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Chapter 15: Problem 155

The pH of a solution is 8 . (a) What is the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration? (b) What is the OH concentration? (c) Is this solution acidic or basic?

Short Answer

Expert verified
(a) The \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration is \(1.00 \times 10^{-8} \mathrm{M}\). (b) The \(\mathrm{OH}^-\) concentration is \(1.00 \times 10^{-6} \mathrm{M}\). (c) The solution is basic.

Step by step solution

01

Understanding pH and related formulas

pH is a measure of the acidity or basicity of a solution. It is defined as the negative logarithm of hydrogen ion concentration, i.e., \(\mathrm{pH}=-\log_{10}\left(\mathrm{[H}_{3} \mathrm{O}^{+}]\right)\). To find the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration, we can use this formula. Additionally, we will also be using the ion product of water, which is \(\mathrm{K}_{\mathrm{w}}=\mathrm{[H}_{3} \mathrm{O}^{+}][\mathrm{OH}^{-}]\), where \(\mathrm{K}_{\mathrm{w}}\) is a constant equal to \(1.0 \times10^{-14} \) at 25 degrees Celsius.
02

Calculate \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration

Using the pH formula and given pH value, we can calculate the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration: \(\mathrm{pH}=-\log_{10}\left(\mathrm{[H}_{3} \mathrm{O}^{+}]\right)\) 8.00 = -\(\log_{10}\left(\mathrm{[H}_{3} \mathrm{O}^{+}]\right)\) Rearranging the equation to solve for \(\mathrm{[H}_{3} \mathrm{O}^{+}]\), we get: \(\mathrm{[H}_{3} \mathrm{O}^{+}] = 10^{-\mathrm{pH}}\) \(\mathrm{[H}_{3} \mathrm{O}^{+}] = 10^{-8.00}\) \(\mathrm{[H}_{3} \mathrm{O}^{+}] = 1.00 \times 10^{-8} \mathrm{M}\)
03

Calculate \(\mathrm{OH}^-\) concentration

Using the ion product of water and the calculated \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration, we can find the \(\mathrm{OH}^-\) concentration: \(\mathrm{K}_{\mathrm{w}}=\mathrm{[H}_{3} \mathrm{O}^{+}][\mathrm{OH}^{-}]\) \(1.0 \times10^{-14} \) = \( (1.00 \times 10^{-8} \mathrm{M})(\mathrm{[OH}^{-}]) \) Now, solve for \(\mathrm{[OH}^{-}]\): \(\mathrm{[OH}^{-}] = \dfrac{1.0 \times10^{-14}}{1.00 \times 10^{-8} \mathrm{M}}\) \(\mathrm{[OH}^{-}] = 1.00 \times 10^{-6} \mathrm{M}\)
04

Determine if the solution is acidic or basic

To determine if a solution is acidic or basic, we can compare the \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{OH}^-\) concentrations: - If \(\mathrm{[H}_{3} \mathrm{O}^{+}] > \mathrm{[OH}^{-}]\), the solution is acidic. - If \(\mathrm{[H}_{3} \mathrm{O}^{+}] < \mathrm{[OH}^{-}]\), the solution is basic. - If \(\mathrm{[H}_{3} \mathrm{O}^{+}] = \mathrm{[OH}^{-}]\), the solution is neutral. In our case, we have: \(\mathrm{[H}_{3} \mathrm{O}^{+}] = 1.00 \times 10^{-8} \mathrm{M} < 1.00 \times 10^{-6} \mathrm{M} = \mathrm{[OH}^{-}]\) Since the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration is less than the \(\mathrm{OH}^-\) concentration, the solution is basic.
05

Answers:

(a) The \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration is \(1.00 \times 10^{-8} \mathrm{M}\). (b) The \(\mathrm{OH}^-\) concentration is \(1.00 \times 10^{-6} \mathrm{M}\). (c) The solution is basic.

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