\) \(\left[\mathrm{OH}^{-}\right] \approx 1.26 \times 10^{-12}\: \mathrm{M}\)
04

Determine if the gastric juice is acidic or basic

A solution is acidic if the \(\left[\mathrm{H}^{+}\right]\) concentration is greater than the \(\left[\mathrm{OH}^{-}\right]\) concentration and basic if the \(\left[\mathrm{H}^{+}\right]\) concentration is lesser than the \(\left[\mathrm{OH}^{-}\right]\) concentration. Here, we have: \(\left[\mathrm{H}^{+}\right] = 7.94 \times 10^{-3}\: \mathrm{M}\) and \(\left[\mathrm{OH}^{-}\right] = 1.26 \times 10^{-12}\: \mathrm{M}\) Since \(\left[\mathrm{H}^{+}\right] > \left[\mathrm{OH}^{-}\right]\), the gastric juice is acidic.

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